Anatomy of Spin and Current Generation from Magnetization Gradients in Topological Insulators and Rashba Metals

TL;DR

This paper investigates how magnetization gradients generate spin and charge currents on the surfaces of topological insulators and Rashba metals, revealing quantized responses and their implications for topological states and superconducting phenomena.

Contribution

It uncovers a quantized interconversion coefficient in topological insulators linked to the parity anomaly and contrasts it with Rashba metals, highlighting their different responses to magnetization gradients.

Findings

Quantized interconversion coefficient in topological insulators proportional to Dirac point vorticity.

Rashba metals exhibit non-protected, discontinuous responses to magnetization gradients.

Implications for magnetic skyrmions, Majorana modes, and superconducting diode effects.

Abstract

We explore the spin density and charge currents arising on the surface of a topological insulator and in a 2D Rashba metal due to magnetization gradients. For topological insulators a single interconversion coefficient controls the generation of both quantities. This coefficient is quantized to a value proportional to the vorticity of the Dirac point which constitutes a hallmark of parity anomaly at finite density. As such, it also unveils a robust route to disentangle and detect the protected states of a topological insulator on a given surface. In stark contrast, Rashba metals do not exhibit such anomalies since they contain an even number of helical branches. Nonetheless, also these are governed by quantized responses which, however, are not protected against weak disorder. Furthermore, we find that for Rashba metals the interconversion coefficients demonstrate discontinuities and a nontrivial interplay upon varying the chemical potential, the strength of the spin-orbit coupling, and a pairing gap. Our results have implications for the binding between magnetic skyrmions and superconducting vortices, the emergence of Majorana zero modes, and pave the way for superconducting diode effects mediated by out-of-plane magnetization gradients.