Channel-resolved Wavefunctions of Transverse Magnetic Focusing

Transverse magnetic focusing (TMF) can be understood as a mass spectrometer for mesoscopic systems, used to probe Fermi surfaces, quasiparticle relaxations, many-body correlations, and so on. The principal figure of these studies is the TMF spectrum, but the spectral lineshape is fundamentally difficult to predict due to competing length scales and variations of device geometry. Naturally, experimental findings often resort to much compromised theories, e.g. quasiclassical raytracing without interference or numerical simulation with weak explanatory power. Working towards a generalizable theory, here we present a comparative study of experimental and simulated TMF, where the channel-resolved contributions of the emitter has been investigated to identify channel-independent features of the TMF wavefunction. The simplest nontrivial case using spinless, quadratic dispersions and double-channel QPCs have been realized using GaAs/AlGaAs heterostructure devices with two-dimensional electron gases, and a numerical procedure based on singular value decomposition has been developed to calculate the wavefunction. From our findings, we propose that quantum TMF may have a near- and far-field regime, where the wavefunction in the near-field regime resembles the emitter mode traced along the classical trajectory and that of the far-field regime is described by the established semiclassical theory.