# Low-energy theory for strained graphene: an approach up to second-order in the strain tensor

## TL;DR

This paper develops a second-order low-energy theory for uniformly strained graphene, revealing anisotropic Fermi velocities, optical properties, and pseudomagnetic effects, advancing understanding of strain-induced electronic phenomena.

## Contribution

It introduces a second-order effective Dirac Hamiltonian for strained graphene, capturing trigonal symmetry and strain direction dependence absent in first-order models.

## Key findings

- Anisotropic Fermi velocity tensor derived
- Optical conductivity tensor calculated
- Dirac point shift related to pseudomagnetic fields

## Abstract

An analytical study of low-energy electronic excited states in an uniformly strained graphene is carried out up to second-order in the strain tensor. We report an new effective Dirac Hamiltonian with an anisotropic Fermi velocity tensor, which reveals the graphene trigonal symmetry being absent in low-energy theories to first-order in the strain tensor. In particular, we demonstrate the dependence of the Dirac-cone elliptical deformation on the stretching direction respect to graphene lattice orientation. We further analytically calculate the optical conductivity tensor of strained graphene and its transmittance for a linearly polarized light with normal incidence. Finally, the obtained analytical expression of the Dirac point shift allows a better determination and understanding of pseudomagnetic fields induced by nonuniform strains.