It's a great pleasure for me to welcome
Francis Helen to Georgia Tech school
physics Francis is visiting us from U.C.
Berkeley where she's in
the first year of physics and
chair of the Department of Physics.
Problems just grew up in New York City
where she had several options one of them
was ski racing which she undertook
that the national level and
another was physics and I learned
yesterday that physics career was inspired
by a teacher who spent more time on black
holes than one if you will to me and I got
myself thinking about this morning the sun
through the indication of a signal about
the way we teach a visit to ourselves
it's great to know that the physics and
the inspirational and
after spectacular effects.
I STRONGLY your crossways adult
college College in New Hampshire and
she majored in physics from there she
writes a Stanford University where she
undertook a Ph D.
in experimental events metaphysics
under the guidance of your biology
is one of the great figures
of the next master here real physics
are still active to this day.
After a Stanford or
Francis list of Bell Labs.
And the other was a post on there
years before setting a professorship
at University of California San Diego
where she built a powerhouse lab
a reputation book on primary but
also time on super inductively she can
relate to the problems of this great
challenge is how to understand these
emergent collective phenomena and
they and in fact they have been out.
For media conventional understanding
of how or when the metals work.
Moving on from U.C.
San Diego Frances moves to a book
League about Slovakia eight years or so
ago and two years after that she
was invited to become chair.
Of the high.
This is very deftly done
absolutely spectacular Joe.
Some of the world's really great.
Stuff.
As it was over so
I should mention that want to address the.
Among those which which is the ability
to understand and measure the.
Stream of the small systems micrograms
uses the bus with that looks
very much to me so I did a little googling
around and found now that I understand
that process is take the study
Mannix off away something like
not one but about a thousand of them and
those were given and letters and
imagine doing physics of this office on
a scale it's really really really truly
truly impressive the process is also along
the way for the five or so the community.
May weigh.
Secure on the physics of
a strong board which is a dying
group of scientists who study your life.
Stages of physics and all of
the doctors nationwide worldwide and
many other users in their physical
society especially Jared committee on
the status of women visit for
the talks so today from just
kind of agreed to give us a colloquialism
title spin spin electronics my medical.
Doctor thought it was.
OK So arm Well thank you very much for
inviting me it's a great pleasure
to be here actually and so.
I am to be talking about moments
that are more for semiconductors and
this is what I've been doing for
a while so.
Very much a large number of collaborators
everything from I don't last as any
other any undergrads.
It's here in the room OK well I had a
large number of other grads of the year is
involved this project and
graduate students and so
forth and as well as colleagues so
I'm going to start
by defining the words the electronics this
is not going to be a technology talk but
the term arose out of technology so
I'm going to introduce it there and
then go on to tell you what I'm going to
be talking about so the idea in Spital in
spin electronics is that you know there's
many components to a computer but
sort of the two key components if
you will one of them is the C.P.U.
which of course consists of
millions of transistors and
there is just an example
of a of a transistor and
the basic idea is that the transistor
is based on semiconductors and
particular silicon primarily and the
charge of the electron which means that
it's all about voltages and currents and
of course one of the primary themes here
is of course the electron has spin but
it is not relevant
to any of these applications so
the transistor it would matter if you had
a magical spinless electron it would not
make any difference to how this operates
and so that's that's all about the charge
of the electrons by contrast if I
turn to the you know probably the other
key component which is the hard drive so
the hard drive and that's an example it's
now a bit out of date even but that's
the hard drive with it's you know there's
the media down there with the zeros and
ones back and forth.
There is the leader in the right head and
so forth.
And the point is that this is based
entirely on the electron spin and
so in this case it's the opposite
of course again the electron has
a charge I'm not saying we've
invented a magical new particle but
the charges in completely irrelevant and
in practical terms the bits that you write
of the media they could be inflating
they could be metallic it wouldn't make
any difference it's the magnetic field
that they produce that you write with
a magnetic field in some form
some of that's changing.
And they could have these these
elements wouldn't make any difference
whether the electrons were mobile or
immobile could have.
Actually hear me or do I need to
move the microphone closer but
OK so the whole idea of an electronics
where this was quiet and
is that it seems like in some global sense
a waste to be not taking advantage of
the fact that electrons have both spin and
charge and the question is So that's where
the turn spin electronics came from let's
take advantage of both properties and
the question then you could ask
quite reasonably is why and so
there's a couple of current
technologies that already do this and
already components in most computers
what's called Giant made a resistance that
I assume you've had talks on J M R In the
past the idea in giant magneto resistance
is I have these Sara magnetic layers that
are separated by a non magnetic spacer and
the resistance of that could be as
little as a trial lawyer by the way
the resistance of that compound you
know that that layer of structure
depends on whether the layers are parallel
or anti parallel and so the N.T.
parallel state they have
a higher resistance and
then when they're you flip it
around become Powell the resistance
goes down and you detect that and
so the field that is being produced
by those zeros ones are able to flip
the to flip those bits around and
so that is an example thought
to be really concrete and
a little bit pedantic The idea is that
the voltage depends on the magnetic field
All right so I have a couple in
between two different components here
there's another example which is called
nonvolatile RAM which uses magnetic
tunnel junctions actually very
related technology except for
instead of having you still have to
let's just call them iron layers but
instead of being separated by a metallic
space or a layer you're separated by
insulating space a layer and so electrons
tunnel from one level to the other but
still the tunneling with distance depends
on whether the layers of power and
the parallel So again what you've got is
a is is you're measuring the voltage but
it is the magnetic field a factor so
those are examples of some electronics and
there already exist in
existence of emus but
what was really wanted was not those but
was the idea was to create a future.
Technology which involve things like
spin transistors which were magnetically
switchable transistors you could imagine
Start for example nonvolatile logic not
just nonvolatile memory but nonvolatile
logic so the idea would be your you have
the power shut down your computer freezes
up you would you would not lose anything
not even like your last few strokes would
just be there you would boot up instantly
you wouldn't have to have anything of you
know booting up everything would just be
there sort of nonvolatile logic perhaps
higher order logic you could perhaps
combine if you start getting exotic
about this you could combine the C.P.U.
and the hard drive together they
are currently literally made in different
factories often in different parts of the
world why why don't we have a C.P.U. and
a hard drive that are integrated together
you can imagine that might be much faster
possible new device functionality
is integrated perhaps different
perhaps more parallel maybe you can start
creating all sorts of exotic things
perhaps feel programmable now one catchin
everything in this is about the last thing
I'm going to say about all of this
every one of those things can be done
without needing spend transistors or
without needing spin electronics
you can have higher order logic right
now if that's what you want it so
again the point of all this is not
to spin Electronics has still has
some future there's some exciting things
about it it's more quite a bit from
the early days of just to spend transistor
but you have to be careful particularly
as a physicist that the technology you're
aiming at is just not instantly obsolete.
So I am not going to actually be talking
much about spent electronics I'm
going to tell you why this is connected
to what I am going to be talking about
sort of in the next slide one of
the interesting things in all of this is
that the idea of a magnetic semiconductor
particularly one that might function
at room temperature was an important step
for a whole variety of reasons but for
those of you who are know about the field
impedance matching at the injection
interface than polarization of carriers
all of that is the subtlety if you can
create a magnetic semiconductor and those
turned out to be very few and far between.
