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Maximally Localized Wannier Orbitals and the Extended Hubbard Model for Twisted Bilayer Graphene

Mikito Koshino, Noah F. Q. Yuan, Takashi Koretsune, Masayuki Ochi, Kazuhiko Kuroki, and Liang Fu
Phys. Rev. X 8, 031087 – Published 28 September 2018
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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.

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  • 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)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Mikito Koshino1,*, Noah F. Q. Yuan2, Takashi Koretsune3, Masayuki Ochi1, Kazuhiko Kuroki1, and Liang Fu2

  • 1Department of Physics, Osaka University, Toyonaka 560-0043, Japan
  • 2Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 3Department of Physics, Tohoku University, Sendai 980-8578, Japan

  • *koshino@phys.sci.osaka-u.ac.jp

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.

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See Also

Symmetry, Maximally Localized Wannier States, and a Low-Energy Model for Twisted Bilayer Graphene Narrow Bands

Jian Kang and Oskar Vafek
Phys. Rev. X 8, 031088 (2018)

Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene

Hoi Chun Po, Liujun Zou, Ashvin Vishwanath, and T. Senthil
Phys. Rev. X 8, 031089 (2018)

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Vol. 8, Iss. 3 — July - September 2018

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