Understanding electron behavior in strained graphene as a reciprocal space distortion

Abstract

The behavior of electrons in strained graphene is usually described using effective pseudomagnetic fields in a Dirac equation. Here we consider the particular case of a spatially constant strain. Our results indicate that lattice corrections are easily understood using a strained reciprocal space, in which the whole energy dispersion is simply shifted and deformed. This leads to a directional-dependent Fermi velocity without producing pseudomagnetic fields. The corrections due to atomic wave function overlap changes tend to compensate such effects. Also, the analytical expressions for the shift of the Dirac points, which do not coincide with the $K$ points of the renormalized reciprocal lattice, as well as the corresponding Dirac equation are found. In view of the former results, we discuss the range of applicability of the usual approach of considering pseudomagnetic fields in a Dirac equation derived from the old Dirac points of the unstrained lattice or around the $K$ points of the renormalized reciprocal lattice. Such considerations are important if a comparison is desired with experiments or numerical simulations.