# Spin-orbit interaction and snake states in graphene $p$-$n$ junctions

## TL;DR

This paper investigates spin-orbit interactions and snake states in graphene p-n junctions under magnetic fields, revealing zero modes with spin polarization and interference effects useful for spintronic devices.

## Contribution

It provides an exact spectrum analysis of spin-resolved Landau levels and identifies wave-vector-dependent zero modes as quantum snake states influenced by Rashba spin-orbit interaction.

## Key findings

- Discovery of linearly dispersing zero modes with spin polarization
- Rashba spin-orbit interaction causes observable wave vector shifts
- Potential application in spin field-effect transistors

## Abstract

We study a model of a $p$-$n$ junction in single-layer graphene in the presence of a perpendicular magnetic field and spin-orbit interactions. By solving the relevant quantum-mechanical problem for a potential step, we determine the exact spectrum of spin-resolved dispersive Landau levels. Close to zero energy, we find a pair of linearly dispersing zero modes, which possess a wave-vector-dependent spin polarization and can be regarded as quantum analogous of spinful snake states. We show that the Rashba spin-orbit interaction, in particular, produces a wave vector shift between the dispersions of these modes with observable interference effects. These effects can in principle provide a way to detect the presence of Rashba spin-orbit interaction and measure its strength. Our results suggest that a graphene $p$-$n$ junction in the presence of strong spin-orbit interaction could be used as a building block in a spin field-effect transistor.