# Valley isospin of interface states in a graphene $pn$ junction in the quantum Hall regime

## TL;DR

This paper investigates how valley isospin influences interface states and conductance in graphene $pn$ junctions under quantum Hall conditions, emphasizing the role of boundary types and isospin conservation.

## Contribution

It demonstrates that valley isospin conservation governs the evolution of edge and interface states in realistic graphene models, impacting junction conductance.

## Key findings

- Valley isospin conservation applies to armchair boundaries.
- Interface state valley isospin affects conductance.
- Electron-hole degeneracy lifting influences isospin behavior.

## Abstract

In the presence of crossed electric and magnetic fields, a graphene ribbon has chiral states running along sample edges and along boundaries between $p$-doped and $n$-doped regions. We here consider the scattering of edge states into interface states, which takes place whereever the $pn$ interface crosses the sample boundary, as well as the reverse process. For a graphene ribbon with armchair boundaries, the evolution of edge states into interface states and {\em vice versa} is governed by the conservation of valley isospin. Although valley isospin is not conserved in simplified models of a ribbon with zigzag boundaries, we find that arguments based on isospin conservation can be applied to a more realistic modeling of the graphene ribbon, which takes account of the lifting of electron-hole degeneracy. The valley isospin of interface states is an important factor determining the conductance of a graphene $pn$ junction in a quantizing magnetic field.