So why.
Let's turn to the periodic table and ask
if I wish to make a magnetic semiconductor
How do I do it well the most natural thing
in the world would be let's start with
the magnetic element so that is all
of the magnetic elements that are.
There is the three D.
elements and there are the four F.
elements down here that's in the periodic
table that's it it's actually
interesting this far more superconductors
than there are magnetic elements that So
there's one list of magnetic materials.
And there's my semiconductors again
elemental I'm not there there's obviously
compounds have a conductor's gallium
arsenide and so forth but of my elements
that's it so that's the pitch in a naive
lady and this is very naive naively
there's my palette to work from I can
start taking it one from the green
column one from the purple column and
mix them together and see what I get and
that might be the way you'd imagine
creating a magnetic semiconductor.
It turns out to be much easier said
than done there are all sorts of
issues that come up there
are major solubility problems so
the elements that I picked have metallic
bonding This is a real chemistry problem
there they're mostly metallic bonding
they don't like to be in a covalent
environment so the silicon germanium
carbon has a particular covalent bonds and
those metallic elements don't fit well so
there are serious solubility problems that
you just you know they exclude each
other they precipitate out that from
magnetic elements are not always in
fact often are not in fact they're more
commonly not magnetic than they are
magnetic so just because I take iron and
stick it in silicon iron in silicon
doesn't necessarily fact it frequently
doesn't have a magnetic moment so
just taking one from column A and
one from column B. does actually not
work all that well even if there are so
local magnetic moments these are often
anti ferromagnetic Lee coupled
to each other and if I want to magnetic
semiconductor I actually really do want.
A fair a magnetic semiconductor not
an anti fair a magnetic semiconductor and
so they're not only that they're often
frustrated that leads to spin losses
all sorts of things that are not very
practical if I'm going to create something
and so those of you who've heard talks in
Gallia manganese arsenic which is the most
popular current magnetic semiconductor
with the highest transition temperature
One problem is if I'm going to create
something that's fair a magnetic
with a high Curie temperature that's
a T.C. not superconducting but three of
which are usually out of direct overlap
way functions which by the time you do
have direct overlap of way functions
you've usually got a very high electron
concentration and you are therefore
usually no longer semiconducting and
oddly enough we have lots of ferromagnetic
metals out there starting with iron so
we already know how to
make ferromagnetic metals
by just sticking a whole ton of manganese
in the gallium arsenide if you have you
know if you start trying to push the Curie
temperature up by just adding more and
more Maggies you finally end up with a
magnetic metal which is really not what we
wanted in the first place something
that often gets glossed over and
talking about the only manganese arsenic
is exactly how metallic it's become so
that's a problem now all reproach to this
to this was to be some of these particular
solid realty We started by working with
amorphous So what can and doping with
worth out of the sometimes for transition
metal atoms and you believe the solubility
problem it turns out there's a very nice
met a stable material amorphous gadolinium
silicon is the one I'm mostly going to
talk about gadolinium in amorphous So
what can actually you can do even not very
much annealing but it's a nice most stable
state it's homogeneous you don't have the
solubility issues so we kind of beat that
problem we also be the magnetic elements
the rare earth have these big four F.
shells so gadolinium is magnetic
in everything you put it in
it just has a half filled shell that's
very protected from its environment so
we've eaten Problem number two we have not
beaten problem number three at all in fact
I'm going to show you not only is this
is this a spent glass it turns out he.
Well actually I'm not going to show you
that today because there isn't time to
show you that today but it actually turns
out to be a not only a spin glass but
a fabulous Lee perfect spent in the house
with a perfectly frustrated interactions
which is actually to do with the amorphous
structure and I'm happy to talk about that
one with somebody that will be
time to go into that today but
we definitely did not beat this problem at
all we did however create something that
has really extraordinary properties and
so I'm now turning to the point of
this talk which is really not about
trying to create a new technology but
is to talk about one of the call
the science Tronics And
my point is going to be that in a class of
materials most of which you have already
heard of the magnetic moments in a whole
set of materials strongly affect
the electrical and by the way the optical
properties of the not going to show
you off of it with a and you start finding
magnetism very not obvious materials and
it turns out that this is seen in low but
not the electron concentration materials
and I'll show you an example of what I
mean and then the point of this talk is
going to be why is that and so the real
the science that I'm taking out of Tronics
is this interplay between charge and
spin in solid materials again electrons of
course have both charge and span but when
you put them in solid What's the things
happen they often there are examples where
the two properties become separated so
that you can move charge around
separately from still am which seems
in a remarkable statement since
ultimately you're moving I
mean electron is an object but
it's a complex object in the solid
material so the properties of spin and
charge can become separated they
can become invisible so that in and
I'll show you more what I mean by that but
that's really the point and
the question this willy a lot of this talk
with me about this issue of what is so
magical about low but not like from
concentration materials so let
me just show you two examples to make this
point this is an example of this is a guy.
When Nicol to a compound that has
a curious temperature about seventy five
Kelvin this is a plot of its electrical
wires the civet is a function
of temperature and you can see the
connectivity is dropping it's a it's about
also the resisted city is dropping even at
the current temperature clearly something
happens so there's a rather abrupt break
at least in the slope of the road and
so that is a couple that's
exactly what I'm talking about so
there's a couple in there of the magnetism
to the electrical properties that's fine
that's precisely the thing I'm interested
in but now notice the scale this is that
you know that's what this is a very slowly
Appleford scale this is not zero so
the Skilly effect here is like one
percent and if you can imagine if I apply
the magnetic field this is the entire size
of the effects of apply magnetic field on
nothing it changes in resistance that are
more than a very old couple of percent or
something like that so
that's a material that's magnetic.
So now let me turn to
a magnetic semiconductor So
this is a magnetic semiconductor
that was known as papers back from
one thousand nine hundred three it's a.
Get William kind of down very small
print here but it's gadolinium dope
three US four gentlemen sulfide with
vacancies in it which act as dope and and
this is the paper this is now a plot not
of reasons to hundred tippity which for
the context of what I'm talking about
today is just one over the other
it turns out that in the where I'm the
materials I'm very working on it's much
better to talk about conduct to Vittie and
not resist tippity and
I'll show you why in a moment for now just
recognize that I've switched whatever so
this is a this is a semiconductor and
that the conduct of a T.
is with sorry this is also part of VS
feel to be so it is a semiconductor
if I plotted vs temperature
would have the other sign of D.
But look at what happens here and
at Womad medic feel I have something
that is completely insulating.
The conduct of a T. is zero.
Zero feel.
And then as I search running on the
magnetic field the conduct of it comes up
and becomes large so that is in effect
an infinite magnet a resistance infinite
negative make the resistance
zero carb activity feel and
the the you turn it into a metal.
This paper was significant mostly because
it was the on here is the Sigma min
which for those of you in the field know
this is the man on the tele conduct of ity
this paper was significant because
at the time it was believed
that the metal to insulator transition
was a first order for phase transition.
