Thermoelectric Hall conductivity of the fractional quantum Hall systems on a disk

TL;DR

This paper investigates how edge states influence thermoelectric transport in fractional quantum Hall systems on a disk, revealing that edges dominate low-temperature behavior and alter universal scaling laws observed in torus geometries.

Contribution

It introduces a detailed analysis of edge effects on thermoelectric conductivity in fractional quantum Hall states, highlighting the impact of edge reconstruction and neutral modes.

Findings

Edge spectra dominate low-temperature thermoelectric behavior.

Edge reconstruction breaks universal scaling laws.

Majorana edge modes significantly affect the Moore-Read state.

Abstract

For the fractional quantum Hall states on a finite disc, we study the thermoelectric transport properties under the influence of an edge and its reconstruction. In a recent study on a torus [Phys. Rev. B 101, 241101 (2020)], Sheng and Fu found a universal non-Fermi liquid power-law scaling of the thermoelectric conductivity $\alpha_{xy} \propto T^{\eta}$ for the gapless composite Fermi-liquid state. The exponent $\eta \sim 0.5$ appears an independence of the filling factors and the details of the interactions. In the presence of an edge, we find the properties of the edge spectrum dominants the low-temperature behaviors and breaks the universal scaling law of the thermoelectric conductivity. In order to consider individually the effects of the edge states, the entanglement spectrum in real space is employed and tuned by varying the area of subsystem. In non-Abelian Moore-Read state, the Majorana neutral edge mode is found to have more significant effect than that of the charge mode in the low temperature.