Valley currents and non-local resistances of graphene nanostructures with broken inversion symmetry from the perspective of scattering theory

TL;DR

This paper theoretically investigates valley currents and non-local resistances in graphene nanostructures with broken inversion symmetry, revealing strong valley currents and enhanced non-local resistance in the tunneling regime, independent of Berry curvature effects.

Contribution

It introduces a scattering theory approach to analyze valley currents and non-local resistances, highlighting the impact of inversion symmetry breaking in graphene nanostructures.

Findings

Valley currents are significantly enhanced in the tunneling regime.

Non-local resistance is strongly increased due to inversion symmetry breaking.

Enhanced non-local resistance is not necessarily linked to valley currents from Berry curvature.

Abstract

Valley currents and non-local resistances of graphene nanostructures with broken inversion symmetry are considered theoretically in the linear response regime. Scattering state wave functions of electrons entering the nanostructure from the contacts represented by groups of ideal leads are calculated by solving the Lippmann- Schwinger equation and are projected onto the valley state subspaces to obtain the valley velocity fields and total valley currents in the nanostructures. In the tunneling regime when the Fermi energy is in the spectral gap around the Dirac point energy, inversion symmetry breaking is found to result in strong enhancement of the nonlocal 4 terminal Buttiker-Landauer resistance and in valley currents several times stronger than the conventional electric current. These strong valley currents are the direct result of the injection of electrons from a contact into the graphene in the tunneling regime. They are chiral and occur near contacts from which electrons are injected into the nanostructure whether or not a net electric current flows through the contact. It is also pointed out that enhanced non-local resistances in the linear response regime are not a signature of valley currents arising from the combined effect of the electric field and Berry curvature on the velocities of electrons.