And this paper was addressing the question
that it clearly isn't the activity goes
very smoothly through Sigma min with no
particular sign of anything happening it
is in fact a second order phase from well
it's more complicated even than that but
the time the point was it was
a second order phase transition so
a magnetic field is able to change the
material from an insulator to a medal and
I claim that the reason for that this is
possible is the electron concentration
the one I showed you on the slide
before was a metal with about ten to
the twenty third electrons for cubic
centimeter this is a material of about
ten of the twentieth electrons per cubic
centimeter Those are both big numbers
you know this isn't astronomy So what's
the difference in ten of the twentieth and
ten of the twenty third it just
doesn't sound terribly significant but
it turns out it is so ten of the twentieth
in that range is sort of this magic
thing where all sorts of stuff happens and
those of you who've heard talk for hi to
see superconductivity on the colossal
negative resistance the man unites
just a whole slew of exotic materials
you will have seen that number
number is like ten to
the twentieth show up a lot and
the point is going to be that things
that have a lot of electrons like ten to
the twenty third are very robust metals
and if I start with a very robust
metallic state I can't do much to it so
if I start with copper and
I start putting little bits of magnetic
moments into them or something like that
nothing really happens I mean I don't
mean to say nothing people spend
a lot of their life
studying things like Con.
Well facts and there's some interesting
critical scattering there are interesting
effects but they're small so the metallic
state is a very robust state and
insulating say we're in is actually zero
is also very robust I can stick magnetic
moments and again I don't mean
to say nothing happens but
it's small it turns out this is kind of
a magical number where it's unstable and
that's really a lot of the point of this
talk it is unstable precisely because
it is perched at the edge between being
a metal and being an insulator and
like anything else when you're perched
at a transition you are unstable so
when you think back on all the things
like height you see in Magnussen
you picture their faces diagrams they're
just littered with different faces.
Or charge ordering things spitting
glasses and the firm magnets for
magnets superconductors you know all
sorts of things because the sea of
electrons is fundamentally unstable
to probations when it's perched
right at this transition so let me show
you a little more what I mean by that and
the do that I'm going to have to I'm going
to have to do my best to introduce you to
all of them instead of physics
in the next half an hour so.
We will see you know that there's
a lot to show you why this happens but
let me start with real basics of course
as I've said a couple times now electrons
do have both spin and
charge I'm not pretending that they don't.
The electrical properties are about the
charge of the electron the current voltage
dielectric response things like that
the spin does NOT couple directly to
an electric field the couples you know by
by a higher order terms are Hamiltonian if
we look at isolated the atoms
the filled core levels are all fair and
so they all exist in a let's just take
helium for example one up one down and
I want to stay.
There paired and so there's no net moment
for helium album but as soon as I have
until the comet shells then I get hundreds
will feel if you are paired electrons so
you know even those simple one up
from their lithium I filled one a.
And I have one extra left on that
one extra like fun is now in
is you know is isn't a has a local
moment it has a spin one house state and
so most isolated out of the fact do
have magnetic moments of an introductory
pharmacare its course as you learn about
how to calculate the orbital angular
momentum the spinning a moment of spin or
a couple plus or minus us etc so
isolated Adams almost the entire periodic
table has a magnetic moment as an isolated
out OK but
what happens when I start combining them.
Chemistry is all about those outermost
electrons so the coral act ons are all
paired already so they have no net
moment those outermost electrons which
are unpaired in general as soon as I start
putting them into a solid material I get
chemical bonding in these bombings they've
caused virtually all of the outermost left
of to also become paired and
therefore the spin ends up cancel.
So let's be concrete about that let's
start with silicon isn't it we're talking
a lot about silicon so this is the silicon
crystal structure it's the diamond diamond
crystal structure so each silicon Adam has
four nearest neighbors this is a two D.
representation of that structure and
the idea is that in the silicon there's
my core Vaillant outermost Pons
silicon as an isolated Adam has two
extra has two extra electrons and
they end up being in the format that you
can put them in a mass spectrometer and
move them around in a field and so forth
but in the context of a solid material
you form these bonding States and
there is no net moment OK So
silicon as most of you know is not
a magnetic material as a solid
we can talk separately about surfaces and
things like that because there
are interesting things about surfaces and
about tiny particles of silicon but
for sticking to solid fully extended
solid structures it's not make that so
in the context of condensed matter
physics instead of chemistry we speak not
about the bonding States per se we usually
represent this in terms of a dancer.
The electrons say and so I plot here the
density of electrons States versus energy
and what happens in something like silicon
as I have a filled conduction band so
as to call the electrons into
these into these bands saved and
that with a completely filled conduction
band completely empty valence band and
there is a gap of about one watt for
unfold in silicon five and
half of carbon the end result is
because these states are all fill
if I apply an electric
field there's no place for
the elect there's no available States for
the electrons so this is an insulator and
in the formal physics sense there is no
distinction between a semiconductor and
an insulator semiconductors are insulators
and I'm going to mean that very
precisely I can ask about the electrical
conductivity and electrical conductivity
of this rather simple structure and here
like your conduct of it it would be X.
that would be activated exponential
with the band gap over T.T. So
an important point here is as he
goes to zero first goes to zero and
it's T. increases this goes up so
the conduct of ity of a semiconductor or
any insulator for
that matter is zero it T. O.
and increases with increasing temperature
and a simple model like this is because
you're promoting the electrons across
the band and leaving behind holes and
they both carry current OK and
the effect of magnetic field or
magnetic impurities is going to be
extremely small and there's just very
little will happen so that's what can
are so the covalent bonds to summarize
that effectively give a close Alectryon
shell so there are no mobile electrons
at the fairly energy which lies in this
country realize model I've done here
that lives right in the middle of this gap
there are no mobile electrons in there for
equal zero at equal zero Now
let's contrast that to copper and
so copper is metallic we bond and so
there is the electronic structure of
a copper atom and has it has an organ
in our shell than ten three D.
electrons and one for us electron
the important one is the four S.
electron because the three D.
By the way is is a for.
Shell So that's a magnetic so and
I put that into it copper likes
to form an F.C.C. Crystal and
there are all of its electrons wandering
around in what we call a fairly see and
the fairly see again I'm not going to
try to all of those metaphysics here but
the end result is the Fermi see you fill
States and they minimize their energy and
in doing that they end up paired so
one up one down and
the important thing to keep in mind is
this has nothing to do with magnetic
interactions This is not dipoles this is
not the electrons interacting via dipoles
with each other anything this is
purely Powell exclusion principle plus
minimising the kinetic energy and so
they end up in these metallic states which
are completely equal.
So the end result of what I've said and
you can extend this across
the periodic table is that in solid
the electron fin is often in fact usually
not visible the electrons are in paired
States whether that's an atomic cunt like
you know take sodium chloride an A plus or
minus you actually transfer an electron
over from one of the other but
you end up with electrons and
paired States whether they're atomic or
fairly C or covalent by and
large they're all in
states that are minimized such
that there is no electron charge.
