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.
Highlights
Electron-electron (e-e) interactions assume a cardinal role in solid-state physics
While not affecting mobility due to conservation of total system momentum, in device geometries constructed using twodimensional electron systems (2DESs) strong MC scattering leads to hydrodynamic phenomena such as vortices[1,2,3,4,5,6,7,8,9,10,11,12,13,14]
We present transverse magnetic focusing (TMF) as a sensitive technique for the measurement of the MC scattering length (‘MC) in a 2DES, which for a circular Fermi surface is equivalent to τMC
Summary
The effect of the RHS of Eq (3) is a thermalization of carriers to local stationary and drifting Fermi-Dirac distributions, f and f This is implemented using a dual relaxation time approximation with scattering length scales ‘MR and ‘MC. We show later that the exceptionally long ‘MR in our 2DES has a minimal effect on the TMF spectra and that the effect of Fermi surface smearing on. Current vortices accompany these cyclotron orbits, even in the absence of all microscopic interactions This observation reinforces the existence of collective phenomena in the ballistic transport regime, as highlighted in recent work[9,10,11]. The ballistic regime exhibits multiple vortices of various scales and at various locations in the device even in the absence of electron–electron interactions (see left panel of Fig. 1e and Supplementary Fig. 4), while the dominance of electron–electron scattering in the hydrodynamic regime favors large device-scale vortices
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