Transverse magnetic focusing as measurement tool for electron-electron interactions in GaAs/AlGaAs

The mesoscopic and ballistic phenomenon of transverse magnetic focusing (TMF) is investigated in a two-dimensional electron system in a high-mobility GaAs/AlGaAs heterostructure at low temperatures 0.4 K < T < 20 K (electron mean free path ~ 68 μm at 4.2 K) using precision nonlocal measurements and high-resolution kinetic simulations. Measurements feature a distance between the injector and collector of 7 μm. The measured TMF amplitude of the nonlocal resistance plotted versus T shows a monotonic decrease as T is increased from 4.2 K to 20 K. A characteristic decay length is extracted by fitting experimental data with an exponential fit, and shows a 1/T² dependence, indicating a dominant role for inelastic electron-electron interactions in limiting TMF amplitude. The simulations, which reveal both cyclotron orbits and current vortices, confirm the experimental observations and determine that the decay length relates to the momentum-conserving electron-electron scattering length. The combined experiments and simulations provide a direct way to measure the momentum-conserving scattering length in a TMF setting.