Pseudogauge field driven acoustoelectric current in two-dimensional hexagonal Dirac materials

Pankaj Bhalla,Habib Rostami,Giovanni Vignale

doi:10.1103/physrevb.105.125407

Abstract

Using a diagrammatic scheme, we study the acoustoelectric effects in two-dimensional (2D) hexagonal Dirac materials due to the sound-induced pseudogauge field. We analyze both uniform and spatially dispersive currents in response to copropagating and counterpropagating sound waves, respectively. In addition to the longitudinal acoustoelectric current, we obtain an exotic transverse charge current flowing perpendicular to the sound propagation direction owing to the interplay of transverse and longitudinal gauge field components ${j}_{T}\ensuremath{\propto}{A}_{L}{A}_{T}^{*}$. In contrast to the almost isotropic directional profile of the longitudinal uniform current, a highly anisotropic transverse component ${j}_{T}\ensuremath{\sim}sin(6\ensuremath{\theta})$ is achieved that stems from the inherited threefold symmetry of the hexagonal lattice. However, both longitudinal and transverse parts of the dispersive current are predicted to be strongly anisotropic $\ensuremath{\sim}{sin}^{2}(3\ensuremath{\theta})$ or ${cos}^{2}(3\ensuremath{\theta})$. We quantitatively estimate the pseudogauge field contribution to the acoustoelectric current that can be probed in future experiments in graphene and other 2D hexagonal Dirac materials.

Highlights

The passage of a sound wave through an electronic system creates an oscillating electric field which accelerates the charge carriers and generates an electric current
VF is the Fermi velocity, p is the momentum of an electron, σi refers to the Pauli matrices, and V = D(uxx + uyy ) + PuL is a scalar deformation potential that describes the coupling of acoustic phonons to electrons in 2D hexagonal Dirac materials, such as graphene, where ui j = (∂iu j + ∂ jui + ∂ih∂ jh)/2 stands for the strain tensor components in terms of the displacement vector u = having h ≡ uz as the normal component of the displacement
The longitudinal AG current is the sum of two contributions j1 cos2(3θ ) and j2 sin2(3θ ), while the transverse one scales as j3 sin(6θ ). (ii) The j1 contribution stands for the longitudinal AG current that is driven by the longitudinal pseudogauge field

Summary

Introduction

The passage of a sound wave through an electronic system creates an oscillating electric field which accelerates the charge carriers and generates an electric current. The acoustoelectric effect (AE) is the dc current that arises to second order in the sound-induced electric field. This intriguing nonlinear phenomenon was first predicted by Parmenter [1] and later discussed by Weinreich [2]. It has been recognized that the coupling between the surface acoustic wave (SAW) and electrons in 2D Dirac materials provides an exciting opportunity to investigate charge transport driven by the strain fields associated with the propagating SAW [12–19]. The AE effect of single-layer graphene has been investigated experimentally, and the AE current has been shown to be tunable by the application of a gate voltage [18]

Methods

Results

Conclusion