2018/04/27 by T. Kikuchi, Kikuchi, Toru
Physics and Astronomy · #FOS: Physical sciences #Magnetic properties of thin films #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum and electron transport phenomena #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.1804.10613
openalex publication_date 2018/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a basic theory of nonrelativistic spinful electrons on curves and surfaces. In particular, we discuss the presence and effects of spin connections, which describe how spinors and vectors couple to the geometry of curves and surfaces. We derive explicit expressions of spin connections by performing simple dimensional reduction from the three-dimensional flat space. The spin connections act on electrons as spin-dependent magnetic fields, which have been known as `pseudomagnetic fields' in the context of, e.g., graphenes and Dirac/Weyl semimetals. We propose that these spin-dependent magnetic fields are present universally on curves and surfaces, acting on electrons regardless of the kinds of their spinorial degrees of freedom and their dispersion relations. We discuss that the curvature effects via spin connections will induce the spin Hall effect and induce the Dzyaloshinskii--Moriya interactions between magnetic moments on curved surfaces, without relying on the relativistic spin-orbit couplings. We also mention the importance of spin connections on orbital physics of electrons on curved geometry.