Sound waves induce Volkov-like states, band structure and collimation effect in graphene

TL;DR

This paper demonstrates that sound waves in graphene can create band structure modifications and collimation effects by inducing Volkov-like states, revealing new ways to control electron behavior with mechanical vibrations.

Contribution

It introduces a novel theoretical approach to describe graphene quasiparticles under dynamic strain using Volkov-like solutions, revealing band warping and collimation effects.

Findings

Sound waves induce band warping in graphene's Dirac cones.

Strain waves cause electron collimation effects.

The spectrum is governed by Mathieu equation solutions.

Abstract

We find exact states of graphene quasiparticles under a time-dependent deformation (sound wave), whose propagation velocity is smaller than the Fermi velocity. To solve the corresponding effective Dirac equation, we adapt the Volkov-like solutions for relativistic fermions in a medium under a plane electromagnetic wave. The corresponding electron-deformation quasiparticle spectrum is determined by the solutions of a Mathieu equation resulting in band tongues warped in the surface of the Dirac cones. This leads to a collimation effect of electron conduction due to strain waves.