Dispersive Landau levels and valley currents in strained graphene nanoribbons

TL;DR

This paper proposes a simple method to generate pure valley currents in strained graphene nanoribbons using uniaxial strain, leading to dispersive pseudo-Landau levels and controllable valley transport without charge flow.

Contribution

It introduces a novel setup for valley current generation in graphene nanoribbons via strain-induced pseudo-magnetic fields and analyzes the resulting dispersive Landau levels and valley transport properties.

Findings

Valley currents can be controlled by strain magnitude and bias voltages.

Pseudo-Landau levels are dispersive with opposite slopes in two valleys.

Charge pumping between valleys demonstrates a valley chiral anomaly.

Abstract

We describe a simple setup generating pure valley currents -- valley transport without charge transport -- in strained graphene nanoribbons with zigzag edges. The crucial ingredient is a uniaxial strain pattern which couples to the low-energy Dirac electrons as a uniform pseudomagnetic field. Remarkably, the resulting pseudo-Landau levels are not flat but disperse linearly from the Dirac points, with an opposite slope in the two valleys. We show how this is a natural consequence of an inhomogeneous Fermi velocity arising in the low-energy theory describing the system, which maps to an exactly-solvable singular Sturm-Liouville problem. The velocity of the valley currents can be controlled by tuning the magnitude of strain and by applying bias voltages across the ribbon. Furthermore, applying an electric field along the ribbon leads to pumping of charge carriers between the two valleys, realizing a valley analog of the chiral anomaly in one spatial dimension. These effects produce unique signatures that can be observed experimentally by performing ordinary charge transport measurements and spectroscopy.