Thermodynamic signatures of edge states in topological insulators

Abstract

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. In this paper, we overcome this challenge with Hill thermodynamics. 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 structure. Furthermore, the subdivision potential reveals phase transitions of the edge even when they are not manifested in the bulk, thus opening a variety of new possibilities for investigating, manipulating, and characterizing topological quantum matter solely in terms of equilibrium boundary physics.

9 pages, 3 figures

References in corpus (4)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• The Big World of Nanothermodynamics
• Thermodynamics of nonadditive systems

Cited by in corpus (23)

• Probing the topology of density matrices
• A generalization of Bloch's theorem for arbitrary boundary conditions: Theory
• Multi-critical Behavior in Topological Phase Transitions
• Universalities of thermodynamic signatures in topological phases
• Unconventional scaling at non-Hermitian critical points
• Generalization of Bloch's theorem for arbitrary boundary conditions: Interfaces and topological surface band structure
• Unifying topological phase transitions in noninteracting, interacting, and periodically driven systems
• Multi-critical topological transition at quantum criticality
• Multipartite-Entanglement Tomography of a Quantum Simulator
• Topological Phase Transition in Quantum Heat Engine Cycles
• Topological phase transitions at finite temperature
• Staircase to Higher-Order Topological Phase Transitions
• Thermodynamics in topological Josephson junctions
• Critical and non critical non-Hermitian topological phase transitions in one dimensional chains
• Thermodynamics and entanglement entropy of the non-Hermitian SSH model
• Internal Geometric Friction in a Kitaev Chain Heat Engine
• Thermodynamics of a Higher-Order Topological Insulator
• Thermal topological phase transition in SnTe from \emph{ab-initio} calculations
• Anomalous photo-thermal effects in multi-layered semi-Dirac black phosphorus
• Exotic quantum statistics and thermodynamics from a number-conserving theory of Majorana fermions
• Topological and Finite Size Effects in a Kitaev Chain Heat Engine
• Multipartite entanglement in quantum phase transitions
• Signatures of topological phase transitions in the s-wave superconductor at finite temperature