So the net electrical charge is
neutralized by the ions in a solid
obviously we know the average clump of
material is not does not have a net charge
the electrons can be mobile which is
a metal or they can be not mobile which
is an insulator but
either way there is no net fan so
I've now hopefully convinced you that this
should be no such thing as magnetism.
So where does magnetism come from how
do we have honored COBOL's a nickel and
even get Linnean by the way being magnetic
room temperature actually comes from
the unfilled three billion for I felt
when I said that chemistry was all about
the outermost electrons chemistry is
really all about the S.P. electrons
the D's and F.'s don't go far enough
away from the central ion to really.
Sharing the chemical bonding that's you
know obviously an oversimplification but
loosely speaking with these enough
still or it is the most complicated F.
of the easy one F. are really still stuck
in the original atomic orbitals and
hence have a moment if there you know
if there was a moment is that out and
there's a moment in a solid the D.S.R.
in the sort of really hard to deal with in
between state where there's somewhere in
between their original atomic orbitals and
a completely fair we see like thing and so
they're actually the most complicated to
work with so
those that those little bands of green in
that I showed you on the periodic table
those are all about until three D.
and for shells you can also
couch this instead of and
thinking of them as atomic states you
can speak of now electron bands and
there's a dualism that
either language works OK So
the end result of that is copper or
that for
us electron if you ask how how many
are there well that's pretty easy copper
has you can just measure the density and
the atomic mass of each element
the end result is because there's
one per copper you have ten to
the twenty third electrons
per cubic centimeter.
And those going back to that to the bands
to not really have such but and
then see the light from say what happens
there is because that was a half filled
shell there's only one electron per album
and also they can have all two you end up
with an exactly half conduction band so
by the time you're done
taking account of all of these and putting
the electrons into their Paoli exclusion
driven independents say you
think that we filled up.
Half the conduction band and that for that
to be seven electron volts just taking
account of the Powell Exclusion Principle
putting them into a unique state by
the time you're done putting particles in
a box you're at seventy even for this many
electrons now seventy they may or may
not connect to it's a huge number I mean
it's not huge compared to the you know
the rest mass of the proton or even the.
West mass of the electron but it is that
enormous compared to say thermal energy so
for example room temperature is about
twenty five million electron volts so
seventy v is just enormous That's
just a very large energy so
why do I care about that I'll start one
more point on one thinks of the reasons
civilly of these metals the end result
is that we write the reasons civilly
as a rule not a residual with the seventy
plus a row of T. and so those of you taken
the physics is kind of learned about
that will not as did when purity of T.
is due to various things like falling on
the electron electron scattering the key
point here is the elect I will be able to
talk about the conduct of any not resist
seventy and in this limit this is just
one over the other the key point is that
the conduct of it he is finite at equals
zero you can also say the resisted he
is is finite is not infinite but
that is the distinction so
insulators have zero conduct of the at
equal zero metals have a finite value that
is actually a very important distinction
so if I apply if I take a long time
something that has any kind activity at
all and I apply a voltage electrons will
move because if I take
an insulator they don't move so
this is actually a precise definition of
enslaver and a model is only actually
formally valid at zero even my
even my summary conducting state
my insulating state had a finite product
of a day when it was not equal zero so
the definition of metals and
insulators is really only precise.
Well you might think well that's kind of a
problem because we can't get to Tikal zero
So what do we do what we do is we
look at the functional form in
the limit as he goes towards zero and
that is where plotting conduct
which we'll see some examples of is much
easier to tell with the same ssion many
people think about Di Rodio the derivative
of the resistivity with temperature of
course copper has a well
copper goes down with these.
Temperature wise semiconductors go up with
the creasing temperature that is actually
not the correct definition of metals and
insulators there are metals that go
the wrong way the non copper way
have the opposite sign of D.O.D.
T. so that will precise definition is is
only one that you really only make it
temperature And I forgot one point I meant
to make again very small dependence of
context to video on magnetic field or
magnetic impurities you have to put a lot
of stuff in the copper before it doesn't
act like a model like really a lot you
pretty much have to make it into something
else like a car outside OK so what's so
magical about these so
I've talked about the strains inflating no
carriers metal carriers so
let's just very crudely let's look
at the kinetic energy of the electrons in
copper so the Fermi energy which was that
half filled balance of the energy of the
talk most most energetic electrons I write
is one half you'll notice I put star but
let's just for those of you know what that
means you couldn't be happy otherwise just
think of those one half empty squared so
one of them before it is the kinetic
energy like it always is if you now put in
the dependence on having to satisfy
the power exclusion principle it turns
out that that goes like in the number
of electrons the electron concentration
to the two thirds power OK
you've got to work through some
mouth to get fresh enough very
much mouth but a good senior level
finance metaclass you will very quickly
derive that end of the two thirds power so
that for that we've got seven electron
volts for copper as this said before.
Now let's ask about the interaction energy
and I'm this is a simple model this is
just the interaction between the electrons
the Coolum interaction nothing complicated
Coolum interaction it's just easy for
it over our and
I thought dielectric constant in there
to make it a little more rigorous but
if you can actually if you think about
it that's also the interaction between
the electron and the iron core so
that's above the generic expression for
interaction energy interaction energy
in general in a solid material.
You've heard of R. and R. is the distance
between them so if I talk about
could be the distance between
the electrons are between the electron and
the iron core if I have one electron
proud of that happens that those are Did
those are the same as each other if I
have something else then of course they'd
be different but
very roughly the distance between
that's just stick to electrons
those end of the one third power.
OK And so if you look at copper that ends
up being about five electron volts you
have real careful what you mean by
dielectric constant here but thought so
that's about five electron volts Sol
just naively I mean a kinetic energy
dominated limit Well let's sort
a good Because these are models so
you'd like to think they are in a kinetic
and kinetic energy is the ability to
move around so copper isn't
a kinetic energy dominated limit but
look at the dependence end of the two
thirds vs end of the one third So
what happens is I start having fewer
electrons in their Your first reaction for
most people at least if I had fewer or
fewer electrons do you think all
the interaction energy goes down obviously
there are further apart the Coolum energy
is less that would be true if you
were electrons means less Coolum
interaction energy but because the kinetic
energy goes like end of the two
thirds power in terms of
kinetic energy drops faster.
So you reach the what is not completely
intuitive limit that's just a few of
the numbers I've mentioned we reached
the not completely intuitive answer.
If that there is a competition
between these two energies.
But it turns out well and few electrons
is dominated by interactions and
many electrons is dominated
by kinetic energy.
OK And it's all because of the palace
Lucian principle so the end result
is you have insulators at what Alectryon
concentration including an equal zero with
a sort of a trivial lemma and you have
models of higher electron concentration.
OK so.
That's something that it's sort of
a remarkable statement it's seen in
you know to the surface to the electron
gas things as well as three D. and
the end result is that you have
a quantum material there a quantum
phase transition at a critical moment
of electrons which I'll call in C..
