Analytical calculation of electron's group velocity surfaces in uniform strained graphene

TL;DR

This paper derives analytical expressions for electron group velocity surfaces in uniformly strained graphene, revealing anisotropic effects, symmetry breaking, and the importance of nonlinear terms near the Fermi energy.

Contribution

It provides the first closed-form analytical calculations of electron velocities in strained graphene, including nonlinear effects and symmetry considerations.

Findings

Fermi velocity becomes highly anisotropic under strain.

Dirac cones merge and Fermi velocity vanishes in one principal axis at high shear strain.

Nonlinear terms are crucial for accurate description near the Fermi energy.

Abstract

Electron group velocity for graphene under uniform strain is obtained analitically by using the Tight-Binding approx- imation. Such closed analytical expressions are useful in order to calculate electronic, thermal and optical properties of strained graphene. These results allow to understand the behavior of electrons when graphene is subjected to strong strain and nonlinear corrections, for which the usual Dirac approach is not longer valid. Some particular cases of uni- axial and shear strain were analized. The evolution of the electron group velocity indicates a break up of the trigonal warping symmetry, which is replaced by a warping consistent with the symmetry of the strained reciprocal lattice. The Fermi velocity becomes strongly anisotropic, i.e, for a strong pure shear-strain (20% of the lattice parameter), the two inequivalent Dirac cones merge and the Fermi velocity is zero in one of the principal axis of deformation. We found that non-linear terms are essential to describe the effects of deformation for electrons near or at the Fermi energy.