Topological Patterning of Polymers on a Substrate
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Thermal fluctuations and interactions often complicate or even ruin topological phenomena, yet are an inherent part of soft matter systems and a prime source of messiness. I'll describe a system of substrate-adsorbed directed polymers in which fluctuations and interactions create, rather than hinder, topologically protected behaviour. The topological index manifests itself in a collective tilt of equilibrium polymer conformations relative to the substrate pattern, whose slope is determined by the Chern number of the substrate potential and is hence quantized. As a classical generalization of the Thouless pump, the mechanism shows that topological transport phenomena can survive the transition to imaginary time in the standard quantum-to-statistical mapping, and could be exploited for robust templating of nanoscale structures.
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