Photo-assisted shot noise probes multiple charge carriers in quantum Hall edges

TL;DR

This paper demonstrates that photo-assisted shot noise can effectively detect multiple charge carriers tunneling in fractional quantum Hall states, even under challenging experimental conditions.

Contribution

It introduces a formalism for using PASN to identify different tunneling charges in hierarchical quantum Hall states, especially for the $ u=2/3$ state.

Findings

PASN can distinguish different tunneling charges even with unequal tunneling amplitudes.

Features of PASN are observable at realistic experimental temperatures and frequencies.

The formalism applies broadly to Abelian quantum Hall systems with multiple edge modes.

Abstract

Fractional charges in the fractional quantum Hall effect were first observed via DC shot noise measurements of anyons tunneling at a quantum point contact (QPC). However, in scenarios with simultaneous tunneling of different types of charges at the QPC, the connection between DC shot noise and tunneling charge is less transparent. Photo-assisted shot noise (PASN), induced by periodic AC voltage, offers a promising alternative. Here, we investigate PASN in the hierarchical states of the fractional quantum Hall effect, where different types of charges are expected to tunnel concurrently at QPCs. In the particular case of the fractional quantum Hall state $\nu = 2/3$, our analysis demonstrates that PASN can be employed as a robust tool to detect different tunneling charges, even when the tunneling amplitude of one type is significantly smaller compared to the other. We show that the features predicted by our calculations are still visible for typical values of temperature and frequency achieved in state-of-the-art experiments. Our general formalism can be used to compute PASN for general Abelian quantum Hall systems with multiple edge modes and charge types.