Fingerprints of a position-dependent Fermi velocity on scanning tunnelling spectra of strained graphene.

Nonuniform strain in graphene induces a position dependence of the Fermi velocity, as recently demonstrated by scanning tunnelling spectroscopy experiments. In this work, we study the effects of a position-dependent Fermi velocity on the local density of states (LDOS) of strained graphene, with and without the presence of a uniform magnetic field. The variation of LDOS obtained from tight-binding calculations is successfully explained by analytical expressions derived within the Dirac approach. These expressions also rectify a rough Fermi velocity substitution used in the literature that neglects the strain-induced anisotropy. The reported analytical results could be useful for understanding the nonuniform strain effects on scanning tunnelling spectra of graphene, as well as when it is exposed to an external magnetic field.

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

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.

Anisotropic AC conductivity of strained graphene.

The density of states and the AC conductivity of graphene under uniform strain are calculated using a new Dirac Hamiltonian that takes into account the main three ingredients that change the electronic properties of strained graphene: the real displacement of the Fermi energy, the reciprocal lattice strain and the changes in the overlap of atomic orbitals. Our simple analytical expressions for the density of states and the AC conductivity generalize previous expressions for uniaxial strain. The results suggest a way to measure the Grüneisen parameter ß that appears in any calculation of strained graphene, as well as the emergence of a sort of Hall effect due to shear strain.