Classification of Topological Phase Transitions and van Hove Singularity Steering Mechanism in Graphene Superlattices

Abstract

We study quantum phase transitions in graphene superlattices in external magnetic fields, where a framework is presented to classify multiflavor Dirac fermion critical points describing hopping tuned topological phase transitions of integer and fractional Hofstadter-Chern insulators. We argue and provide numerical support for the existence of transitions that can be explained by a nontrivial interplay of Chern bands and van Hove singularities near charge neutrality. This work provides a route to critical phenomena beyond conventional quantum Hall plateau transitions.

Published version

References in corpus (15)

• The electronic properties of graphene
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Fractional quantum Hall effect in the absence of Landau levels
• Zero modes of tight binding electrons on the honeycomb lattice
• Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Engineering artificial graphene in a two-dimensional electron gas
• Dirac-point engineering and topological phase transitions in honeycomb optical lattices
• Hofstadter Topology: Non-crystalline Topological Materials at High Flux
• The Colored Hofstadter Butterfly for the Honeycomb Lattice
• Band Collapse and the Quantum Hall Effect in Graphene
• Self-similar occurrence of massless Dirac particles in graphene under magnetic field
• The Hall conductance, topological quantum phase transition and the Diophantine equation on honeycomb lattice

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• Fractional Chern insulators with a non-Landau level continuum limit
• Unconventional Self-Similar Hofstadter Superconductivity from Repulsive Interactions
• Fractional Chern Insulators in Twisted Bilayer MoTe${}_2$: A Composite Fermion Perspective
• Topological phases of the dimerized Hofstadter butterfly
• Symmetry indicators in commensurate magnetic flux
• Replica Higher-Order Topology of Hofstadter Butterflies in Twisted Bilayer Graphene
• Topological van Hove singularities at phase transitions in Weyl metals
• Tunable interface states between Floquet-Weyl semimetals
• Correlated phases and topological phase transition in twisted bilayer graphene at one quantum of magnetic flux
• Magnetic Bloch States at Integer Flux Quanta Induced by Super-moiré Potential in Graphene Aligned with Twisted Boron Nitride
• Electromagnetic response and emergent topological orders in transition metal dichalcogenide MoTe${}_2$ bilayers
• Quantum Fractality on the Surface of Topological Insulators
• Bloch and Bethe ansatze for the Harper model: A butterfly with a boundary
• Topological constraints on the electronic band structure of hexagonal lattice in a magnetic field
• Hofstadter Butterfly in Graphene
• Theory of Hofstadter Superconductors
• Critical magnetic flux for Weyl points in the three-dimensional Hofstadter model
• Localization phase diagram of the Hexagonal Lattice with irrational magnetic flux