Abstract
We develop an effective extended Hubbard model to describe the low-energy electronic properties of the twisted bilayer graphene. By using the Bloch states in the effective continuum model and with the aid of the maximally localized algorithm, we construct the Wannier orbitals and obtain an effective tight-binding model on the emergent honeycomb lattice. We find that the Wannier state takes a peculiar three-peak form in which the amplitude maxima are located at the triangle corners surrounding the center. We estimate the direct Coulomb interaction and the exchange interaction between the Wannier states. At the filling of two electrons per supercell, in particular, we find an unexpected coincidence in the direct Coulomb energy between a charge-ordered state and a homogeneous state, which could possibly lead to an unconventional many-body state.
- Received 21 May 2018
DOI:https://doi.org/10.1103/PhysRevX.8.031087
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Twisted bilayer graphene is a sandwich of two graphene layers rotated relative to one another. Electron correlation is not expected to play an important role in carbon, so a recent experiment suggesting superconductivity originating from electron correlation in twisted bilayer graphene has attracted much attention. There is a slight rotation that gives rise to a moiré interference pattern, so that a group of more than 10 000 carbon atoms mimics a very small number of “effective atoms.” We have derived an electronic model for these effective atoms, which captures the essence of the physics needed to study the effects of electron correlation and superconductivity in such systems.
Our model takes into account realistic electronic band structure and electron-electron interactions. We replace the huge moiré unit cell with only two effective atoms arranged on a honeycomb lattice. The effective atomic orbital has a characteristic three-peak structure, and it leads to unexpected properties of many-body states. In particular, we find that an electronic excitation can be viewed as a pair creation of fractional charges, which would possibly give rise to exotic many-body physics.
This effective model dramatically reduces the fundamental complexity of the electronic system of twisted bilayer graphene and opens the way for explorations of the underlying many-body physics.