Understanding electron behavior in strained graphene as a reciprocal space distortion

TL;DR

This paper investigates how uniform strain affects electron behavior in graphene by analyzing reciprocal space distortions, revealing shifts in energy dispersion and Fermi velocity without pseudomagnetic fields, and clarifying the limits of existing models.

Contribution

It provides analytical expressions for Dirac point shifts and the Dirac equation under strain, offering a clearer understanding of lattice corrections in strained graphene.

Findings

Reciprocal space distortion explains energy dispersion shifts.

Fermi velocity becomes direction-dependent under strain.

Pseudomagnetic fields are not produced by uniform strain.

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 wavefunction overlap changes tend to compensate such effects. Also, the analytical expressions for the shift of the Dirac points 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. Such considerations are important if a comparison is desired with experiments or numerical simulations.