Influence of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>e</mml:mi></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>e</mml:mi></mml:math>scattering on the temperature dependence of the resistance of a classical ballistic point contact in a two-dimensional electron system

Abstract

We experimentally investigate the temperature ($T$) dependence of the resistance of a classical ballistic point contact (PC) in a two-dimensional electron system (2DES). The split-gate PC is realized in a high-quality AlGaAs/GaAs heterostructure. The PC resistance is found to drop by more than 10$%$ as $T$ is raised from 0.5 K to 4.2 K. In the absence of a magnetic field, the $T$ dependence is roughly linear below 2 K and tends to saturate at higher $T$. Perpendicular magnetic fields on the order of a few 10 mT suppress the $T$-dependent contribution $\ensuremath{\delta}R$. This effect is more pronounced at lower temperatures, causing a crossover to a nearly parabolic $T$ dependence in a magnetic field. The normalized magnetic field dependencies $\ensuremath{\delta}R(B)$ permit an empiric single parameter scaling in a wide range of PC gate voltages. These observations give strong evidence for the influence of electron-electron ($e$-$e$) scattering on the resistance of ballistic PCs. Our results are in qualitative agreement with a recent theory of the $e$-$e$ scattering based $T$ dependence of the conductance of classical ballistic PCs [Phys. Rev. Lett. 101, 216807 (2008) and Phys. Rev. B 81, 125316 (2010)].