Valley focusing effect in a rippled graphene superlattice

TL;DR

This paper demonstrates that a rippled graphene superlattice can induce valley-dependent electron focusing effects through surface curvature-induced hybridization, without external fields, enabling control over electron trajectories.

Contribution

It introduces a novel method to achieve valley-dependent focusing in graphene using a periodically rippled superlattice, exploiting curvature-induced orbital hybridization.

Findings

Valley focusing effects can be controlled by superlattice element number.

Surface curvature influences electron momentum distribution.

Valley selectivity occurs without external electric or magnetic fields.

Abstract

Graphene corrugations affect hybridization of $\pi$ and $\sigma$ orbitals of carbon atoms in graphene based systems. It can as well break differently the symmetry of the electron transfer integrals for different strip boundaries. Using these facts, we found that the momentum distribution of electrons in ballistically propagating beam can be selective without external electric and/or magnetic fields in the graphene strip under experimentally feasible periodic potential. Such a potential is created by means of the superlattice that consists of periodically repeated graphene elements (flat+rippled junction) with different hybridization of carbon orbits, produced by variation of the graphene surface curvature. As a result it gives rise to the valley dependent focusing effects that can be controlled by alteration of number of superlattice elements.