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.

19 pages(one column), 8 figures, Publish version

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Cited by in corpus (11)

• $2^n$-root weak, Chern, and higher-order topological insulators, and $2^n$-root topological semimetals
• Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries
• Transition from metal to higher-order topological insulator driven by random flux
• Kaleidoscopes of Hofstadter Butterflies and Aharonov-Bohm caging from $2^n$-root topology in decorated square lattices
• Symmetry indicators in commensurate magnetic flux
• Replica Higher-Order Topology of Hofstadter Butterflies in Twisted Bilayer Graphene
• Topological metals constructed by sliding quantum wire arrays
• Chern numbers for the two-body Hofstadter-Hubbard butterfly
• Hofstadter Butterflies in Topological Insulators
• Floquet topological properties in the Non-Hermitian long-range system with complex hopping amplitudes
• Variational approach for the two-body problem in a multiband extended-Hubbard model