Valley splitter and transverse valley focusing in twisted bilayer graphene

TL;DR

This paper demonstrates how electrostatic barriers in twisted bilayer graphene can act as valley splitters and induce valley-selective transverse focusing, revealing new control mechanisms for valleytronics.

Contribution

It introduces a method to achieve valley splitting and focusing in twisted bilayer graphene using electrostatic barriers and Lifshitz transitions.

Findings

Electrostatic barriers can selectively transmit electrons from different valleys to specific layers.

Valley-dependent transverse deflections lead to valley-selective focusing at zero magnetic field.

A Lifshitz transition across the junction is key to valley splitting.

Abstract

We study transport in twisted bilayer graphene and show that electrostatic barriers can act as valley splitters, where electrons from the $K$ ($K'$) valley are transmitted only to e.g.\ the top (bottom) layer, leading to valley-layer locked currents. We show that such a valley splitter is obtained when the barrier varies slowly on the moir\'e scale and induces a Lifshitz transition across the junction, i.e.\ a change in the Fermi surface topology. Furthermore, we show that for a given valley the reflected and transmitted current are transversely deflected, as time-reversal symmetry is effectively broken in each valley separately, resulting in valley-selective transverse focusing at zero magnetic field.