A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields

TL;DR

This paper develops a semiclassical framework to analyze spinor topological effects in driven, inhomogeneous insulators, linking spin transport phenomena to geometric and topological invariants in higher-dimensional phase space.

Contribution

It introduces a semiclassical method for spinor degrees of freedom in driven insulators, connecting spin responses to topological invariants and multipole moments.

Findings

Derived spin current and density up to third order in modulations.

Linked spin responses to spin-Chern fluxes and topological numbers.

Validated results with analytical calculations in tight-binding models.

Abstract

Introducing internal degrees of freedom in the description of topological insulators has led to a myriad of theoretical and experimental advances. Of particular interest are the effects of periodic perturbations, either in time or space, as they considerably enrich the variety of electronic responses, with examples such as Thouless's charge pump and its higher dimensional cousins, or, higher-order topological insulators. Here, we develop a semiclassical approach to transport and accumulation of general spinor degrees of freedom, such as physical spin, valley, or atomic orbits, in adiabatically driven, weakly inhomogeneous insulators of dimensions one, two and three under external electromagnetic fields. Specifically, we focus on physical spins and derive the spin current and density up to third order in the spatio-temporal modulations of the system. We, then, relate these contributions to geometrical and topological objects -- the spin-Chern fluxes and numbers -- defined over the higher-dimensional phase-space of the system, i.e., its combined momentum-position-time coordinates. Furthermore, we provide a connection between our semiclassical analysis and the modern theory of multipole moments by introducing spin analogues of the electric dipole, quadrupole and octapole moments. The results are showcased in concrete tight-binding models where the induced responses are calculated analytically.