# Universality of low-energy Rashba scattering

## TL;DR

This paper demonstrates that low-energy Rashba scattering exhibits universal features such as potential-range independence and anisotropic cross sections, applicable to various circularly symmetric, spin-independent, finite-range potentials.

## Contribution

It proves the universality of low-energy Rashba scattering behavior for any circularly symmetric, spin-independent, finite-range potential using a nonperturbative T-matrix approach.

## Key findings

- Low-energy Rashba scattering features are potential-range independent.
- All partial waves contribute equally near the van Hove singularity.
- Total cross section exhibits quantized plateaus.

## Abstract

We investigate the scattering of a quantum particle with a two-dimensional (2D) Rashba spin-orbit coupled dispersion off of circularly symmetric potentials. As the energy of the particle approaches the bottom of the lowest spin-split band, i.e., the van Hove singularity, earlier work has shown that scattering off of an infinite circular barrier exhibits a number of features unusual from the point of view of conventional 2D scattering theory: the low-energy S-matrix is independent of the range of the potential, all partial waves contribute equally, the differential cross section becomes increasingly anisotropic and 1D-like, and the total cross section exhibits quantized plateaus. Via a nonperturbative determination of the T-matrix and an optical theorem which we prove here, we show that this behavior is universal for Rashba scattering off of any circularly symmetric, spin independent, finite-range potential. This is relevant both for impurity scattering in the noninteracting limit as well as for short-range two-particle scattering in the interacting problem.