Topological quantum and classical materials can exhibit robust properties that are protected against disorder, for example, for noninteracting particles and linear waves. Here, we demonstrate how to construct topologically protected states that arise from the combination of strong interactions and thermal fluctuations inherent to soft materials or miniaturized mechanical structures. Specifically, we consider fluctuating lines under tension (e.g., polymer or vortex lines), subject to a class of spatially modulated substrate potentials. At equilibrium, the lines acquire a collective tilt proportional to an integer topological invariant called the Chern number. This quantized tilt is robust against substrate disorder, as verified by classical Langevin dynamics simulations. This robustness arises because excitations in this system of thermally fluctuating lines are gapped by virtue of interline interactions. We establish the topological underpinning of this pattern via a mapping that we develop between the interacting-lines system and a hitherto unexplored generalization of Thouless pumping to imaginary time. Our work points to a new class of classical topological phenomena in which the topological signature manifests itself in a structural property observed at finite temperature rather than a transport measurement.
Pedro, R. P., Paulose, J., Souslov, A., Dresselhaus, M., & Vitelli, V. (2019). Topological Protection Can Arise from Thermal Fluctuations and Interactions. Physical Review Letters, 122(11). doi:10.1103/physrevlett.122.118001
We thank Benny van Zuiden for programming assistance, and Vadim Cheianov, Michel Fruchart, Alexander Grosberg, Charles L. Kane, David R. Nelson, Philip Pincus, D. Zeb Rocklin, and Tom Witten for insightful discussions. V. V. was primarily supported by the University of Chicago Materials Research Science and Engineering Center, which is funded by the National Science Foundation under Grant No. DMR-1420709. J. P. acknowledges funding from NWO through a Delta ITP Zwaartekracht grant. R. P. P. gratefully acknowledges the Office of Graduate Education of MIT for the support of the graduate Unitec Blue Fellowship, and the King Abdullah University of Science and Technology for support under Contract No. OSR-2015-CRG4-2634.