Nature of the Correlated Insulator States in Twisted Bilayer Graphene

Xie, Ming; MacDonald, A.  H.

doi:10.1103/physrevlett.124.097601

Title: Nature of the Correlated Insulator States in Twisted Bilayer Graphene

Abstract

We use self-consistent Hartree-Fock calculations performed in the full $$\pi$$-band Hilbert space to assess the nature of the recently discovered correlated insulator states in magic-angle twisted bilayer graphene (TBG). In this work, we find that gaps between the flat conduction and valence bands open at neutrality over a wide range of twist angles, sometimes without breaking the system’s valley projected $$\mathcal{C}_2\mathcal{T}$$ symmetry. Broken spin-valley flavor symmetries then enable gapped states to form not only at neutrality, but also at total moiré band filling $$\textit{n}$$ = ± $$\textit{p}/4$$ with integer $$\textit{p}$$ = 1, 2, 3, when the twist angle is close to the magic value at which the flat bands are most narrow. Because the magic-angle flat band quasiparticles are isolated from remote band quasiparticles only for effective dielectric constants larger than ~20, the gapped states do not necessarily break $$\mathcal{C}_2\mathcal{T}$$ symmetry and as a consequence the insulating states at $$\textit{n}$$ = ± 1/ 4 and $$\textit{n}$$ = ± 3/4 need not exhibit a quantized anomalous Hall effect.

Authors:

^[1]; MacDonald, A. H. ^[1]

Univ. of Texas, Austin, TX (United States)

Publication Date:: Mon Mar 02 00:00:00 EST 2020

Research Org.:: Univ. of Texas, Austin, TX (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1800054

Alternate Identifier(s):: OSTI ID: 1602366

Grant/Contract Number:: FG02-02ER45958

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Volume: 124; Journal Issue: 9; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Physics

Citation Formats


                    Xie, Ming, and MacDonald, A.  H. Nature of the Correlated Insulator States in Twisted Bilayer Graphene.  United States: N. p., 2020. 
Web.  doi:10.1103/physrevlett.124.097601.

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                    Xie, Ming, & MacDonald, A.  H. Nature of the Correlated Insulator States in Twisted Bilayer Graphene.  United States.  https://doi.org/10.1103/physrevlett.124.097601

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                    Xie, Ming, and MacDonald, A.  H. Mon .  
"Nature of the Correlated Insulator States in Twisted Bilayer Graphene".  United States.  https://doi.org/10.1103/physrevlett.124.097601.  https://www.osti.gov/servlets/purl/1800054.

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@article{osti_1800054,

  title        = {Nature of the Correlated Insulator States in Twisted Bilayer Graphene},

  author       = {Xie, Ming and MacDonald, A.  H.},

  abstractNote = {We use self-consistent Hartree-Fock calculations performed in the full $\pi$-band Hilbert space to assess the nature of the recently discovered correlated insulator states in magic-angle twisted bilayer graphene (TBG). In this work, we find that gaps between the flat conduction and valence bands open at neutrality over a wide range of twist angles, sometimes without breaking the system’s valley projected $\mathcal{C}_2\mathcal{T}$ symmetry. Broken spin-valley flavor symmetries then enable gapped states to form not only at neutrality, but also at total moiré band filling $\textit{n}$ = ± $\textit{p}/4$ with integer $\textit{p}$ = 1, 2, 3, when the twist angle is close to the magic value at which the flat bands are most narrow. Because the magic-angle flat band quasiparticles are isolated from remote band quasiparticles only for effective dielectric constants larger than ~20, the gapped states do not necessarily break $\mathcal{C}_2\mathcal{T}$ symmetry and as a consequence the insulating states at $\textit{n}$ = ± 1/ 4 and $\textit{n}$ = ± 3/4 need not exhibit a quantized anomalous Hall effect.},

  doi          = {10.1103/physrevlett.124.097601},

  journal      = {Physical Review Letters},

  number       = 9,

  volume       = 124,

  place        = {United States},

  year         = {Mon Mar 02 00:00:00 EST 2020},

  month        = {Mon Mar 02 00:00:00 EST 2020}

}

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Title: Nature of the Correlated Insulator States in Twisted Bilayer Graphene

Abstract

Citation Formats

Topological Superconductivity in Twisted Multilayer Graphene text, January 2018

Unconventional superconductivity in nearly flat bands in twisted bilayer graphene journal, March 2019

Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene text, January 2018

Topological Superconductivity in Twisted Multilayer Graphene journal, August 2018

