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

2018/08/31 by Junyeong Ahn, Sungjoon Park, Bohm‐Jung Yang +1 · 11 citations
Materials Science · Mathematics · Physics and Astronomy · #Bilayer #Bilayer graphene #Condensed matter physics #Dirac (video compression format) #Geometry #Graphene #Graphene research and applications #Magic angle #Mathematics #Membrane #Physics #Point reflection #Quantum many-body systems #Quantum mechanics #Quasiparticle #Superconductivity #Symmetry (geometry) #Theoretical physics #Topological Materials and Phenomena #Topology (electrical circuits) #cond-mat.mes-hall #cond-mat.str-el

paper · pdf · doi:10.1103/physrevx.9.021013

published as Phys. Rev. X 9, 021013 (2019) · 23 pages, 13 figures

openalex publication_date 2019/04/22 · arxiv created 2019/04/23 · arxiv updated 2019/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A new theory reveals the topological origin of the mismatch between the number of left- and right-handed Dirac quasiparticles in twisted bilayer graphene, which is a step toward identifying new topological phases of matter.

Citations

• New classes of three-dimensional topological crystalline insulators: Nonsymmorphic and magnetic
• Classification of topological quantum matter with symmetries
• Electronic structure of turbostratic graphene
• Differential Forms in Algebraic Topology
• A no-go theorem for regularizing chiral fermions
• Time Reversal Polarization and a Z₂ Adiabatic Spin Pump
• Moire bands in twisted double-layer graphene
• Quantised singularities in the electromagnetic field,
• Superlattice-Induced Insulating States and Valley-Protected Orbits in Twisted Bilayer Graphene
• Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators
• Theory of Emergent Josephson Lattice in Neutral Twisted Bilayer Graphene (Moiŕe is Different)
• On magic angles and band flattening in twisted bilayer graphene

Cited by

• Annihilation of Dirac points and its topological obstruction in a photonic Kagome lattice
• Magnetononlinear Hall effect from multigap topology in metal-organic frameworks
• Current-Induced Reversal of Anomalous Hall Conductance in Twisted Bilayer Graphene
• Substrate screening approach for quasiparticle energies of two-dimensional interfaces with lattice mismatch
• Converting PT-Symmetric Topological Classes by Floquet Engineering
• Inducing a many-body topological state of matter through Coulomb-engineered local interactions
• Evolution between quantum Hall and conducting phases: Simple models and some results
• Non-Abelian Dirac node braiding and near-degeneracy of correlated phases at odd integer filling in magic-angle twisted bilayer graphene
• Bicircular Light Floquet Engineering of Magnetic Symmetry and Topology and Its Application to the Dirac Semimetal Cd3As2
• Tuning superconductivity in twisted bilayer graphene
• Theories for the correlated insulating states and quantum anomalous Hall effect phenomena in twisted bilayer graphene
• Triply degenerate nodal lines in topological and nontopological metals

Related

• Stiefel-Whitney classes and topological phases in band theory
• Euler band topology in spin-orbit coupled magnetic systems
• Euler band topology in superfluids and superconductors
• Real space representation of topological system: twisted bilayer graphene as an example
• Robustness of real-space topology in moiré systems