Chiral persistent currents and magnetic susceptibilities in the parafermion quantum Hall states in the second Landau level with Aharonov-Bohm flux

TL;DR

This paper uses conformal field theory to analyze chiral persistent currents and magnetic susceptibilities in parafermion quantum Hall states, revealing universal decay behaviors and the importance of neutral sector contributions.

Contribution

It introduces a compact scheme for computing flux periodicity and temperature dependence of persistent currents in Z_k parafermion quantum Hall states, highlighting the role of non-holomorphic factors.

Findings

Persistent currents are periodic with one flux quantum.

Currents exhibit diamagnetic behavior.

Amplitudes decay exponentially at high temperatures.

Abstract

Using the effective conformal field theory for the quantum Hall edge states we propose a compact and convenient scheme for the computation of the periods, amplitudes and temperature behavior of the chiral persistent currents and the magnetic susceptibilities in the mesoscopic disk version of the Z_k parafermion quantum Hall states in the second Landau level. Our numerical calculations show that the persistent currents are periodic in the Aharonov-Bohm flux with period exactly one flux quantum and have a diamagnetic nature. In the high-temperature regime their amplitudes decay exponentially with increasing the temperature and the corresponding exponents are universal characteristics of non-Fermi liquids. Our theoretical results for these exponents are in perfect agreement with those extracted from the numerical data and demonstrate that there is in general a non-trivial contribution coming from the neutral sector. We emphasize the crucial role of the non-holomorphic factors, first proposed by Cappelli and Zemba in the context of the conformal field theory partition functions for the quantum Hall states, which ensure the invariance of the annulus partition function under the Laughlin spectral flow.