Kane-Mele with a twist: Quasicrystalline higher-order topological insulators with fractional mass kinks

Abstract

We establish an analytic low-energy theory describing higher-order topological insulator (HOTI) phases in quasicrystalline systems. We apply this to a model consisting of two stacked Haldane models with oppositely propagating edge modes, analogous to the Kane-Mele model, and with a $30^{\circ }$ twist. We show that the resulting localized modes at corners, characteristic of a HOTI, are not associated with conventional mass inversions but are instead associated with what we dub "fractional mass kinks". By generalizing the low-energy theory, we establish a classification for arbitrary $n$-fold rotational symmetries. We also derive a relationship between corner modes in a bilayer and disclination modes in a single layer. By using numerics to go beyond the weak-coupling limit, we show that a hierarchy of additional gaps occurs due to the quasiperiodicity, which also harbor corner-localized modes.

11 pages, 8 figures

References in corpus (12)

• Topological Crystalline Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• The space group classification of topological band insulators
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Topological quantum matter in synthetic dimensions
• A fractional corner anomaly reveals higher-order topology
• Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
• Topological Hofstadter Insulators in a Two-Dimensional Quasicrystal
• Bound States of Conical Singularities in Graphene-Based Topological Insulators
• Boundary edge networks induced by bulk topology

Cited by in corpus (32)

• Classical higher-order topological insulators
• Higher-order topological phases on fractal lattices
• Higher-Order topological insulator in a dodecagonal quasicrystal
• Topological states in quasicrystals
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Higher-order topological Anderson insulators in quasicrystals
• Quantum many-body topology of quasicrystals
• Amorphous topological phases protected by continuous rotation symmetry
• Higher-order topological phases emerging from the Su-Schrieffer-Heeger stacking
• Topological Anderson insulators in an Ammann-Beenker quasicrystal and a snub-square crystal
• Average Symmetry Protected Higher-order Topological Amorphous Insulators
• Quasicrystalline second-order topological semimetals
• High-Angular-Momentum Topological Superconductivity in the Largest-Angle Twisted Homo-bilayer Systems
• Density-driven higher-order topological phase transitions in amorphous solids
• Role of the edges in a quasicrystalline Haldane model
• Colloquium: Synthetic quantum matter in non-standard geometries
• Topological quantum transition driven by charge-phonon coupling in higher-order topological insulators
• Quasiperiodic pairing in graphene quasicrystals
• Higher-dimensional Hofstadter butterfly on Penrose lattice
• Bilayer Haldane system: Topological characterization and adiabatic passages connecting Chern phases
• Confined states and topological phases in two-dimensional quasicrystalline $\pi$-flux model
• Time-Reversal Soliton Pairs In Even Spin-Chern-Number Higher-Order Topological Insulators
• Band engineered bilayer Haldane model: Evidence of multiple topological phase transitions
• Higher-order topology in twisted multilayer systems: a review
• Tunable corner states in topological insulators with long-range hoppings and diverse shapes
• Quasiperiodic Quadrupole Insulators
• Boundary topological insulators and superconductors of Altland-Zirnbauer tenfold classes
• Effects of the Vertices on the Topological Bound States in a Quasicrystalline Topological Insulator
• Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators
• Zeeman field induced corner states in the Kane-Mele-Hubbard model
• Tunable cornerlike states in topological type-II hyperbolic lattices
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal