Thermopower and thermoelectric power factor of ${\mathbb Z}_k$ parafermion quantum dots

TL;DR

This paper demonstrates that thermoelectric power factors in $ ext{Z}_k$ parafermion quantum dots can reliably distinguish topological orders of fractional quantum Hall states, especially through sensitivity to neutral modes, aiding experimental identification.

Contribution

It introduces a conformal field theory-based method to analyze thermoelectric properties, highlighting the power factor as a sensitive signature for topological order differentiation in quantum Hall states.

Findings

Power factors are more sensitive to neutral modes than conductance peaks.

Smaller $r=v_n/v_c$ leads to greater asymmetries in power factors.

Complete profiles for $ ext{Z}_3$ and $ ext{Z}_4$ states are provided for experimental comparison.

Abstract

Using the conformal field theory approach to the thermoelectric characteristics of fractional quantum Hall states, previously developed in Nucl. Phys. B 894 (2015) 284, we show that the thermoelectric power factor of Coulomb-blockaded islands, realized by point contacts in Fabry--P\'erot interferometers in the $\mathbb{Z}_k$ parafermion Hall states, could give reliable signatures for distinguishing the topological orders of different quantum Hall states having identical electric properties. For example, while the conductance peak patterns in the Coulomb blockade regime for such states are practically indistinguishable for $v_n \ll v_c$ even at finite temperature, where $v_n$ and $v_c$ are the Fermi velocities of the neutral and charged modes respectively, the power factors $\mathcal{P}_T$ of the corresponding states are much more sensitive to the neutral modes. In particular, the smaller $r=v_n/v_c$ the bigger the asymmetries in the power factor which combined with the thermal broadening of the conductance peaks due to the neutral modes' multiplicities could give us the ultimate tool to figure out which of the competing quantum Hall universality classes are indeed realized in the experiments. We give a complete description of the power factor profiles in the $\mathbb{Z}_3$ and $\mathbb{Z}_4$ parafermion states with arbitrary number of quasiparticles localized in the bulk which could be useful for comparison with the experiments.