# Precision measurement of electron-electron scattering in GaAs/AlGaAs using transverse magnetic focusing

## TL;DR

This paper introduces a precise method using transverse magnetic focusing to measure electron-electron scattering lengths in high-mobility GaAs/AlGaAs systems, revealing their temperature dependence and the impact on transport phenomena.

## Contribution

It demonstrates that TMF can accurately quantify e-e scattering lengths and shows their dominant role in limiting TMF amplitudes in high-mobility materials.

## Key findings

- TMF amplitude decays exponentially with e-e scattering length
- E-e scattering length varies with temperature in GaAs/AlGaAs
- Current vortices are observed alongside cyclotron orbits

## Abstract

Electron-electron (e-e) interactions assume a cardinal role in solid-state physics. Quantifying the e-e scattering length is hence critical. In this paper we show that the mesoscopic phenomenon of transverse magnetic focusing (TMF) in two-dimensional electron systems forms a precise and sensitive technique to measure this length scale. Conversely we quantitatively demonstrate that e-e scattering is the predominant effect limiting TMF amplitudes in high-mobility materials. Using high-resolution kinetic simulations, we show that the TMF amplitude at a maximum decays exponentially as a function of the e-e scattering length, which leads to a ready approach to extract this length from the measured TMF amplitudes. The approach is applied to measure the temperature-dependent e-e scattering length in high-mobility GaAs/AlGaAs heterostructures. The simulations further reveal current vortices that accompany the cyclotron orbits - a collective phenomenon counterintuitive to the ballistic transport underlying a TMF setting.

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Source: https://tomesphere.com/paper/1907.00836