Cristiane Morais Smith Monday, 09:35 - 10:05
Universalities of thermodynamic signatures in topological phases
Topological insulators are states of matter distinguished by the presence of
symmetry protected metallic boundary states. These edge modes have been
characterised in terms of transport and spectroscopic measurements, but a
thermodynamic description has been lacking. The challenge arises because in
conventional thermodynamics the potentials are required to scale linearly with
extensive variables like volume, which does not allow for a general treatment of
boundary effects. Recently, this challenge has been overcome by using Hill
thermodynamics to describe the Bernevig-Hughes-Zhang model in two dimensions
[1]. In this extension of the thermodynamic formalism, the grand potential is split into
an extensive, conventional contribution, and the subdivision potential, which is the
central construct of Hill’s theory. For topologically non-trivial electronic matter, the
subdivision potential captures measurable contributions to the density of states and
the heat capacity: it is the thermodynamic manifestation of the topological edge
Subsequently, we extended 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
[2]. Moreover, we derived the topological phase diagram at finite temperature using
this thermodynamic description, and showed 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 [2].
[1] A. Quelle, E. Cobanera, and C. Morais Smith, Phys. Rev. B 94, 075133 (2016).
[2] S. N. Kempkes, A. Quelle, and C. Morais Smith, Nature Scientific Reports 6,
38530 (2016).