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

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.

Revised version

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• Acoustically Induced Giant Synthetic Hall Voltages in Graphene
• Topological edge states on time-periodically strained armchair graphene nanoribbons
• Dynamical band gap tuning in Weyl semi-metals by intense elliptically polarized normal illumination and its application to $8-Pmmn$ borophene
• Dynamic local strain in graphene generated by surface acoustic waves
• Dimensionality-driven photoproduction of massive Dirac pairs near threshold in gapped graphene monolayers
• Band Gaps and Wavefunctions of Electrons Coupled to Pseudo Electromagnetic Waves in Rippled Graphene