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

Measurements of the energy relaxation in the integer quantum Hall edge at filling factor ??? = 2 suggest the breakdown of heat current quantization [H. le Sueur et al., Phys. Rev. Lett. 105, 056803 (2010)]. 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:1908.01213]. This hydrodynamic model relies on the introduction of an artificial high-energy cutoff 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 quantum Hall edge to a transmission line by analogy and used the Langevin equations and scattering theory to extract the heat current in the presence of dissipation.