Snake states and their symmetries in graphene

TL;DR

This paper explores snake states in graphene under varying magnetic fields and carrier densities, revealing their topological nature and gauge equivalence through a Nambu doubled framework, with implications for edge mode protection.

Contribution

It demonstrates the gauge equivalence of different domain wall configurations in graphene and maps snake states to p-wave paired states using a Nambu doubled formulation.

Findings

Snake states are topologically protected edge modes.

Different domain wall configurations are gauge equivalent.

Interfacial modes map to p-wave quasiparticles.

Abstract

Snake states are open trajectories for charged particles propagating in two dimensions under the influence of a spatially varying perpendicular magnetic field. In the quantum limit they are protected edge modes that separate topologically inequivalent ground states and can also occur when the particle density rather than the field is made nonuniform. We examine the correspondence of snake trajectories in single-layer graphene in the quantum limit for two families of domain walls: (a) a uniform doped carrier density in an antisymmetric field profile and (b) antisymmetric carrier distribution in a uniform field. These families support different internal symmetries but the same pattern of boundary and interface currents. We demonstrate that these physically different situations are gauge equivalent when rewritten in a Nambu doubled formulation of the two limiting problems. Using gauge transformations in particle-hole space to connect these problems, we map the protected interfacial modes to the Bogoliubov quasiparticles of an interfacial one-dimensional p-wave paired state. A variational model is introduced to interpret the interfacial solutions of both domain wall problems.