Rashba scattering in the low-energy limit

TL;DR

This paper investigates how Rashba spin-orbit coupling affects potential scattering in a two-dimensional electron gas at low energies, revealing universal, qualitatively distinct scattering behavior from conventional cases.

Contribution

It demonstrates that low-energy Rashba scattering exhibits universal features such as off-diagonal scattering matrices and quantized cross-section plateaus, differing from higher-energy and no-spin-orbit cases.

Findings

Scattering matrix is purely off-diagonal with equal elements

Differential cross section peaks in forward and backward directions

Total cross section shows quantized plateaus

Abstract

We study potential scattering in a two-dimensional electron gas with Rashba spin-orbit coupling in the limit that the energy of the scattering electron approaches the bottom of the lower spin-split band. Focusing on two spin-independent circularly symmetric potentials, an infinite barrier and a delta-function shell, we show that scattering in this limit is qualitatively different from both scattering in the higher spin-split band and scattering of electrons without spin-orbit coupling. The scattering matrix is purely off-diagonal with both off-diagonal elements equal to one, and all angular momentum channels contribute equally; the differential cross section becomes increasingly peaked in the forward and backward scattering directions; the total cross section exhibits quantized plateaus. These features are independent of the details of the scattering potentials, and we conjecture them to be universal. Our results suggest that Rashba scattering in the low-energy limit becomes effectively one-dimensional.