Robust propagating in-gap modes due to spin-orbit domain walls in graphene

TL;DR

This paper theoretically investigates in-gap propagating modes in graphene caused by spin-orbit domain walls, revealing robust states linked to valley-Zeeman coupling and analyzing their stability and potential experimental signatures.

Contribution

It introduces a novel analysis of spin-orbit domain walls in graphene, demonstrating the existence of robust in-gap modes using spectral flow and interface Chern number methods.

Findings

Sign-changing valley-Zeeman domain walls host robust Kramers pairs.

Rashba coupling influences the bulk gap and topological states.

Mapping to bilayer graphene domain walls suggests experimental relevance.

Abstract

Recently, great experimental efforts towards designing topological electronic states have been invested in layered incommensurate heterostructures which form various nano- and meso-scale domains. In particular, it has become clear that a delicate interplay of different spin-orbit terms is induced in graphene on transition metal dichalcogenide substrates. We therefore theoretically study various types of domain walls in spin-orbit coupling in graphene looking for robust one-dimensional propagating electronic states. To do so, we use an interface Chern number and a spectral flow analysis in the low-energy theory and contrast our results to the standard arguments based on valley-Chern numbers or Chern numbers in continuum models. Surprisingly, we find that a sign-changing domain wall in valley-Zeeman spin-orbit coupling binds two robust Kramers pairs, within the bulk gap opened due to a simultaneous presence of Rashba coupling. We also study the robustness to symmetry breaking and lattice backscattering effects in tight-binding models. We show an explicit mapping of our valley-Zeeman domain wall to a domain wall in gated spinless bilayer graphene. We discuss the possible spectroscopic and transport signatures of various types of spin-orbit coupling domain walls in heterostructures.