Electronic and Phonon Instabilities in Bilayer Graphene under Applied External Bias

E. L. Silva, M. C. Santos, J. M. Skelton, Tao Yang, T. Santos, S. C. Parker, A. Walsh

Research output: Contribution to journalConference articlepeer-review

3 Scopus citations


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" 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 layersliding dynamical instabilities.

Original languageEnglish
Pages (from-to)373-382
Number of pages10
JournalMaterials Today: Proceedings
StatePublished - 2020
Event11th International conference on Advanced Nanomaterials, ANM 2018 - Aveiro, Portugal
Duration: 18 Jul 201820 Jul 2018

Bibliographical note

Funding Information:
This work was supported by EPSRC Programme Grants (nos. EP/K004956/1 and EP/K016288/1) and the ERC (Grant No. 277757); as well as from the European Union Horizon 2020 research and innovation programme under Marie Sklodowska-Curie grant agreement No. 785789-COMEX; and by the Science and Technology Commission of the Military Commission of China, with the project NO. 18-H863-00-TS-002-006-01. We acknowledge use of the ARCHER supercomputer through the PRACE Research Infrastructure (award no. 13DECI0313). The authors also acknowledge computing support from the University of Bath Computing Services, which maintains the Balena HPC cluster.

Publisher Copyright:
© 2018 Elsevier Ltd. All rights reserved.


  • Bilayer grapheme
  • Electric field
  • Electronic properties
  • Lattice dynamics


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