And the end of the value
of N C depends on things
lots of things including the dielectric
constant which I sort of glossed over but
the there is a there is a value of N. C.
that lies somewhere between about ten
to the eighteen and ten to
the twentieth of the twenty first and
that's just built into this these trade
off here and see not surprisingly like any
unstable point probations create wars
effects and so at this transition
from insulating to metal you find that
adding a magnetic field adding disorder or
adding magnetic impurities almost anything
you do will will change the state and
that's inherently why all
of the materials we find so
interesting these days are all have
about that electron concentration and
where being dominated completely by
kinetic energy leaves you with a really
good model which is great for wiring up
for lighting in your house making a really
good insulator is really good for window
glass but it's not going to lead you to
all this wealth of intrinsic
transitions so all the other
thing that's kind of critical here is
like almost everything you learn about.
I'm not I'm not really going to try and
teach you about Fairy Liquid theory today
briefly I will mention that but it's.
In the two extremes in the level like
trying concentration limit you can start
from an insulating state and start adding
probations in your lowance of like hot for
example so you can take an insulator and
introduce a little bit of
hopping probability from Alan the album
starting from the atomic states you can
start from the opposite extreme you can
start from the metallic state with its
you know with its particle in
a box of wave functions and
introduce probations in which
is actually that little M four
right there you can sort of
think of as a probation or.
Roach.
At the point where you're
you're exactly in between
you can think of this rather globally.
There is no small private or you're not
a metal with a little bit of insulating
properties or an insulator with a little
bit of extended hopping you've got the two
are equal in energy by definition at the
metal to insulator transition the kinetic
energy and the potential energy are sort
of they're competing with each other so
not one thing that happens here is that
it turns out that those single particle
approaches that underlie first
free electron theory and
secondly fairly liquid theory you they
don't work so they fall apart and
weighted this transition is where you
start have you add one more electron to
the system and instead of just adding
one more electron to a state that
already exists which is the orbital
theory of the matter physics
you end up you have one more electron and
everything has to rearrange
you have to recalculate the entire problem
which by the way should make sense to you
how is it that I get to treat you know the
electrons in a solid as though I had one
like you know as I had not interacting
single electrons OK so I thought M.
Star little star on top of the arrow but
how is that that that is even faintly
plausible in the answer is remarkable and
is the underlying basis of what's called
Fairy Liquid theory you can't do that
here there is no small parameter and so
you end up with you know that
you really have to calculate a.
Many body physics and
this is goes under the general term
of highly correlated electron materials so
you've undoubtedly or
probably if you've been coming cloakroom
heard this term before these highly
correlated electron materials what that's
a way of saying is that the independent
electron approximation even with an effect
of mass doesn't work turns out and
this in these highly forward the electron
materials it turns out the electron spin
often becomes visible meaning I now see
it they're not just equal in office.
It often becomes important effect
deliberately adding spins is very
large and you get all these instabilities
you get phase transitions and things and
that's all connected to this
the fact that this transition so
this shows up in these materials I've
already mentioned the croissant I did
a resistance prostates light such as one
of them calcium a nice oxide the high T.C.
oxides and the part where I'm going to be
focusing the days on don't semiconductors
which includes phosphorus silicon sort
of the traditional dot semiconductor.
So there so when I add one electron
per extra phosphorus atom and
it also turns out to a two
story it also turns out to be
the physics of these Where are thought
to morph the semiconductors as well.
OK so now I want to talk to switch
gears just a little bit and
talk about amorphous.
And this amorphous which
includes the seven conductors
if you start from
the crystal in structure.
If you pick up any condensed matter
physics book it's usually chapter one
chapter one starts off by talking about
the crystal a graphic symmetries so
you can particularly have to tell but
virtually everything is not a book starts
off by talk about symmetries and
things like that and so in a crystal in
structure we have very well developed
theories for metal for semiconductors for
insulators we have found structure we have
dispersion relations with what we have
description we have family gas or
Fairy Liquid theory etc.
What happens when it becomes the more so
this is just sort of a schematic
of a Morpheus meeting Dawn Crystal it's
not even supposed to now McChrystal and
there was a lot of debate in the early
days of Morpheus materials whether they
really were just tiny little crystals and
they are both thermodynamically and
structurally distinct you can this you
can actually there is a very formal way
of distinguishing between an amorphous
system and just tiny little crystals
neither have long range order but they're
nonetheless not the same structure so
in that system the interesting part
of course now is that I don't have.
Symmetries So let's start with the basics
K. is no longer a good quantum number
there is no block way of this question but
this is the part that I find so
remarkable about introductory condensed
matter physics have you with a few key
exceptions but most of the properties that
are being described by the introductory
condensed matter physics textbooks
like the novels and influence and
semiconductors and superconductors and
from Agnes almost all the properties that
we're attempting to describe are found
in amorphous systems as well.
So we don't have great theories
to describe amorphous metals or
more first semiconductors we sort of
fall back on chemistry models somewhat.
But in fact virtually all
the phenomena are found there so
I guess I would make a rather global point
at this at this moment which is to say
we have to be careful that our models.
Are not more specific than the phenomena
they're describing and the best example I
will give of that is superconductivity if
you take a crystal and molybdenum the T.C.
because the superconducting transition
temperature is about one Calvin if you
take a more first molybdenum
it's seven Calvin.
So personally I find it more remarkable
that electrons can travel through in
awfully a periodic random collected
literally random because there's no
short range repulsion but this collection
of very disordered structure the lections
can travel through that without scattering
seems more amazing that they can travel
through that without scattering so
and in fact that led to Anderson's
we casting of D.C.'s theory which was
originally cast as plus and minus K.
States paring into time
reversed States pairing so that
the realization that amorphous systems
could also super If I can only could but
did with higher transition
temperatures even in some cases
led to a generalization of D.C.'s
theory that's much more profound.
And so again it's we don't
always have the models but.
We have to recognize when our models are
limiting our thinking I guess is the point
and so the interesting thing is we don't
have a but we do still have energy so
all of the scattering in the world does
not lose energy as a good quantum number
as long as it's a lasting scattering and
so atomic energy levels are a lot so
we still have energy bans the reason
I thought of density of states and
not not just virtualization chips is
because energy is a perfectly good
quantum number still of the electron
this is safe we still have a thermal
energy the fairly energy can
even be quite large so and so
most importantly both crystalline silicon
and amorphous thought and exhibit
a transition from insulator to metal with
increasing electron concentration and
in both cases increasing what fun
concentration is introduced by doping so
I introduce phosphorus or
introduce them or introduce whatever
element I'm introducing something that is
you know the give me after electrons and
I increase from any calls zero which
is inflating up to up to high and
work becomes a mill and
the probably remarkable thing is that much
of the properties are actually the same
between Crystal and phosphorus don't so
what can and amorphous literally
silicon both economic that So
how does this translate into these bands
Well first thing is there's the crystal
in bands very grossly simplified but the
crystal inbounds of silicon let's say and
when I make it a more first I make
There's the crystal in periodic lattice
the periodic potential of
a crystal lattice of the whole
the ionic potential oscillates and
there it is in a disordered structure so
the depths of the potentials are different
typically actually the distances
are different this is often modeled
by keeping the distances regular and
just letting the depth of the potentials
vary but that's the electron
potential seen by the electron and what
that does the first thing that that does
is it broadens out what used
to have sharp edges because.
