Higher-order topological phases on fractal lattices

Abstract

Electronic materials harbor a plethora of exotic quantum phases, ranging from unconventional superconductors to non-Fermi liquids, and, more recently, topological phases of matter. While these quantum phases in integer dimensions are well characterized by now, their presence in fractional dimensions remains vastly unexplored. Here, we theoretically show that a special class of crystalline phases, namely, higher-order topological phases that via an extended bulk-boundary correspondence feature robust gapless modes on lower dimensional boundaries, such as corners and hinges, can be found on a representative family of fractional materials: \emph{quantum fractals}. To anchor this general proposal, we demonstrate realizations of second-order topological insulators and superconductors, supporting charged and neutral Majorana corner modes, on planar Sierpiński carpet and triangle fractals, respectively. These predictions can be experimentally tested on designer electronic fractal materials, as well as on various highly tunable metamaterial platforms, such as photonic and acoustic lattices.

Published version: 6+epsilon Pages, 3 Figures (Supplementary Material as ancillary file)

References in corpus (15)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• 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
• Photonic Floquet topological insulators in a fractal lattice
• 3D hinge transport in acoustic higher-order topological insulators
• Realization of quasicrystalline quadrupole topological insulators in electrical circuits
• Higher-order topological states mediated by long-range coupling in $D_4$-symmetric lattices
• A Higher-Order Topological Insulator Phase in a Modulated Haldane Model
• Floquet higher-order Weyl and nexus semimetals
• Bulk-boundary correspondence in disordered higher-order topological insulators
• Controlling Majorana modes by $p$-wave pairing in two-dimensional $p+id$ topological superconductors
• Higher-Order Topological Superconductivity in Twisted Bilayer Graphene
• Observation of fractal topological states in acoustic metamaterials
• Higher-order topological phase in an acoustic fractal lattice

Cited by in corpus (43)

• Inner Skin Effects on Non-Hermitian Topological Fractals
• Higher-order topological insulators in hyperbolic lattices
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Observation of nonlinear fractal higher-order topological insulator
• Topological edge and corner states in Bi fractals on InSb
• Noncrystalline topological superconductors
• Haldane model on the Sierpiński gasket
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
• Non-Hermitian Quantum Fractals
• Gapless higher-order topology and corner states in Floquet systems
• Multi higher-order Dirac and nodal line semimetals
• Loop current states and their stability in small fractal lattices of Bose-Einstein condensates
• Corner and Edge States in Topological Sierpinski Carpet Systems
• Anomalous quantum transport in fractal lattices
• Many-body localization on finite generation fractal lattices
• Higher-order topology in twisted multilayer systems: a review
• Josephson effect in a fractal geometry
• Topological Phases in Fractals: Local Spin Chern Marker in the Sierpinski carpet Kane-Mele-Rashba Model
• Two-dimensional orbital-obstructed insulators with higher-order band topology
• Unconventional hybrid-order topological insulators
• Topological insulators on fractal lattices: A general principle of construction
• A new class of higher-order topological insulators that localize energy at arbitrary multiple sites
• Entanglement Fractalization
• The Fractal-Lattice Hubbard Model
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- part II: Higher-dimensional spectral invariants
• Higher-order topological phases for time-reversal-symmetry breaking superconductivity in UTe${}_2$
• Properties of Laughlin states on fractal lattices
• Bose-Einstein condensation in exotic lattice geometries
• Quasiperiodic Quadrupole Insulators
• Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry
• Thresholdless corner vortex solitons in fractal Sierpiński topological insulators
• Network model for magnetic higher-order topological phases
• Interaction-Induced Higher-Order Topological Insulator via Floquet Engineering
• Resonant helical multi-edge transport in Sierpiński carpets
• The Quadrupole Moment of Higher-Order Topological Insulator at Finite temperature
• Tunable cornerlike states in topological type-II hyperbolic lattices
• Zeeman field induced corner states in the Kane-Mele-Hubbard model
• Nodal higher-order topological superconductivity from C6-symmetric Dirac semimetals
• Topological states and flat bands in exactly solvable decorated Cayley trees
• Coupled-wire construction of non-Abelian higher-order topological phases
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Higher-order topological phases protected by noninvertible and subsystem symmetries
• Breakdown of the symmetry constraint in a Floquet topological insulator