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 12-filling the topological quadrupole insulator phase with a quadrupole moment quantized to e2 and associated corner-localized mid-gap states exists in certain parameter regime for all magnetic fluxes. At 14 filling, the system can host obstructed atomic limit phases or Chern insulator phases. For those configurations gapped at fillings below 14, 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.