Dirac-Kronig-Penney model for strain-engineered graphene

TL;DR

This paper models how one-dimensional strain patterns in graphene affect its electronic properties, revealing significant pseudo-gaps and transport suppression, with implications for strain-engineered graphene devices.

Contribution

It provides an exact solution to the Dirac-Kronig-Penney model for strained graphene, analyzing the impact of periodic strain on electronic transport and density of states.

Findings

Periodic strains induce large pseudo-gaps.

Charge transport is suppressed along strain directions.

Strain effects are stronger when atomic distance variations exceed a certain threshold.

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 pseudo-gaps 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 of inter-atomic distance exceeds the value a^2/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.