Topological phases of the dimerized Hofstadter butterfly

Abstract

In this work, we study the topological phases of the dimerized square lattice in the presence of an external magnetic field. The dimerization pattern in the lattice's hopping amplitudes can induce a series of bulk energy gap openings in the Hofstadter spectrum at certain fractional fillings, giving rise to various topological phases. In particular, we show that at $\frac{1}{2}$-filling the topological quadrupole insulator phase with a quadrupole moment quantized to $\frac{e}{2}$ and associated corner-localized mid-gap states exists in certain parameter regime for all magnetic fluxes. At $\frac{1}{4}$ filling, the system can host obstructed atomic limit phases or Chern insulator phases. For those configurations gapped at fillings below $\frac{1}{4}$, the system is in Chern insulator phases of various non-vanishing Chern numbers. Across the phase diagram, both bulk-obstructed and boundary-obstructed topological phase transitions exist in this model.

arXiv comment19 pages(one column), 8 figures, Publish version

References in corpus (61)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Quantized Electric Multipole Insulators
• Hofstadter's butterfly in moire superlattices: A fractal quantum Hall effect
• Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• The (High Quality) Topological Materials In The World
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topolectrical circuit realization of topological corner modes
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• Catalogue of Topological Electronic Materials
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Acoustic higher-order topological insulator on a Kagome lattice
• Higher-Order Topology in Bismuth
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Topolectrical circuits
• Topological protection of photonic mid-gap cavity modes
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Time Reversal Invariant Topologically Insulating Circuits
• Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
• Realistic Time-Reversal Invariant Topological Insulators With Neutral Atoms
• Majorana corner modes in a high-temperature platform
• Observation of Quadrupole Transitions and Edge Mode Topology in an LC network
• Weak-Pairing Higher Order Topological Superconductors
• Helical Topological Edge States in a Quadrupole Phase
• Classification of Two Dimensional Topological Crystalline Superconductors and Majorana Bound States at Disclinations
• An anomalous higher-order topological insulator
• Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices
• Topological Quadrupolar Semimetals
• Tunable Majorana corner states in a two-dimensional second-order topological superconductor induced by magnetic fields
• Topological Phase Transitions in Disordered Electric Quadrupole Insulators
• Many-Body Electric Multipole Operators in Extended Systems
• Many-Body Order Parameters for Multipoles in Solids
• Boundary-obstructed topological phases
• Higher-order topological odd-parity superconductors
• Edge modes in band topological insulators
• Second-order Topological Superconductors with Mixed Pairing
• Fractional corner charges in spin-orbit coupled crystals
• The Landau Level of Fragile Topology
• Hofstadter Topology: Non-crystalline Topological Materials at High Flux
• Time-Reversal-Invariant Hofstadter-Hubbard Model with Ultracold Fermions
• Fractional quantum Hall effect in the interacting Hofstadter model via tensor networks
• Multiple Flat Bands and Topological Hofstadter Butterfly in Twisted Bilayer Graphene Close to the Second Magic Angle
• Engineering topological materials in microwave cavity arrays
• Boundary-obstructed topological high-T${}_c$ superconductivity in iron pnictides
• Topological Edge States with Zero Hall Conductivity in a Dimerized Hofstadter Model
• Exact Solutions of Fractional Chern Insulators: Interacting Particles in the Hofstadter Model at Finite Size
• Tunable Band Topology Reflected by Fractional Quantum Hall States in Two-Dimensional Lattices
• Fractional Topological Phases in Generalized Hofstadter Bands with Arbitrary Chern Numbers
• Higher-order topological insulators in a magnetic field
• Classification of Topological Phase Transitions and van Hove Singularity Steering Mechanism in Graphene Superlattices
• Boundary-obstructed topological phases of a massive Dirac fermion in a magnetic field
• BCS theory of time-reversal-symmetric Hofstadter-Hubbard model

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• Replica Higher-Order Topology of Hofstadter Butterflies in Twisted Bilayer Graphene
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