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

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.