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All Magic Angles in Twisted Bilayer Graphene are Topological

https://doi.org/10.1103/physrevlett.123.036401
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50/50 checkable references clean · checked 2026-07-23

Every reference with a DOI in the deposited reference list resolved to a known work in Crossref or DataCite at the dated check, and none carried a retraction, withdrawal, or removal notice.

1 without a DOI — not checked. A reference deposited without a DOI is never matched by title or guessed at; it stays outside the checked set, and this line discloses that.

The 50 checked references that resolve
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Unconventional superconductivity in nearly flat bands in twisted bilayer graphene
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Superconductivity from valley fluctuations and approximate SO(4) symmetry in a weak coupling theory of twisted bilayer graphene
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Unconventional Superconductivity and Density Waves in Twisted Bilayer Graphene
resolves10.1103/PhysRevLett.121.257001
Theory of Phonon-Mediated Superconductivity in Twisted Bilayer Graphene
resolves10.1103/PhysRevB.98.075154
Phases of a phenomenological model of twisted bilayer graphene
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Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene
resolves10.1021/acs.nanolett.8b02033
Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization, Not Mott Insulation
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Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice
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Moiré bands in twisted double-layer graphene
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Topology of crystalline insulators and superconductors
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New classes of three-dimensional topological crystalline insulators: Nonsymmorphic and magnetic
resolves10.1103/PhysRevB.92.081201
Topological nodal line semimetals with and without spin-orbital coupling
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Topological Insulators from Group Cohomology
resolves10.1103/PhysRevB.81.245412
Transport between twisted graphene layers
resolves10.1107/S1600576717011712
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Symmetry-based indicators of band topology in the 230 space groups
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Tight-binding description of graphene
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Tight-binding model for graphene<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi></mml:math>-bands from maximally localized Wannier functions
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resolves10.1126/science.aah6442
Quantized electric multipole insulators
resolves10.1103/PhysRevB.83.035108
Wannier representation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>topological insulators
resolves10.1103/PhysRevB.56.12847
Maximally localized generalized Wannier functions for composite energy bands
resolves10.1103/PhysRevB.54.11169
Efficient iterative schemes for<i>ab initio</i>total-energy calculations using a plane-wave basis set
resolves10.1103/PhysRevB.59.1758
From ultrasoft pseudopotentials to the projector augmented-wave method
resolves10.1103/PhysRevB.50.17953
Projector augmented-wave method
resolves10.1103/PhysRev.136.B864
Inhomogeneous Electron Gas
resolves10.1107/S0021889812042185
Magnetic symmetry in the Bilbao Crystallographic Server: a computer program to provide systematic absences of magnetic neutron diffraction
resolves10.1038/nature23268
Topological quantum chemistry
resolves10.1103/PhysRevE.96.023310
Graph theory data for topological quantum chemistry
resolves10.1103/PhysRevLett.120.266401
Topology of Disconnected Elementary Band Representations
resolves10.1103/PhysRevLett.121.126402
Fragile Topology and Wannier Obstructions
resolves10.1103/PhysRevB.83.245132
Inversion-symmetric topological insulators
resolves10.1103/PhysRevB.82.241102
Entanglement and inversion symmetry in topological insulators
resolves10.1103/PhysRevB.86.115112
Bulk topological invariants in noninteracting point group symmetric insulators
resolves10.1103/PhysRevLett.121.106403
Band Topology and Linking Structure of Nodal Line Semimetals with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> Monopole Charges
resolves10.1103/PhysRevX.8.031088
Symmetry, Maximally Localized Wannier States, and a Low-Energy Model for Twisted Bilayer Graphene Narrow Bands
resolves10.1103/PhysRevLett.99.256802
Graphene Bilayer with a Twist: Electronic Structure
resolves10.1038/ncomms9944
Superfluidity in topologically nontrivial flat bands
resolves10.1103/PhysRevB.99.195455
Faithful tight-binding models and fragile topology of magic-angle bilayer graphene
resolves10.1103/PhysRevX.9.021013
Failure of Nielsen-Ninomiya Theorem and Fragile Topology in Two-Dimensional Systems with Space-Time Inversion Symmetry: Application to Twisted Bilayer Graphene at Magic Angle
The 1 reference without a DOI — listed, not checked
no DOI — not checkedThe Mathematical Theory of Symmetry in Solids: Representation Theory for Point Groups and Space Groups
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