# Theory of electron spin resonance in one-dimensional topological insulators with spin-orbit couplings

## TL;DR

This paper investigates how spin-orbit coupling and next-nearest neighbor hopping influence the electron spin resonance spectrum of edge states in a one-dimensional topological insulator, providing analytical and numerical insights.

## Contribution

It introduces a generalized SSH model with NNN hopping and spin-orbit coupling, deriving an analytical formula for ESR frequency shifts caused by these effects.

## Key findings

- ESR spectrum unaffected by spin-orbit coupling without NNN hopping due to chiral symmetry
- Presence of NNN hopping and spin-orbit coupling causes a nontrivial ESR frequency shift
- Analytical formula for ESR shift matches numerical calculations

## Abstract

Edge/surface states often appear in a topologically nontrivial phase, when the system has a boundary. The edge state of a one-dimensional topological insulator is one of the simplest examples. Electron Spin Resonance (ESR) is an ideal probe to detect and analyze the edge state for its high sensitivity and precision. We consider ESR of the edge state of a generalized Su-Schrieffer-Heeger model with a next-nearest neighbor (NNN) hopping and a staggered spin-orbit coupling. The spin-orbit coupling is generally expected to bring about nontrivial changes on the ESR spectrum. Nevertheless, in the absence of the NNN hoppings, we find that the ESR spectrum is unaffected by the spin-orbit coupling thanks to the chiral symmetry. In the presence of both the NNN hopping and the spin-orbit coupling, on the other hand, the edge ESR spectrum exhibits a nontrivial frequency shift. We derive an explicit analytical formula for the ESR shift in the second order perturbation theory, which agrees very well with a non-perturbative numerical calculation.