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

Pseudospin magnetism in graphene journal, January 2008

Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene journal, October 2019

Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice with possible applications to twisted bilayer graphene journal, September 2018

Possible correlated insulating states in magic-angle twisted bilayer graphene under strongly competing interactions journal, August 2018

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

Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene journal, March 2017

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

Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene journal, July 2019

Wannier pairs in superconducting twisted bilayer graphene and related systems journal, April 2019

Tuning superconductivity in twisted bilayer graphene text, January 2018

Maximized electron interactions at the magic angle in twisted bilayer graphene journal, July 2019

Theory of Phonon-Mediated Superconductivity in Twisted Bilayer Graphene journal, December 2018

Unconventional topological superconductivity and phase diagram for an effective two-orbital model as applied to twisted bilayer graphene text, January 2018

Fragile Topology and Wannier Obstructions journal, September 2018

Electrostatic effects, band distortions, and superconductivity in twisted graphene bilayers journal, December 2018

Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization not Mott Insulation text, January 2018

Dirac points, spinons and spin liquid in twisted bilayer graphene text, January 2018

Dirac Points, Spinons, and Spin Liquid in Twisted Bilayer Graphene journal, May 2018

Fragile Topology and Wannier Obstructions text, January 2017

Triangular antiferromagnetism on the honeycomb lattice of twisted bilayer graphene journal, August 2018

An exact continuum model for low-energy electronic states of twisted bilayer graphene text, January 2019

Unconventional superconductivity in nearly flat bands in twisted bilayer graphene text, January 2018

Pseudospin order in monolayer, bilayer and double-layer graphene journal, January 2012

Charge-transfer insulation in twisted bilayer graphene text, January 2018

Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene journal, July 2019

Correlated electronic phases in twisted bilayer transition metal dichalcogenides journal, June 2020

Nearly flat Chern bands in moiré superlattices journal, February 2019

Mean-field theory for superconductivity in twisted bilayer graphene journal, December 2018

Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization, Not Mott Insulation journal, September 2018

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

Moire bands in twisted double-layer graphene text, January 2010

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

Chiral Spin Density Wave and d + i d Superconductivity in the Magic-Angle-Twisted Bilayer Graphene journal, November 2018

Charge-transfer insulation in twisted bilayer graphene journal, December 2018

Faithful tight-binding models and fragile topology of magic-angle bilayer graphene journal, May 2019

Ferromagnetic Mott State in Twisted Graphene Bilayers at the Magic Angle text, January 2018

Phases of a phenomenological model of twisted bilayer graphene journal, August 2018

Antiferromagnetically ordered Mott insulator and d + i d superconductivity in twisted bilayer graphene: a quantum Monte Carlo study journal, March 2019

Exact continuum model for low-energy electronic states of twisted bilayer graphene journal, August 2019

Theory of phonon-mediated superconductivity in twisted bilayer graphene text, January 2018

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

Unconventional topological superconductivity and phase diagram for an effective two-orbital model as applied to twisted bilayer graphene journal, August 2018

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

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Ab initio theory of moiré superlattice bands in layered two-dimensional materials journal, May 2014

Strongly correlated Chern insulators in magic-angle twisted bilayer graphene journal, December 2020

Antiferromagnetically ordered Mott insulator and $d+id$ superconductivity in twisted bilayer graphene: A quantum Monte carlo study text, January 2018

Tuning superconductivity in twisted bilayer graphene journal, January 2019

Model for Metal-Insulator Transition in Graphene Superlattices and Beyond text, January 2018

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Cleaning interfaces in layered materials heterostructures journal, December 2018

Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene journal, September 2018

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

Strong Coupling Phases of Partially Filled Twisted Bilayer Graphene Narrow Bands journal, June 2019

Maximally Localized Wannier Orbitals and the Extended Hubbard Model for Twisted Bilayer Graphene journal, September 2018

Ferromagnetic Mott state in Twisted Graphene Bilayers at the Magic Angle journal, June 2019

Pairing symmetry of interacting fermions on twisted bilayer graphene superlattice text, January 2018

Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene journal, July 2019

All Magic Angles in Twisted Bilayer Graphene are Topological journal, July 2019

Topological Superconductivity in Twisted Multilayer Graphene
text, January 2018

Unconventional superconductivity in nearly flat bands in twisted bilayer graphene
journal, March 2019

Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene
text, January 2018

Topological Superconductivity in Twisted Multilayer Graphene
journal, August 2018

