Strain and Electric Field Modulation of the Electronic Structure of Bilayer Graphene

TL;DR

This study investigates how electric fields and strain influence the electronic properties of bilayer graphene, revealing electric field-induced band gaps, Dirac circle behavior, and screening effects through ab initio calculations.

Contribution

It provides new insights into the effects of electric field and strain on bilayer graphene's electronic structure, including band gap control and Dirac cone behavior, with detailed tight-binding parameters.

Findings

Electric field induces a band gap in Bernal-stacked BLG.

Dirac circles with linear dispersion appear in hexagonal stacking.

Screening effects significantly reduce the band gap and Dirac circle size.

Abstract

We study how the electronic structure of the bilayer graphene (BLG) is changed by electric field and strain from {\it ab initio} density-functional calculations using the LMTO and the LAPW methods. Both hexagonal and Bernal stacked structures are considered. The BLG is a zero-gap semiconductor like the isolated layer of graphene. We find that while strain alone does not produce a gap in the BLG, an electric field does so in the Bernal structure but not in the hexagonal structure. The topology of the bands leads to Dirac circles with linear dispersion in the case of the hexagonally stacked BLG due to the interpenetration of the Dirac cones, while for the Bernal stacking, the dispersion is quadratic. The size of the Dirac circle increases with the applied electric field, leading to an interesting way of controlling the Fermi surface. The external electric field is screened due to polarization charges between the layers, leading to a reduced size of the band gap and the Dirac circle. The screening is substantial in both cases and diverges for the Bernal structure for small fields as has been noted by earlier authors. As a biproduct of this work, we present the tight-binding parameters for the free-standing single layer graphene as obtained by fitting to the density-functional bands, both with and without the slope constraint for the Dirac cone.