Higher-order topological insulators in a magnetic field

Abstract

Two-dimensional (2D) generalization of the Su-Schriffer-Heeger (SSH) model serves as a platform for exploring higher-order topological insulators (HOTI). We investigate this model in a magnetic field which interpolates two models studied so far with zero flux and $\pi$ flux per plaquette. We show that in the Hofstadter butterfly there appears a wide gap around the $\pi$ flux, which belongs to the same HOTI discovered by Benalcazar-Bernevig-Hughes (BBH). It turns out that in a weak field regime HOTI could exist even within a small gap disconnected from the wider gap around $\pi$ flux. To characterize HOTI, we employ the entanglement polarization (eP) technique which is useful even if the basic four bands split into many Landau levels under a magnetic field.

9 pages, 10 figures, final version

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Cited by in corpus (15)

• Hofstadter Topology: Non-crystalline Topological Materials at High Flux
• Field-Tunable One-Sided Higher-Order Topological Hinge States in Dirac Semimetals
• Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries
• A Higher-Order Topological Insulator Phase in a Modulated Haldane Model
• Transition from metal to higher-order topological insulator driven by random flux
• Boundary-obstructed topological phases of a massive Dirac fermion in a magnetic field
• 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 Corner States in Graphene by Bulk and Edge Engineering
• Higher-order topological insulator in a modified Haldane-Hubbard model
• Topological analysis of the complex SSH model using the quantum geometric tensor
• Floquet topological phases with time-reversal and space inversion symmetries and dynamical detection of topological charges
• Coupled-wire construction of non-Abelian higher-order topological phases
• Hofstadter Butterflies in Topological Insulators