Full counting statistics of chiral Luttinger liquids with impurities

TL;DR

This paper develops a method to compute charge transfer statistics in chiral Luttinger liquids with impurities, revealing how the third cumulant can measure fractional charge at higher temperatures than traditional methods.

Contribution

It introduces an integrability-based procedure for calculating the cumulant generating function in chiral Luttinger liquids with impurities, focusing on the third cumulant's role in fractional charge detection.

Findings

Third cumulant C_3 varies with voltage, temperature, and barrier height.

C_3 can measure fractional charge at higher temperatures than second cumulant.

Identifies the component of C_3 that encodes fractional charge information.

Abstract

We study the statistics of charge transfer through an impurity in a chiral Luttinger liquid (realized experimentally as a quantum point contact in a fractional quantum Hall edge state device). Taking advantage of the integrability we present a procedure for obtaining the cumulant generating function of the probability distribution to transfer a fixed amount of charge through the constriction. Using this approach we analyze in detail the behaviour of the third cumulant C_3 as a function of applied voltage, temperature and barrier height. We predict that C_3 can be used to measure the fractional charge at temperatures, which are several orders of magnitude higher than those needed to extract the fractional charge from the measurement of the second cumulant. Moreover, we identify the component of C_3, which carries the information about the fractional charge.