skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

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. Here, 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.

Authors:
; ; ; ; ;
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1474783
Alternate Identifier(s):
OSTI ID: 1499092
Grant/Contract Number:  
SC0010526
Resource Type:
Published Article
Journal Name:
Physical Review. X
Additional Journal Information:
Journal Name: Physical Review. X Journal Volume: 8 Journal Issue: 3; Journal ID: ISSN 2160-3308
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Koshino, Mikito, Yuan, Noah F. Q., Koretsune, Takashi, Ochi, Masayuki, Kuroki, Kazuhiko, and Fu, Liang. Maximally Localized Wannier Orbitals and the Extended Hubbard Model for Twisted Bilayer Graphene. United States: N. p., 2018. Web. doi:10.1103/PhysRevX.8.031087.
Koshino, Mikito, Yuan, Noah F. Q., Koretsune, Takashi, Ochi, Masayuki, Kuroki, Kazuhiko, & Fu, Liang. Maximally Localized Wannier Orbitals and the Extended Hubbard Model for Twisted Bilayer Graphene. United States. doi:10.1103/PhysRevX.8.031087.
Koshino, Mikito, Yuan, Noah F. Q., Koretsune, Takashi, Ochi, Masayuki, Kuroki, Kazuhiko, and Fu, Liang. Fri . "Maximally Localized Wannier Orbitals and the Extended Hubbard Model for Twisted Bilayer Graphene". United States. doi:10.1103/PhysRevX.8.031087.
@article{osti_1474783,
title = {Maximally Localized Wannier Orbitals and the Extended Hubbard Model for Twisted Bilayer Graphene},
author = {Koshino, Mikito and Yuan, Noah F. Q. and Koretsune, Takashi and Ochi, Masayuki and Kuroki, Kazuhiko and Fu, Liang},
abstractNote = {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. Here, 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.},
doi = {10.1103/PhysRevX.8.031087},
journal = {Physical Review. X},
number = 3,
volume = 8,
place = {United States},
year = {2018},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevX.8.031087

Citation Metrics:
Cited by: 71 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Optical absorption in twisted bilayer graphene
journal, May 2013


Graphene Bilayer with a Twist: Electronic Structure
journal, December 2007

  • Lopes dos Santos, J. M. B.; Peres, N. M. R.; Castro Neto, A. H.
  • Physical Review Letters, Vol. 99, Issue 25
  • DOI: 10.1103/PhysRevLett.99.256802

Local sublattice-symmetry breaking in rotationally faulted multilayer graphene
journal, January 2011


Energy spectrum and quantum Hall effect in twisted bilayer graphene
journal, May 2012


Atomic corrugation and electron localization due to Moiré patterns in twisted bilayer graphenes
journal, October 2014


Unconventional superconductivity in magic-angle graphene superlattices
journal, March 2018


Relaxation of moiré patterns for slightly misaligned identical lattices: graphene on graphite
journal, July 2015


Structural analysis of multilayer graphene via atomic moiré interferometry
journal, March 2010


Pairing symmetry of interacting fermions on a twisted bilayer graphene superlattice
journal, June 2018


Model for the metal-insulator transition in graphene superlattices and beyond
journal, July 2018


Localization of Dirac Electrons in Rotated Graphene Bilayers
journal, March 2010

  • Trambly de Laissardière, G.; Mayou, D.; Magaud, L.
  • Nano Letters, Vol. 10, Issue 3
  • DOI: 10.1021/nl902948m

Electronic Properties of Incommensurate Atomic Layers
journal, December 2015

  • Koshino, Mikito; Moon, Pilkyung
  • Journal of the Physical Society of Japan, Vol. 84, Issue 12
  • DOI: 10.7566/JPSJ.84.121001

Flat bands in slightly twisted bilayer graphene: Tight-binding calculations
journal, September 2010


Lattice relaxation and energy band modulation in twisted bilayer graphene
journal, August 2017


Structure of twisted and buckled bilayer graphene
journal, November 2016


Twisted Bilayer Graphene: Moiré with a Twist
journal, August 2016


Maximally localized generalized Wannier functions for composite energy bands
journal, November 1997


Why Multilayer Graphene on 4 H SiC ( 000 1 ¯ ) Behaves Like a Single Sheet of Graphene
journal, March 2008


Moire bands in twisted double-layer graphene
journal, July 2011

  • Bistritzer, R.; MacDonald, A. H.
  • Proceedings of the National Academy of Sciences, Vol. 108, Issue 30
  • DOI: 10.1073/pnas.1108174108

Correlated insulator behaviour at half-filling in magic-angle graphene superlattices
journal, March 2018


Commensuration and interlayer coherence in twisted bilayer graphene
journal, April 2010


Numerical studies of confined states in rotated bilayers of graphene
journal, September 2012


Electronic Confinement and Coherence in Patterned Epitaxial Graphene
journal, May 2006


Structural properties of the multilayer graphene/ 4 H Si C ( 000 1 ¯ ) system as determined by surface x-ray diffraction
journal, June 2007


Superlattice-Induced Insulating States and Valley-Protected Orbits in Twisted Bilayer Graphene
journal, September 2016


Symmetry, Maximally Localized Wannier States, and a Low-Energy Model for Twisted Bilayer Graphene Narrow Bands
journal, September 2018


Electronic structure of turbostratic graphene
journal, April 2010


Effects of electrostatic fields and charge doping on the linear bands in twisted graphene bilayers
journal, August 2011


Interlayer interaction in general incommensurate atomic layers
journal, January 2015


Continuum model of the twisted graphene bilayer
journal, October 2012

  • Lopes dos Santos, J. M. B.; Peres, N. M. R.; Castro Neto, A. H.
  • Physical Review B, Vol. 86, Issue 15
  • DOI: 10.1103/PhysRevB.86.155449

Observation of Van Hove singularities in twisted graphene layers
journal, November 2009

  • Li, Guohong; Luican, A.; Lopes dos Santos, J. M. B.
  • Nature Physics, Vol. 6, Issue 2
  • DOI: 10.1038/nphys1463

The growth of AA graphite on (111) diamond
journal, December 2008

  • Lee, Jae-Kap; Lee, Seung-Cheol; Ahn, Jae-Pyoung
  • The Journal of Chemical Physics, Vol. 129, Issue 23
  • DOI: 10.1063/1.2975333

Single-Layer Behavior and Its Breakdown in Twisted Graphene Layers
journal, March 2011