Well and it so
there was the crystal instruction and
there red thing is sort of mushed out if
you will this is very very schematic and
not really even to scale but
it was just to get the point across so
you got this distribution of distances
gives what are called Band tails so
you have these states that all the way
through the gap what's interesting
what does that tell me the let's start
with I said I'm still going to introduce
things that don't fit so
I will introduce more phosphorus or
something like that and if I end up with
enough electrons that the Fermi energy is
down here in the middle of
this big broad band then.
I get an amorphous metal and worth of
metals are perfectly happy metals in fact
people have learned to make a more
fist metals and you know giant
things that you can make I've seen a golf
club made out of an amorphous novel so
you can even call it what they've
gotten good enough at making that you
can call them rather slowly and
still have the same office but
the end result is that amorphous metal the
electrons travel through their elastically
scatter at pretty much every time
every inner tonic spacing so
the mean free path is very close
to the inner tonic spacing
which means in turn that photons don't
make much difference so the resistance of
the of an amorphous metal turns out to
be independent of temperature roughly.
It's like you already staggering every
time you had it out and so there's not
much else you can do to it so follow
ons don't do much election electrons
nothing does that much so basically with
a thirty versus temperature is flat and
for typical amorphous metals where you
have about one electron per hour again two
orders of magnitude that turns into about
one hundred fifty to three hundred microns
centimeters just this is just rough That's
for about one electron proud of OK And so
the differ were is not all that important.
They really just still act
like novels semiconductor so
that's fine that was with the fairy
energy down here you can see it kind of
you know I maybe drop the number of
states a little bit not a big deal but
what happens up here when they found
the energy lies in the middle of the gas.
Well that seems to be a problem because
we're before it there I told you that it
was an insulator because there were no
states there so when I applied an electric
field the electrons were down here they
had no place they could go there were no
available States what if the now of the
family energy lights here I have states
I mean I have a lot of states and this is
you know this is this is down to a very
small number compared to appear I don't
have a lot of states that have song so
it seems a priori that I should have lost
the ability that an amorphous state would
not support an insulator that it would be
always maybe not a very good model but
at least weekly metallic at
least a kind of poor model
we know that's not true you know that's
not true you may not know that you don't
know that you know that's not true
the fact that window glass is transparent
is the best example of that window
glass is amorphous F.I.O.S.
two it has these band tails then you
know again this is not to scale so
they're really tiny you can see through
window glass you can even see through very
thick window glass the fact that you can
see through it means that electromagnetic
waves propagate perfectly happily through
window glass that means that there are not
there may be states there but it is
an insulator so how can that possibly be
the answer to that is there are some
localization and so the key to Anderson
localization is that that that that
potential with varying the varying
potential that I showed before leads
to something called a mobility edge and
the idea of the mobility edge is that it
creates in some limits a wave function
a block or something like a block
wave that still has sort of the way
like a piece that oscillates like the
electron way function normally does but
with an envelope and so this envelope
is called the localization line.
And that localization length
depends on all sorts of things but
the end result is if it's not the size
of the sample then the electrons don't
travel across the whole sample as
a model and the end result of all that
is I create what are called mobility
edges which I was just shown here.
So the idea is that electrons that have
energy above the mobility edge up in
the region of extended States or holes
that lie below down here are mobile so
I get extended states up here and
then in here they're actually localized.
So that's so I'm so that So
that's the concept of mobility edge.
And so the end result of
that is an insulating state
fully inflating Well if you stick a vent
meter on your window glass it will not
one temperature it carries a tiny bit
again it will there this is very formally
defined it equals zero window glass
will not carry a current OK so
how do I think about the electrical
properties of that well these localized
States it's very important understand the
that what I call the localization length
that is not one atom so this is not
the same as creating a crystal of
perfect as to where you might think of the
electrons being localized like on a single
atomic states these states are actually
quite extended in fact the localization
like to be very long localization
like to be hundreds of angstroms So
the electrons are not localized in
one angstrom Carvell only bonded
States at least in a band picture of
this they're there localized over and
over distance and then I'm not going to
go through the derivation of my hopping
probability Well that's not what I
meant to do it all come back here.
OK that's not good.
Back Thank you.
So.
OK so the end result of this and
again anybody who wants to look at not
variable rate hopping you can the end
result is that you get a formally
activated hopping process just like I did
back when I talked about insulators But
you'll notice the so it looks so
similar There's an there's the conduct of
it is exponential it still goes to zero
zero but I know a picture of this will
one fourth power in there and that is.
You know phenomenon happy to talk offline
about any anybody but where that comes
from it arises out of tradeoffs between
energy and distance and things like that
and so I end up with an activated behavior
hundred simply goes to zero two equals
zero goes up with increasing temperature
but with a different power factor.
OK And important to note this is
still a single electron picture so
I've drawn all these little vast
lines to represent the energy
of the electron states and I've acted
as though the energy of those states
did not depend on whether they
were occupied or not occupied so
this is this this is the basic of
non-interacting electron theory or
even Fairy Liquid theory I created I saw
all the Hamiltonian I have a bunch of
saved and then I start sticking electrons
into them and the states are viewed as
independent of their occupation so
here like if I promote if this electron
wants to hop these states will fall then
if it wants to hop it let's say it hops or
there's just a little bit higher in energy
when it close to there that doesn't change
the energy of any of the other states now
if you think about how ridiculous that is
that's impossible These are cool warm
interactions how could you not have
to recalculate the entire problem once you
put an electron in a place different from
where it was before but that's really
the heart of Fairy Liquid theory and
those if you're interested should take
a condensed matter physics course and
learn about where this comes from because
it's a remarkable statement that this
works very profound very deep that
that works that you can treat
create you can consider the occupation of
the states separately from what states
there are so that's obviously
not completely accurate so
interacting electrons on this is this is
not to do more than mention is this is so
this light is really just for
the experts in the audience
there is quantum backscattering there for
this much study phenomena to do with
forming loop where things
interfere with each other
there's the interaction
between the electron.
Gets gets put in
is part of that little innocuous star
on top of the AM is actually built
into the thing to up there with with
theory that's not the part I really want
to talk about the part I really want
to talk with is this next piece.
There is in addition to the M.
Star part of interacting electrons
what's commonly called a cool one gap and
so the cool want gap is an electron
electron interaction of fact it is a many
body a fact it introduces what I will call
a cool long gap and
that takes two forms one if the fermion or
G why's here in the middle of what I call
the insulating States then this isn't
exactly solvable problem and you dig out
what is actually called the cool and
that cool one has this little quadratic
form so the density of states has whatever
density it would have originally had with
an east east where if I don't have squared
with each square is actually a minus the
family from or here I'm going to show you
that but eastward is the is the energy
minus the Fermi energy square so
this could one touches zero so
the fairly energy now has no states so
I told you a second ago that an Anderson
localization even if I had States that to
be localized and not more mobile when I
add in the school long gap there actually
are no states it's called a soft gap
because while it's not a hard gap there
is there is a node goes disease square
there is a big gap there more importantly
unlike the traditional band structure
gaps I can't dope away from now so
I've shown that here are the purple
curve if I add a few more electrons so
like I wanted to move the family
energy away from that minimum
you know like just move it up
a little bit maybe up to here
this cool on gap is fundamentally
a many body gap and the Gap
moves with it that is actually
the signature of these cool on gas
you can't dope away from them
you can't add a few electrons or
take a few electrons away that coolant gap
is fundamentally tied to the Fermi energy
and it is fundamentally tied
to electrons repelling.
