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

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.

Gate voltage dependent Rashba spin splitting in hole transverse magnetic focusing

“…Magnetic focussing is the solid state realisation of a mass spectrometer. Originally proposed as a way to measure the Fermi surface in metals, [1,2] it has subsequently been used to probe band structures in graphene, [3] spatially separate spin states, [4][5][6], extract electron-electron scattering lengths, [7] and measure spin polarisation. [4,[8][9][10][11] In 2D hole systems in GaAs, magnetic focussing has been used to measure scattering [12,13] and demonstrate spatial separation of spin.…”

Breathing mode in open-orbit magnetotransport: A magnetic lens with a quantum mechanical focal length

“…At a field of 1 T and for a lattice constant a = 0.5 nm the focal length = h/eBa ≈ 8 μm-an order of magnitude larger than in semiconductor electron-focusing experiments [29]. Magnetic focusing is an effective way to study scattering processes [30], and in clean systems a large focal length would be an advantage.…”

Hydrodynamic approach to two-dimensional electron systems

“…Hydrodynamic flow of electrons in solids should be observable not only in graphene, but in any material that is clean enough to satisfy the condition that the electron-electron scattering length is much shorter than the disorder mean free path. In particular, modern semiconductor technology allows fabricating ultra-high-mobility heterostructures [30,32,36,55,56,57], a noticeable improvement since the original observation of the Gurzhi effect [58].…”

“…For a long time such a material was not known. In recent years, several extremely pure materials became available bringing electronic hydrodynamics within experimental reach [27,28,29,30,31,32,33,34,35,36].…”