Universalities of thermodynamic signatures in topological phases

Abstract

Topological insulators (superconductors) are materials that host symmetry-protected metallic edge states in an insulating (superconducting) bulk. Although they are well understood, a thermodynamic description of these materials remained elusive, firstly because the edges yield a non-extensive contribution to the thermodynamic potential, and secondly because topological field theories involve non-local order parameters, and cannot be captured by the Ginzburg-Landau formalism. Recently, this challenge has been overcome: by using Hill thermodynamics to describe the Bernevig-Hughes-Zhang model in two dimensions, it was shown that at the topological phase change the thermodynamic potential does not scale extensively due to boundary effects. Here, we extend this approach to different topological models in various dimensions (the Kitaev chain and Su-Schrieffer-Heeger model in one dimension, the Kane-Mele model in two dimensions and the Bernevig-Hughes-Zhang model in three dimensions) at zero temperature. Surprisingly, all models exhibit the same universal behavior in the order of the topological-phase transition, depending on the dimension. Moreover, we derive the topological phase diagram at finite temperature using this thermodynamic description, and show that it displays a good agreement with the one calculated from the Uhlmann phase. Our work reveals unexpected universalities and opens the path to a thermodynamic description of systems with a non-local order parameter.

14 pages, 6 figures

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• Topological phase transitions at finite temperature
• Quantum thermodynamics of nonequilibrium processes in lattice gauge theories
• Critical and non critical non-Hermitian topological phase transitions in one dimensional chains
• Thermodynamics in topological Josephson junctions
• Thermodynamics and entanglement entropy of the non-Hermitian SSH model
• Thermal topological phase transition in SnTe from \emph{ab-initio} calculations
• Universal scaling in far-from-equilibrium quantum systems: an equivalent differential approach
• Signatures of topological phase transitions in the s-wave superconductor at finite temperature