Other They are also and this is going to
be a really crucial point singly occupied
this is to do with the fact that electrons
do not actually like to be near each other
so if I put one of my Tron here a second
one even if it spin down the Coolum
energy is large enough that that will
happen so I don't break the spin up and
down that requires of it that IT field but
I do make it be single be occupied so
the promise that I started with all of
these wave functions all in
the doubly occupied breaks down here.
OK these are singularly occupied States so
they could be up or
down that's the general but since I
apply fuel that's not the general So
I've now created a magnetic
moment out of say phosphorus
sought him which a priori does not
say that anything magnetic about it.
Your tree and don't saw him all these
non-magnetic things I've created a system
not found magnetic but I've at least got
the starting point which is I now have
the have local moments they can interact
with each other they create a magnetic
susceptibility not actually complicated
magnetic susceptibility it's not just
Curie law because they do interact with
each other has specific heat associated
with the degeneracy you want to apply
a magnetic field etc So that's the first
example of what I'm talking about just the
fact that I have these interactions has
suddenly made and electrons then become
visible what happens when the family
energies up in the metallic region like up
here well then I get some that is often
called a precursor gaff and the precursor
gap has a has a different form but
it's sort of got like a it's a rude
behavior so there is my email to see
if there me so that's the precursor
Gaffin is there are references for
loosely listed up here that precursor
get out there it's different so as
again has the same property wherever the
family energy is that's where that lies so
if I start for example reducing
the electron concentration so
the feminity starts moving down this
moves down with that and in fact what is.
Experimentally observed is that
the metal insulator transition happens
we don't really know where the mobility
edges in any of this metal inflated
transition actually happens when this
point as it moves down gets deeper and
deeper and deeper and finally hit zero and
once it hits zero there are no
states of the fairly energy and
once there's no states at the family
energy there is no contact to Vittie So
the transition from metal to insulator
is actually determined by this cool long
gap now underlying all that is the
Andersen localization and things like that
there is it's not that there isn't a
mobility edge there is it's important for
all this but the kind of crucial point
is there is no actual theory that
combines all these things together there's
nothing that says put in disorder and
then here's where the mobility edges and
here's how the coolant gap and
this is where the metal insulator
transition happens so it's a rather
we don't have a theory that can include
all of these on equal footing so the way
it's usually done is to put these cool and
gaps in you know after the fact and
that's actually the way I'm
going to present the data to so
that who want perfect Not surprisingly
profoundly affects the conduct of it
in its temperature dependence.
So on the fermion if you lay up in
the extended state region you get metallic
conduction which again specifically
means finite conduct to zero nothing
about the road ity we don't know anything
about that yet but in fact it's friends
out that this kind of activity increases
the temperature increases not surprisingly
I have this little tiny gap as temperature
increases you might think gosh what you
just promoted electrons across this little
tiny gap that would be an incomplete
understanding of what happens because
the gap itself is a many body gap so
not only do I promote things across but
actually make the gap go away so
I'm like a semiconductor gap all I have to
do is think about for motion across that
this is a self consistent statement once
I start moving things across I affect
the states themselves the states don't sit
there independently of their occupation so
I start occupying other states I think
this and the gap of self goes away.
With temperature OK so the end result
of all of this is I get the following
form for the electron density of states
with that square root thing and if I get
that out for the electrical conductivity
where I have a square root of T..
And the lotus that there is a Sigma not so
I get my definition of a metal as T.
goes to zero Sigma goes to Sigma not find
I conduct the wrong side of the road which
he compared a normal model but
finite connectivity at equal zero.
If the Fermi energy lies
in the localized regime
then I get an insulator with
a thermal activated behavior and
you're now going to get to see yet another
form of activation This isn't freedom and
actually there's a lot of
this in three dimensions.
Of whatever it does so sixty three so the
colleague seventy again is activated so
people zero zero but
it now has a one half hour long.
And that's the form of the Electrical
of the electron density of states and
I still change the thermal energy by
doping so none of that has changed so
just to prove you this is why I
have to kind of wrap it up so
we'll wrap it up I think I'm
within a few grass home quickly so
this is this is not just made up stuff
this is a Morpheus get room so it can and
we have metals here and we have insulators
down here and this is my point here is to
show you that color to be even from metal
is a better thing to pot when you're near
this metal insulator transmission it's
very easy to see that these are going to
hit people if I don't gravity pulls there
are this one down to I think one tell me.
You can see unless something rather unless
there's some drastic phase transition like
structurally that is going to
hit with a finite intercept so
those two are models and
these guys are insulators.
OK And a key point that the phosphorus has
exactly the same sort of metal and
insulators the one interesting
point that I will leave you all with
a mirror showing a couple more thoughtful.
One interesting point is that
the intrinsic Alectryon concentration in
the amorphous systems is much higher by
about two to three orders of magnitude so
the N C in phosphorus silicon is
ten to be eighteen and see in.
More facility it is about ten to the
twenty or so it's two orders of magnitude
larger it's still have the inflated
transition because of all the disorder and
the localization of facts so this is the
same at the metal insulator transition but
because the there are so many more
electrons things like the underlying
fermion or G.
is about tours of magnitude higher so
the very practical level I can be at
the low temperature limit at much higher
temperatures phosphorus don't select and
you have to be below about one tell them
to see these low temperature facts
amorphous yet for thought and
I could be up at fifty sixty seventy
Kelvin and still be seeing one correlation
gaps because the temperature Well it's
up to the Fermi energy is low OK so
I read this comment was great
past this once but really it's
clear to everybody these are single
reoccupied so they have they have a span.
OK so the wearer thought.
The basic statements we made a lot more
valid always mostly worked with gadolinium
which as I have and what we did some work
with him which is a nice non-magnetic and
all together when am I did a lot of work
also with a couple of transition not all
of which I'm happy to talk offline and
not to talk about that day we didn't
these are prepared by a lecturer when
Kovacs operation also had a vacuum we've
over the past this is been fifteen
years of work we've done on will a lot
of work by now lots of high resolution.
If you can see the long list
of things we've done so
at level of theoretical analysis.
Work will be a.
Fairly linear augment a plane where
something like this is a cooperative mind
and so we've we've we have answers to
a lot of questions if you want to ask me
after the talk this is image of
the structure which I really like.
There's the gadolinium the big blue out by
thought hims the interesting thing about
the structure is that there are two types
of thought in atoms there are ones that
only have silicon is nearest neighbors
which are still in a fully you know four
little tetrahedral form and there are ones
that are surrounding the gadolinium
that are really in a cage like
structure and they lead to two very
different types of things one of them
has a gap much like it would have.
Thought them and the other has sort
of a metallic like structure so
because this is a calculation you can do
projections on to the different albums and
so it's just it's interesting to note that
the more the structure is very forgiving
it's like one out of the way
it's back to making.
