Theory for Strained Graphene Beyond the Cauchy–Born Rule

Abstract

The low‐energy electronic properties of strained graphene are usually obtained by transforming the bond vectors according to the Cauchy–Born rule. In this work, we derive a new effective Dirac Hamiltonian by assuming a more general transformation rule for the bond vectors under uniform strain, which takes into account the strain‐induced relative displacement between the two sublattices of graphene. Our analytical results show that the consideration of such relative displacement yields a qualitatively different Fermi velocity with respect to previous reports. Furthermore, from the derived Hamiltonian, we analyze effects of this relative displacement on the local density of states and the optical conductivity, as well as the implications on the scanning tunneling spectroscopy, including external magnetic field, and optical transmittance experiments of strained graphene.

Photonic graphene under strain with position-dependent gain and loss

“…Supersymmetric quantum mechanics is a useful tool to find solutions of the Dirac equation under external magnetic fields [5][6][7][8][9]. Following this approach, a mechanical deformation in a graphene lattice is equivalent to introducing an external magnetic field [10,11].…”

Sensitivity to strains and defects for manipulating the conductivity of graphene

“…The parameter ν enters into the equations for the deformed bond lengths (in units of a 0 ) [4,5]: for armchair strains. We assume that the deformation is homogeneous and bond vectors are transformed according to the standard Cauchy-Born rule, neglecting additional (internal) degrees of freedom associated with the sublattices of graphene [46,47]. Theories beyond the homogeneous Cauchy-Born deformation correct the Fermi velocity and optical (ac) conductivity [47,48], however this does not result in (sufficiently) new effects in (local) density of states [47] and thus in dc conductivity.…”