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

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.

15 pages, 5 figures

References in corpus (9)

• Observation of neutral modes in the fractional quantum Hall regime
• Local Thermometry of Neutral Modes on the Quantum Hall Edge
• Tuning Energy Relaxation along Quantum Hall Channels
• Edge-State Velocity and Coherence in a Quantum Hall Fabry-Perot Interferometer
• Chargeless heat transport in the fractional quantum Hall regime
• Extracting net current from an upstream neutral mode in the fractional quantum Hall regime
• Relaxation in driven integer quantum Hall edge states
• Thermoelectric probe for neutral edge modes in the fractional quantum Hall regime
• Probing the neutral edge modes in transport across a point contact via thermal effects in the Read-Rezayi non-abelian quantum Hall states

Cited by in corpus (12)

• Hall Effect Gyrators and Circulators
• Interference induced thermoelectric switching and heat rectification in quantum Hall junctions
• Vibrational cooling and thermoelectric response of nanoelectromechanical systems
• Optimal quantum interference thermoelectric heat engine with edge states
• Local Temperatures Out of Equilibrium
• Minimal excitation states for heat transport in driven quantum Hall systems
• Heat current across a capacitively coupled double quantum dot for high magnetic field
• Optimal thermoelectricity with quantum spin-Hall edge states
• Enhanced thermoelectric response in the fractional quantum Hall effect
• Helical spin thermoelectrics controlled by a side-coupled magnetic quantum dot in the quantum spin Hall state
• Statistics of heat transport across capacitively coupled double quantum dot circuit
• Quantum thermocouples: nonlocal conversion and control of heat in nanostructures