Bonds again OK so.
Who have their their so this is just
quick T.M. images high resolution to
their nice the amorphous no
no crystal face segregation.
We've also done X. lots of other
structural stuff there is the it for
me again I showed you that already and
now I'm going to show you
what happens when I add gadolinium which
is sort of the point of all of this so
why a gallon even a copper not much
happens when I add gadolinium in
into silicon in place of the yet for him
to look almost identical the black curves
are they you trim the level what are
called the Star I get this sudden moment
of the conduct of eighty so just focus
on those two curves the fourteen percent
gallon in which is purple and the it true
that the fifteen percent yet trim which
is outside of Earth so I think that's
real I don't know if it's significant but
there's your tree and silicon so you can
see fifteen percent your trim comes down
very small temperature dependence not
much going on and definitely about all
the prep will one blow this to start
the contact of any plummets and
that actually is a solid insulator.
And in fact it's best
to look at insulators.
Far and then with the magnetic field that
comes up that's kind of the key point here
so when I apply a magnetic field.
That conduct to be head
on goes back up again.
And this is best displayed on a log scale
so the in that metal the metals are best
displayed on a linear linear scale the
insulator the best the final won't feel so
this is the log of the conduct of a vs T.
to the minus one house so
that's how you display activated
temperature dependent this thing this lock
curve is that in Vero magnetic
field there's an in not to test for
to full successful a Tesla so
that may not look dramatic but
to pick a point like
there is one Kelvin so
one cold in the middle resistance is
five orders of magnitude hundred fifty
military what we couldn't measure at one
hundred fifty and in zero field there it
is high field these are beautiful to the
minus one half the havior it is not hard
to extrapolate that down to
the cut activity is just it's so
that's not hard to extrapolate down and
what you'd find if you were ten of
the seventeen at one hundred fifty
million Helfen So these are just asked in
fact these curves are exponentially
diverge NG as you go to zero you have
an infinite making it a resistance now
you know seventeen orders of magnitude
at one hundred fifty no one Calvin is
a very large number we kind of ran out of
adjectives colossal was already used up so
we're stuck with extremely large
Nobody is suggesting that this is going to
be the basis of the next hard drive we're
not going to be cooling our computers down
to one hundred fifty military but this is
this is seventeen orders of magnitude
is a very large change in resistance.
And kind of interesting part so
I need to flip through and
let me just show you I'll show you
this curve and then I'll summarize.
We can do a simple model
of what's going on so
if you go back to mag to Anderson
localization imagine that what I
have is in this material I have a lecture
on moving around and I have gadolinium
magnetic moments those gadolinium magnetic
moments and zero field all misaligned.
I have an S.F. exchange interaction and
because the get Williams are all
misaligned that gives
an additional force of disorder.
Which is what is shown.
Here so I have extra disorder I now
have magnetic disorder on top of
the structural disorder So now imagine
that I turn on a magnetic field and
I line up together when the i've
now reduced the disorder and
when I reduce the disorder I move
the mobility edge back down so
what I'm doing is moving around the
mobility edge which changes the conduct of
it by orders of magnitude now you can't
get there from thinking of battery
This is miles outside of any means
the mean free path this isn't a mean
free path probably would never change mean
that it's completely disordered already so
this extra disorder does not
come in in the form of changing
the mean free path of the electrons it
comes in in changing that coolant gap and
in fact that's what we see.
So what we can do is probe this is of an
example of a set of data and I'm going to
put past this pretty quickly this is four
different samples near the metal insulator
transition all different magnetic fields
you can see they all look exactly the same
and the interesting point is that
the data completely overlays and
I want to get to understand show that
quickly and get to the real point.
When I so I've shown you parts of
conduct those all mapped beautifully
onto that metal insulator physics you can
also look at you know how did I know that
about the coolant gap for example how do
I know that it looks like a routine or
it looks like a nice square
the answer is experimental so
we made we've made tunnel junctions either
there are superconducting normal thing
with a lot of aluminum that
is not displaced that is
the one I'm showing right now is a from
the metallic side that is the cool long
gap that I showed you the precursor cool
of that with its root dependence on the.
Side and
there it is on the insulating side and
those are not displaced curve that is
the actual data as it comes out of the you
know out of the measuring equipment so
what you're seeing here is.
The End zero changing that is the cooling
gap of the family energy right there and
as I change the magnetic field I
don't change the family energy
I change the mobility edge and
what that doesn't turn is change the
density is say at the fairly energy same
thing here on the insulating side I can't
go very far in slipping so I don't get
the real you squared property you can see
clearly it's not at that really anymore so
I get the sort of the square like behavior
a little bit on the insulating side and
again what happens as they move as they
change magnetic field is the density of
states with off of zero so.
This is a this is my last year of
my last flight before some icing so
hang in there So
to summarize everything I've told you
on the metallic side there is the form of
the conduct of eighty there's the form
the conduct of it in the insulating
side there is the density of save and
by change by adding these gadolinium what
I do is I modify just those parameters and
purple So it's sort of a remarkable
thing that I don't change any of
the forms of these That's why those curves
lead parallel to each other I just change
the pretty factor of the Sigma not
the end not the team in the end too and
you can do some interesting
things looking at scaling so
the beauty of this whole thing is that on
a single sample we're able to move through
the quantum phase transition
of just using a magnetic field
it is a remarkably simple set
of parameters with no underlying
theory beyond that what I said just
the the Anderson localization you have you
have a whole set of parameters that change
in a way that we sort of understand but
without being able to
predict their values OK so.
The last day I forgot I had one more
data slide which I'll just mention
there's a part we don't understand at all.
Which is the tease start the thing of
where does this word of the moment start
mattering very high temperatures belief
my belief without theory to back this
up is that this is the onset of the cool
one hour but we not be able to do tumbling
at these kind of temperatures so I can't
prove at the onset of the tunneling but
it's hard to imagine you know what is
happening at these temperatures and
this I think is a topic I'll
talk about offline with some but
if you're curious the question of what
controls to star is we've done a lot
of experiments to understand it
it's clearly a many body effect but
again we're out of time so
let me just get to the conclusions.
OK so what I hope left you with is
the sense that the at this novel insulator
transition is very exotic many body
physics and adding magnetic impurities
into it changes things radically in fact
we can pass right through the insulator
trying the metal and slow transition this
is very much like what is seen in things
like galley manganese arsenic in various
other night that exactly conductors but
the theories in all those other systems
those of you who've heard talks will have
heard about things like magnetic pole
on magnetic pole or answer awfully in
a pleasurable here so that the the
theories that have been developed for
the crystal and systems have to at least
be brought to mean the they are very
specific and we see the same phenomena
across the board in all the properties so
can we generalize the level temperature
properties can be dicks played with field
dependent parameters of those
little purple things which rely on
many body physics known as correlation
of facts but there is no simple
scaling of these things and so
you what controls two starts are and
finally the other properties not
surprisingly are also exotic we've seen
very remarkable thermal conductivity as
much as you see in all of
the Megan is the so forth and
we've been able to use this to study
the mental inflated transition Thank you.