Universal spatial correlations in random spinor fields

TL;DR

This paper uncovers universal spatial fluctuations in spinor fields within 2D electron gases with spin-orbit interaction, demonstrating that certain correlations are system-independent and can be explained via linear response theory.

Contribution

The study identifies and numerically verifies universal spatial correlations in spinor fields, linking them to response functions and extending understanding of spin dynamics in condensed matter systems.

Findings

Numerical results match universal spatial correlation predictions.

Correlations are system-independent and valid both in bulk and near boundaries.

A theoretical identity relates these correlations to linear response functions.

Abstract

We identify universal spatial fluctuations in systems with non trivial spin dynamics. To this end we calculate by exact numerical diagonalization a variety of experimentally relevant correlations between spinor amplitudes, spin polarizations and spin currents both in the bulk and near the boundary of a confined two-dimensional clean electron gas in the presence of spin-orbit interaction and a single magnetic impurity. We support or claim of universality with the excellent agreement between the numerical results and system-independent spatial correlations of a random field defined on both the spatial and spin degrees of freedom. A rigorous identity relating our universal predictions with response functions provides a direct physical interpretation of our results in the framework of linear response theory.