Finite-temperature effective boundary theory of the quantized thermal Hall effect

Abstract

A finite-temperature effective free energy of the boundary of a quantized thermal Hall system is derived microscopically from the bulk two-dimensional Dirac fermion coupled with a gravitational field. In two spatial dimensions, the thermal Hall conductivity of fully gapped insulators and superconductors is quantized and given by the bulk Chern number, in analogy to the quantized electric Hall conductivity in quantum Hall systems. From the perspective of effective action functionals, two distinct types of the field theory have been proposed to describe the quantized thermal Hall effect. One of these, known as the gravitational Chern-Simons action, is a kind of topological field theory, and the other is a phenomenological theory relevant to the Středa formula. In order to solve this problem, we derive microscopically an effective theory that accounts for the quantized thermal Hall effect. In this paper, the two-dimensional Dirac fermion under a static background gravitational field is considered in equilibrium at a finite temperature, from which an effective boundary free energy functional of the gravitational field is derived. This boundary theory is shown to explain the quantized thermal Hall conductivity and thermal Hall current in the bulk by assuming the Lorentz symmetry. The bulk effective theory is consistently determined via the boundary effective theory

18 pages

References in corpus (6)

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• Topological Field Theory of Time-Reversal Invariant Insulators
• Thermal Hall Effect and Geometry with Torsion
• Low-energy effective theory in the bulk for transport in a topological phase
• Topological field theory and thermal responses of interacting topological superconductors
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• Geometric description of the Kitaev honeycomb lattice model
• The non-commutative topology of two-dimensional dirty superconductors
• Bulk thermal transport coefficients in a quantum Hall system and the fundamental difference between thermal and charge response
• Torsion, energy magnetization and thermal Hall effect
• Geometric and computational aspects of chiral topological quantum matter
• Topology of Fermi Surfaces and anomaly inflows