Parallel spin transport and holonomy in non-Euclidean curved circuits on a spherical two-dimensional electron gas

TL;DR

This paper investigates how curvature in spherical 2DEGs affects spin transport and interference patterns, revealing broken symmetries due to holonomy and parallel transport effects, with implications for quantum circuit design.

Contribution

It introduces the impact of non-Euclidean curvature on spin transport and interference symmetry, highlighting the role of holonomy in curved quantum circuits.

Findings

Symmetry breaks down in curved 1D circuits on spherical 2DEGs.

Parallel transport causes holonomy effects altering interference patterns.

Symmetry can be restored by considering parallel transport as an offset.

Abstract

The quantum conductance of one-dimensional (1D) circuits built on flat (Euclidean) two-dimensional electron gases (2DEGs) is known to display a symmetric response to the inversion of Rashba spin-orbit coupling fields in Aharonov-Casher (AC) interference patterns. Here, we show that this symmetry breaks down in curved (non-Euclidean) 1D circuits defined on spherical 2DEGs. We demonstrate that this is a consequence of parallel transport and holonomy of the electronic spin on the surface of the sphere, and that a symmetric response can be recovered when considering the parallel transport condition as an offset shifting the AC pattern. We discuss 1D triangular circuits defined along geodesic arcs on the sphere as a case study, and generalize it to regular polygons and parallel curves of given latitude.