Dirac-Kronig-Penney model for strain-engineered graphene

Abstract

Motivated by recent proposals on strain engineering of graphene electronic circuits we calculate conductivity, shot noise and the density of states in periodically deformed graphene. We provide the solution to the Dirac-Kronig-Penney model, which describes the phase-coherent transport in clean monolayer samples with an one-dimensional modulation of the strain and the electrostatic potentials. We compare the exact results to a qualitative band-structure analysis. We find that periodic strains induce large pseudogaps and suppress charge transport in the direction of strain modulation. The strain-induced minima in the gate-voltage dependence of the conductivity characterize the quality of graphene superstructures. The effect is especially strong if the variation in interatomic distance exceeds the value a2/ℓ, where a is the lattice spacing of free graphene and ℓ is the period of the superlattice. A similar effect induced by a periodic electrostatic potential is weakened due to Klein tunnelling.