Heat transport through quantum Hall edge states: Tunneling versus capacitive coupling to reservoirs

TL;DR

This paper investigates heat transport along quantum Hall edge states with two models of reservoir coupling, revealing how different contact types and temperature regimes influence thermal conductance and finite-size effects.

Contribution

It provides exact solutions for heat transport in quantum Hall edge states with tunneling and capacitive couplings, highlighting distinct temperature-dependent behaviors and non-universal effects.

Findings

Heat propagates chirally along the edge in both models.

Thermal conductance exhibits different power laws depending on contact type.

Finite-size effects are significant at low temperatures, affecting heat transport.

Abstract

We study the heat transport along an edge state of a two-dimensional electron gas in the quantum Hall regime, in contact to two reservoirs at different temperatures. We consider two exactly solvable models for the edge state coupled to the reservoirs. The first one corresponds to filling $\nu=1$ and tunneling coupling to the reservoirs. The second one corresponds to integer or fractional filling of the sequence $\nu=1/m$ (with $m$ odd), and capacitive coupling to the reservoirs. In both cases we solve the problem by means of non-equilibrium Green function formalism. We show that heat propagates chirally along the edge in the two setups. We identify two temperature regimes, defined by $\Delta$, the mean level spacing of the edge. At low temperatures, $T< \Delta$, finite size effects play an important role in heat transport, for both types of contacts. The nature of the contacts manifest themselves in different power laws for the thermal conductance as a function of the temperature. For capacitive couplings a highly non-universal behavior takes place, through a prefactor that depends on the length of the edge as well as on the coupling strengths and the filling fraction. For larger temperatures, $T>\Delta$, finite-size effects become irrelevant, but the heat transport strongly depends on the strength of the edge-reservoir interactions, in both cases. The thermal conductance for tunneling coupling grows linearly with $T$, whereas for the capacitive case it saturates to a value that depends on the coupling strengths and the filling factors of the edge and the contacts.