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

TL;DR

This paper introduces a transmission line formalism to accurately model heat transport in dissipative chiral quantum Hall systems, confirming the quantization of heat flux across all modes.

Contribution

It develops a novel formalism using transmission line analogy, Langevin equations, and scattering theory to model dissipation and establish heat flux quantization in quantum Hall edges.

Findings

Heat flux quantization is maintained despite dissipation.

The transmission line model effectively captures dissipative effects.

The formalism overcomes previous limitations of high-energy cut-offs.

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.