Thermodynamics of a Higher-Order Topological Insulator

Abstract

We investigate the order of the topological quantum phase transition in a two dimensional quadrupolar topological insulator within a thermodynamic approach. Using numerical methods, we separate the bulk, edge and corner contributions to the grand potential and detect different phase transitions in the topological phase diagram. The transitions from the quadrupolar to the trivial or to the dipolar phases are well captured by the thermodynamic potential. On the other hand, we have to resort to a grand potential based on the Wannier bands to describe the transition from the trivial to the dipolar phase. The critical exponents and the order of the phase transitions are determined and discussed in the light of the Josephson hyperscaling relation.

arXiv comment13 pages, accepted for publication in Physical Review Research

References in corpus (31)

• Classification of topological insulators and superconductors in three spatial dimensions
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological Crystalline Insulators
• Quantized Electric Multipole Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topolectrical circuit realization of topological corner modes
• Acoustic higher-order topological insulator on a Kagome lattice
• Higher-Order Topology in Bismuth
• The space group classification of topological band insulators
• A beginner's guide to the modern theory of polarization
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Robust zero-energy modes in an electronic higher-order topological insulator: the dimerized Kagome lattice
• Higher Order Topological Phases: A General Principle of Construction
• Observation of Quadrupole Transitions and Edge Mode Topology in an LC network
• Higher-order topological electric circuits and topological corner resonance on the breathing Kagome and pyrochlore lattices
• Higher-order topological insulators in amorphous solids
• Edge modes in band topological insulators
• Connecting higher-order topological insulators to lower-dimensional topological insulators
• The Big World of Nanothermodynamics
• Universality classes of topological phase transitions with higher-order band crossing
• Thermodynamics of nonadditive systems
• Multi-critical Behavior in Topological Phase Transitions
• Universalities of thermodynamic signatures in topological phases
• Weakly Interacting Topological Insulators: Quantum Criticality and Renormalization Group Approach
• Generating quantum multi-criticality in topological insulators by periodic driving
• Scaling Theory of ${\mathbb{Z}}_2$ Topological Invariants
• Hill's nano-thermodynamics is equivalent with Gibbs' thermodynamics for curved surfaces
• Thermodynamic signatures of edge states in topological insulators
• Unifying topological phase transitions in noninteracting, interacting, and periodically driven systems
• Staircase to Higher-Order Topological Phase Transitions
• Decoding quantum criticalities from fermionic/parafermionic topological states

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