Electronic and Phonon Instabilities in Bilayer Graphene under Applied External Bias

TL;DR

This study investigates how external electric bias affects the electronic and phonon properties of bilayer graphene, revealing phase transitions, symmetry changes, and dynamical instabilities through detailed calculations.

Contribution

It provides a comprehensive analysis of electronic and phonon instabilities in bilayer graphene under bias, including new insights into phase transitions and layer-sliding dynamical instabilities.

Findings

Bias induces a semi-metal-to-semiconductor transition with a tunable band gap.

External bias causes symmetry reduction and charge inhomogeneities.

Phonon spectra are perturbed, with instabilities in AA stacking under bias.

Abstract

We have performed electronic-structure and lattice-dynamics calculations on the AB and AA structures of bilayer graphene. We study the effect of external electric fields and compare results obtained with different levels of theory to existing theoretical and experimental results. Application of an external field to the AB bilayer alters the electronic spectrum, with the bands changing under bias from a parabolic to a "Mexican hat" double-well structure. This results in a semi-metal-to-semiconductor phase transition, with the size of the induced electronic band-gap being tuneable through the field strength. A reduction of continuous symmetry from a hexagonal to a triangular lattice is also evidenced through in-plane electronic charge inhomogeneities between the sublattices. When spin-orbit coupling is turned on for the AB system, we find that the bulk gap decreases, gradually increasing for larger intensities of the bias. Under large bias the energy dispersion recovers the Mexican hat structure, since the energy interaction between the layers balances the coupling interaction. We find that external bias perturbs the harmonic phonon spectra and leads to anomalous behaviour of the out-of-plane flexural ZA and layer-breathing ZO' modes. For the AA system, the electronic and phonon dispersions both remain stable under bias, but the phonon spectrum exhibits zone-center imaginary modes due to layer-sliding dynamical instabilities.