Bulk thermal transport coefficients in a quantum Hall system and the fundamental difference between thermal and charge response

Abstract

We derive and calculate thermal transport coefficient for a quantum Hall system in the linear response regime, and show that they are exponentially small in the bulk, in contrast to the quantized value of the charge Hall coefficient, thus violating Wiedemann-Franz law. This corroborates earlier reports about the essential difference between the charge and thermal quantum Hall effect, that originates from the different behavior of the corresponding $U(1)$ and gravitational anomalies. We explicitly calculate the bulk currents when a temperature profile is applied within the bulk, and show that they are proportional to the second derivative of the respective gravitational potential (tidal force), and nonuniversal, in contrast to the charge current which is proportional to the first derivative of the electrochemical potential.

References in corpus (28)

• Topological Insulators
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• Observation of half-integer thermal Hall conductance
• Quantized Thermal Transport in the Fractional Quantum Hall Effect
• Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors
• Thermoelectric Response of an Interacting Two-Dimensional Electron Gas in Quantizing Magnetic Field
• Energy Magnetization and Thermal Hall Effect
• Observed Quantization of Anyonic Heat Flow
• Thermal Transport in Chiral Conformal Theories and Hierarchical Quantum Hall States
• Gravitational Anomalies and Thermal Hall effect in Topological Insulators
• Thermal Transport in the Kitaev Model
• Low-energy effective theory in the bulk for transport in a topological phase
• Quantization of the thermal Hall conductivity at small Hall angles
• Topological field theory and thermal responses of interacting topological superconductors
• Approximately quantized thermal Hall effect of chiral liquids coupled to phonons
• Quantum Thermal Hall Effect in a Time-Reversal-Symmetry-Broken Topological Superconductor in Two Dimensions : Approach From Bulk Calculations
• On the Interpretation of Thermal Conductance of the nu=5/2 Edge
• Partial equilibration of integer and fractional edge channels in the thermal quantum Hall effect
• Comment on S. H. Simon, Interpretation of thermal conductance of the $\nu =5/2$ edge, arXiv:1801.09687
• Thermodynamics of Chiral Spin Liquids with Abelian and Non-Abelian Anyons
• Phenomenological theory of heat transport in the fractional quantum Hall effect
• Probing topological superconductors with emergent gravity
• Laughlin's argument for the quantized thermal Hall effect
• Finite-temperature effective boundary theory of the quantized thermal Hall effect

Cited by in corpus (4)

• Fundamental relations for anomalous thermoelectric transport coefficients in the non-linear regime
• Thermal Hall response: violation of gravitational analogues and Einstein relations
• Torsion, energy magnetization and thermal Hall effect
• Quantized thermal Hall conductance from edge current calculations in lattice models