# Valley-Dependent Topological Interface States in Biased Armchair Nanoribbons of Gapless Single-Layer Graphene for Transport Applications

## TL;DR

This paper explores how valley-dependent topological effects in graphene can be used to create nanoscale devices with controlled electron transport.

## Contribution

The novel contribution is the demonstration of valley-polarized topological interface states in biased graphene nanoribbons for transport applications.

## Key findings

- Applying opposite electrical biases creates valley-polarized interface states in graphene nanoribbons.
- Quasi-localized states lead to Fano anti-resonances in transmission spectra.
- A band-stop electron energy filter is proposed using these topological interface states.

## Abstract

Valley-dependent topological physics offers a promising avenue for designing nanoscale devices based on gapless single-layer graphene. To demonstrate this potential, we investigate an electrical bias-controlled topological discontinuity in valley polarization within a two-segment armchair nanoribbon of gapless single-layer graphene. This discontinuity is created at the interface by applying opposite in-plane, transverse electrical biases to the two segments. An efficient tight-binding theoretical formulation is developed to calculate electron states in the structure. In a reference configuration, we obtain energy eigenvalues and probability distributions that feature interface-confined electron eigenstates induced by the topological discontinuity. Moreover, to elucidate the implications of interface confinement for electron transport, a modified configuration is introduced to transform the eigenstates into transport-active, quasi-localized ones. We show that such states result in Fano “anti-resonances” in transmission spectra. The resilience of these quasi-localized states and their associated Fano fingerprints is examined with respect to fluctuations. Finally, a proof-of-concept band-stop electron energy filter is presented, highlighting the potential of this confinement mechanism and, more broadly, valley-dependent topological physics in designing nanoscale devices in gapless single-layer graphene.