Coupled edge states in topological domain walls: Creating anti-chirality in graphene

Topological matter exhibits unique phenomena such as robust topological edge states (TES) that decay exponentially into the bulk of a material. The interfaces between two inequivalent topological domains are known as topological domain walls (TDWs) [1]. Edge states in TDWs aim to achieve topologically protected localization away from the physical edges of the material. Recent studies have demonstrated the existence of currents that propagate exclusively through topologically protected states along TDWs of arbitrary shapes, even in the presence of bulk states [2].

It is essential to consider that TES from two adjacent domains lie close enough to each other to couple, modifying their energy spectrum. We address this issue by modeling infinite graphene nanoribbons in the quantum Hall regime with TDWs that are parallel to the physical edges of the system. The resulting band structures reveal that the edge states near the TDWs couple to each other. Our results show that the coupled TES produce anti-chirality and local currents with valley polarization. These findings show the potential of TDW-induced localization for the design of low-dimensional electronic circuits.

[1] K. Yasuda, et al., Science 358 (2017) 1311

[2] S. Yin, et al., Science Bulletin 69, (2024) 1660