Non-equilibrium noise in the (non-)Abelian fractional quantum Hall effect

TL;DR

This paper investigates the non-equilibrium noise characteristics of edge currents in fractional quantum Hall systems, revealing a non-equilibrium fluctuation-dissipation relation influenced by tunnelling current correlations.

Contribution

It introduces a non-equilibrium fluctuation-dissipation theorem for fractional quantum Hall edge states, incorporating non-Abelian and multi-channel effects using Ward identities and Kubo formulas.

Findings

Derived a non-equilibrium fluctuation-dissipation relation for edge noise.

Identified the correction term linked to tunnelling and edge current correlations.

Applicable to generic edge theories, including non-Abelian states.

Abstract

We analyse the noise of the edge current of a generic fractional quantum Hall state in a tunnelling point contact system. We show that the non-symmetrized noise in the edge current for the system out-of-equilibrium is completely determined by the noise in the tunnelling current and the Nyquist-Johnson (equilibrium) noise of the edge current. Simply put, the noise in the tunnelling current does not simply add up the equilibrium noise of the edge current. A correction term arises associated with the correlation between the tunnelling current and the edge current. We show, using a non-equilibrium Ward identity, that this correction term is determined by the anti-symmetric part of the noise in the tunnelling current. This leads to a non-equilibrium fluctuation-dissipation theorem and related expressions for the excess and shot noise of the noise in the edge current. Our approach makes use of simple properties of the edge, such as charge conservation and chirality, and applies to generic constructions of the edge theory which includes edges of non-Abelian states and edges with multiple charged channels. Two important tools we make use of are the non-equilibrium Kubo formula and the non-equilibrium Ward identity. We discuss these identities in the appendix.