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

Pseudospin magnetism in graphene
journal, January 2008

Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene
journal, October 2019

Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice with possible applications to twisted bilayer graphene
journal, September 2018

Possible correlated insulating states in magic-angle twisted bilayer graphene under strongly competing interactions
journal, August 2018

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

Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene
journal, March 2017

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

Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
journal, July 2019

Wannier pairs in superconducting twisted bilayer graphene and related systems
journal, April 2019

Tuning superconductivity in twisted bilayer graphene
text, January 2018

Maximized electron interactions at the magic angle in twisted bilayer graphene
journal, July 2019

Theory of Phonon-Mediated Superconductivity in Twisted Bilayer Graphene
journal, December 2018

Unconventional topological superconductivity and phase diagram for an effective two-orbital model as applied to twisted bilayer graphene
text, January 2018

Fragile Topology and Wannier Obstructions
journal, September 2018

Electrostatic effects, band distortions, and superconductivity in twisted graphene bilayers
journal, December 2018

Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization not Mott Insulation
text, January 2018

Dirac points, spinons and spin liquid in twisted bilayer graphene
text, January 2018

Dirac Points, Spinons, and Spin Liquid in Twisted Bilayer Graphene
journal, May 2018

Fragile Topology and Wannier Obstructions
text, January 2017

Triangular antiferromagnetism on the honeycomb lattice of twisted bilayer graphene
journal, August 2018

An exact continuum model for low-energy electronic states of twisted bilayer graphene
text, January 2019

Unconventional superconductivity in nearly flat bands in twisted bilayer graphene
text, January 2018

Pseudospin order in monolayer, bilayer and double-layer graphene
journal, January 2012

Charge-transfer insulation in twisted bilayer graphene
text, January 2018

Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene
journal, July 2019

Correlated electronic phases in twisted bilayer transition metal dichalcogenides
journal, June 2020

Nearly flat Chern bands in moiré superlattices
journal, February 2019

Mean-field theory for superconductivity in twisted bilayer graphene
journal, December 2018

Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization, Not Mott Insulation
journal, September 2018

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

Moire bands in twisted double-layer graphene
text, January 2010

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

Chiral Spin Density Wave and $d + i d$ Superconductivity in the Magic-Angle-Twisted Bilayer Graphene
journal, November 2018

Charge-transfer insulation in twisted bilayer graphene
journal, December 2018

Faithful tight-binding models and fragile topology of magic-angle bilayer graphene
journal, May 2019

Ferromagnetic Mott State in Twisted Graphene Bilayers at the Magic Angle
text, January 2018

Phases of a phenomenological model of twisted bilayer graphene
journal, August 2018

Antiferromagnetically ordered Mott insulator and $d + i d$ superconductivity in twisted bilayer graphene: a quantum Monte Carlo study
journal, March 2019

Exact continuum model for low-energy electronic states of twisted bilayer graphene
journal, August 2019

Theory of phonon-mediated superconductivity in twisted bilayer graphene
text, January 2018

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

Unconventional topological superconductivity and phase diagram for an effective two-orbital model as applied to twisted bilayer graphene
journal, August 2018

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

Unconventional Superconductivity and Density Waves in Twisted Bilayer Graphene
journal, December 2018

Ab initio theory of moiré superlattice bands in layered two-dimensional materials
journal, May 2014

Strongly correlated Chern insulators in magic-angle twisted bilayer graphene
journal, December 2020

Antiferromagnetically ordered Mott insulator and $d+id$ superconductivity in twisted bilayer graphene: A quantum Monte carlo study
text, January 2018

Tuning superconductivity in twisted bilayer graphene
journal, January 2019

Model for Metal-Insulator Transition in Graphene Superlattices and Beyond
text, January 2018

Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene
text, January 2018

The nature of correlations in the insulating states of twisted bilayer graphene
journal, March 2019

Cleaning interfaces in layered materials heterostructures
journal, December 2018

Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene
journal, September 2018

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

Strong Coupling Phases of Partially Filled Twisted Bilayer Graphene Narrow Bands
journal, June 2019

Maximally Localized Wannier Orbitals and the Extended Hubbard Model for Twisted Bilayer Graphene
journal, September 2018

Ferromagnetic Mott state in Twisted Graphene Bilayers at the Magic Angle
journal, June 2019

Pairing symmetry of interacting fermions on twisted bilayer graphene superlattice
text, January 2018

Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene
journal, July 2019

All Magic Angles in Twisted Bilayer Graphene are Topological
journal, July 2019