Abstract

Flat bands with extremely narrow bandwidths on the order of a few millielectron volts can appear in twisted multilayer graphene systems for appropriate system parameters. Here we investigate the electronic structure of a twisted bi-bilayer graphene, or twisted double bilayer graphene, to find the parameter space where isolated flat bands can emerge as a function of twist angle, vertical pressure, and interlayer potential differences. We find that in twisted bi-bilayer graphene the bandwidth is generally flatter than in twisted bilayer graphene by roughly up to a factor of 2 in the same parameter space of twist angle $\ensuremath{\theta}$ and interlayer coupling $\ensuremath{\omega}$, making it in principle simpler to tailor narrow bandwidth flat bands. Application of vertical pressure can enhance the first magic angle in minimal models at $\ensuremath{\theta}\ensuremath{\sim}1.{05}^{\ensuremath{\circ}}$ to larger values of up to $\ensuremath{\theta}\ensuremath{\sim}1.{5}^{\ensuremath{\circ}}$ when $P\ensuremath{\sim}2.5$ GPa, where $\ensuremath{\theta}\ensuremath{\propto}\ensuremath{\omega}/{\ensuremath{\upsilon}}_{F}$. Narrow bandwidths are expected in bi-bilayers for a continuous range of small twist angles, i.e., without magic angles, when intrinsic bilayer gaps open by electric fields, or due to remote hopping terms. We find that moderate vertical electric fields can contribute in lifting the degeneracy of the low-energy flat bands by enhancing the primary gap near the Dirac point and the secondary gap with the higher energy bands. Distinct valley Chern bands are expected near ${0}^{\ensuremath{\circ}}$ or ${180}^{\ensuremath{\circ}}$ alignments.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.