Hydrodynamic and Ballistic Transport over Large Length Scales in GaAs/AlGaAs

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

“…The methods and transport properties are described in Supplementary Notes 1 and 2 . Experiments were performed on multiprobe Hall mesas in three devices—Device1, Device2, and Device3 11 bearing numerous in-line TMF geometries with L c ranging from 7–10.5 μm in Device1, 3–15 μm in Device2, and 1.3–20.5 μm in Device3 (Fig. 1a–c ).…”

“…We simulate magnetotransport in the actual experimental device geometry using BOLT, a high-resolution solver for kinetic theories 9 , 11 , 37 , which solves the Boltzmann transport equation: where f ( x , p , t ) is the probability distribution of electrons along the spatial coordinates x ≡ ( x , y ) and momentum coordinates , where θ denotes the angle on the Fermi surface, t denotes time, and v F denotes the Fermi velocity. The Lorentz force due to B appears in the third term on the left, which for a circular Fermi surface simplifies to the form shown.…”

“…However, direct measurements of τ MC have been more elusive, only so far achieved at lower temperature T (≲4 K) by loss of quantum interference 19 – 21 , tunneling measurements 22 , or scattering measurements 23 , 24 . At higher T ≳ 4 K, the effect of MC scattering is to impose a local thermal equilibrium, and here experimental measurements of τ MC have only recently been enabled by the hydrodynamic transport regime 11 , 25 .…”

“…We present transverse magnetic focusing (TMF) as a sensitive technique for the measurement of the MC scattering length ( ) in a 2DES, which for a circular Fermi surface is equivalent to τ MC . The 2DES is hosted by an ultraclean GaAs/AlGaAs heterostructure grown by optimized MBE process, and is well-suited for this study because the very long momentum-relaxing (MR) scattering length ( mobility mean-free path ≃ 65 μm at T = 4.2 K) provides high sensitivity to MC scattering 11 . MR scattering (mediated by lattice defects and phonons) is responsible for dissipation of the system’s momentum to the lattice.…”

“…A collective phenomenon such as vortices being observed in a TMF setting, which is widely regarded as a purely ballistic experiment, is counterintuitive. Yet, at B = 0 it has been shown both theoretically and experimentally that even ballistic dynamics can lead to collective phenomena 9 – 11 . Here we show additional evidence in the presence of B .…”