Determination of tunneling charge via current measurements

TL;DR

This paper introduces three practical current-based methods to determine tunneling charge in various non-linear systems, including quantum Hall edges and graphene, without requiring detailed model knowledge or noise measurements.

Contribution

It proposes novel, model-independent techniques for tunneling charge detection using AC conductance and photo-assisted current, suitable for diverse systems and low-voltage regimes.

Findings

Methods are easier than noise measurements.

Applicable to fractional quantum Hall edge states.

Effective in low-voltage, low-heating conditions.

Abstract

We consider a tunnel junction between two arbitrary non-linear systems in any dimension, which can be different. We show that the tunneling charge can be detected using three alternative methods based on current measurements. Besides being technically easier compared to noise measurements, these methods present valuable advantages: they do not require the knowledge of the underlying models, and some are accessible in the experimentally convenient low-voltage regime, where heating effects are reduced. The first method is based on the AC conductance, while the two others are based on photo-assisted current (PAC) and can be implemented for any time-dependence of the tunneling amplitude. These are promising for edge states in the regime of the fractional quantum Hall effect (FQHE): the Hamiltonian does not have to be specified and can incorporate non-universal interactions between the edges, and it is more convenient to use an AC gate voltage rather than an AC bias. These methods apply for instance to weak barriers in 1-D systems, Superconductor-Insulator-Normal (SIN) or graphene-like structures.