Valley-momentum locking in a graphene superlattice with Y-shaped Kekul\'e bond texture

TL;DR

This paper investigates how a Y-shaped Kekul'e bond texture in a graphene superlattice leads to valley-momentum locking, resulting in unique Landau level degeneracy properties under magnetic fields.

Contribution

It demonstrates that the Kek-Y texture creates valley-momentum locking and analyzes its effects on Landau levels and degeneracy in a graphene superlattice.

Findings

Y-shaped Kekul'e texture induces valley-momentum locking.

Valley degeneracy is lifted in magnetic fields except for a zero-mode.

Zero-mode remains valley-degenerate and independent of magnetic field.

Abstract

Recent experiments by Guti\'errez $\textit{et al.}$ [Nature Phys. $\textbf{12}$, 950 (2016)] on a graphene-copper superlattice have revealed an unusual Kekul\'e bond texture in the honeycomb lattice --- a Y-shaped modulation of weak and strong bonds with a wave vector connecting two Dirac points. We show that this so-called "Kek-Y" texture produces two species of massless Dirac fermions, with valley isospin locked parallel or antiparallel to the direction of motion. In a magnetic field $B$ the valley degeneracy of the $B$-dependent Landau levels is removed by the valley-momentum locking --- but a $B$-independent and valley-degenerate zero-mode remains.