Transmission line approach to transport of heat in chiral systems with dissipation

Abstract

Measurements of the energy relaxation in the integer quantum hall edge at filling factor $\nu =2$ suggest the breakdown of heat current quantization [H. le Sueur et al., Phys. Rev. Lett. 105, 056803]. It was shown, in a hydrodynamic model, that dissipative neutral modes contributing apparently less than a quantum of heat can be an explanation for the missing heat flux [A Goremykina et al., arXiv preprint arXiv:1908.01213]. This hydrodynamic model relies on the introduction of an artificial high-energy cut-off and lacks a way of a priori obtaining the correct definition of the heat flux. In this work we overcome these limitations and present a formalism, effectively modeling dissipation in the quantum hall edge, proving the quantization of heat flux for all modes. We mapped the QHE to a transmission line by analogy and used the Langevin equations and scattering theory to extract the heat current in the presence of dissipation.

References in corpus (26)

• Topological Insulators
• Observation of half-integer thermal Hall conductance
• Sharp and Smooth Boundaries of Quantum Hall Liquids
• Quantized Thermal Transport in the Fractional Quantum Hall Effect
• Observed Quantization of Anyonic Heat Flow
• Energy Relaxation in the Integer Quantum Hall Regime
• Novel Edge Excitations of Two-dimensional Electron Liquid in a Magnetic Field
• Local Thermometry of Neutral Modes on the Quantum Hall Edge
• Reconstruction of Fractional Quantum Hall Edges
• Observation of Chiral Heat Transport in the Quantum Hall Regime
• Edge reconstruction in the $\nu =2/3$ fractional quantum Hall state
• Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
• Field Theoretical Description of Quantum Hall Edge Reconstruction
• Composite Edge States in the $\nu =2/3$ Fractional Quantum Hall Regime
• Transport in a disordered $\nu =2/3$ fractional quantum Hall junction
• Energy relaxation at quantum Hall edge
• Equilibration of quantum Hall edge states by an Ohmic contact
• Imaging the Conductance of Integer and Fractional Quantum Hall Edge States
• Edge reconstructions in fractional quantum Hall systems
• Relaxation and revival of quasiparticles injected in an interacting quantum Hall liquid
• Theoretical investigation of edge reconstruction in the $\nu$=5/2 and 7/3 fractional quantum Hall states
• Scattering theory approach to bosonization of non-equilibrium mesoscopic systems
• Auger-spectroscopy in quantum Hall edge channels: a possible resolution to the missing energy problem
• Topological dephasing in the $\nu =2/3$ fractional Quantum Hall Regime
• Statistical theory of relaxation of high energy electrons in quantum Hall edge states
• Interaction-induced charge transfer in a mesoscopic electron spectrometer