One-dimensional $2^n$-root topological insulators and superconductors

Abstract

Square-root topology is a recently emerged subfield describing a class of insulators and superconductors whose topological nature is only revealed upon squaring their Hamiltonians, i.e., the finite energy edge states of the starting square-root model inherit their topological features from the zero-energy edge states of a known topological insulator/superconductor present in the squared model. Focusing on one-dimensional models, we show how this concept can be generalized to $2^n$-root topological insulators and superconductors, with $n$ any positive integer, whose rules of construction are systematized here. Borrowing from graph theory, we introduce the concept of arborescence of $2^n$-root topological insulators/superconductors which connects the Hamiltonian of the starting model for any $n$, through a series of squaring operations followed by constant energy shifts, to the Hamiltonian of the known topological insulator/superconductor, identified as the source of its topological features. Our work paves the way for an extension of $2^n$-root topology to higher-dimensional systems.

19 pages, 15 figures

References in corpus (48)

• Topological Insulators
• Unpaired Majorana fermions in quantum wires
• Quantized Electric Multipole Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Bosonic Condensation and Disorder-Induced Localization in a Flat Band
• Coherent driving and freezing of bosonic matter wave in an optical Lieb lattice
• Experimental observation of Aharonov-Bohm cages in photonic lattices
• End states, ladder compounds, and domain wall fermions
• Topological characterization of chiral models through their long time dynamics
• Topological edge states of interacting photon pairs emulated in a topolectrical circuit
• Topological tight-binding models from non-trivial square roots
• Realization of the square-root higher-order topological insulator in electric circuits
• Exact holographic mapping and emergent space-time geometry
• Aspects of Chiral Symmetry and the Lattice
• Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices
• Square-root higher-order topological insulator on a decorated honeycomb lattice
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization
• Acoustic square-root topological insulators
• Topology and interactions in the photonic Creutz and Creutz-Hubbard ladders
• Observation of Antichiral Edge States in a Circuit Lattice
• Experimental observation of Aharonov-Bohm caging using orbital angular momentum modes in optical waveguides
• Nonlinear dynamics of Aharonov-Bohm cages
• Topological edge states with ultracold atoms carrying orbital angular momentum in a diamond chain
• Systematic construction of square-root topological insulators and superconductors
• Designer Flat Bands in Quasi-One-Dimensional Atomic Lattices
• Nonlinear caging in All-Bands-Flat Lattices
• Multihole edge states in Su-Schrieffer-Heeger chains with interactions
• One-dimensional topological insulators with noncentered inversion symmetry axis
• Machine Learning Holographic Mapping by Neural Network Renormalization Group
• Square-root topological semimetals
• Second-order topological corner states with ultracold atoms carrying orbital angular momentum in optical lattices
• Holographic duality between $(2+1)$-d quantum anomalous Hall state and $(3+1)$-d topological insulators
• Topological edge states and Aharanov-Bohm caging with ultracold atoms carrying orbital angular momentum
• Quantum Caging in Interacting Many-Body All-Bands-Flat Lattices
• Exact holographic mapping in free fermion systems
• Interaction-induced topological properties of two bosons in flat-band systems
• Non-Abelian braiding of Majorana-like edge states and topological quantum computations in electric circuits
• Topological bound states in interacting Su-Schrieffer-Heeger rings
• Extended flat-bands, entanglement and topological properties in a Creutz ladder
• Matryoshka approach to Sine-Cosine topological models
• Interaction induced doublons and embedded topological subspace in a complete flat-band system
• Analytical solution of open crystalline linear 1D tight-binding models
• Influence of different disorder types on Aharonov-Bohm caging in the diamond chain
• Engineering topological phase transition and Aharonov-Bohm caging in a flux-staggered lattice
• Non-Abelian Aharonov-Bohm Caging in Photonic Lattices
• Enhanced repulsively bound atom pairs in topological optical lattice ladders
• Edge States of a Periodic Chain with Four-Band Energy Spectrum
• Flat-band full localization and symmetry-protected topological phase on bilayer lattice systems

Cited by in corpus (28)

• Square-root higher-order Weyl semimetals
• Observation of pi/2 modes in an acoustic Floquet system
• Non-Hermitian Floquet Topological Matter -- A Review
• $2^n$-root weak, Chern, and higher-order topological insulators, and $2^n$-root topological semimetals
• Square-root Floquet topological phases and time crystals
• Long-range hopping and indexing assumption in one-dimensional topological insulators
• Topological properties of a class of Su-Schrieffer-Heeger variants
• Higher-Order Topological Insulator on a Martini Lattice and Its Square Root Descendant
• Kaleidoscopes of Hofstadter Butterflies and Aharonov-Bohm caging from $2^n$-root topology in decorated square lattices
• Isolated flat bands in 2D lattices based on a novel path-exchange symmetry
• Local Hilbert space fragmentation and weak thermalization in Bose-Hubbard diamond necklaces
• Topological $n$-root Su-Schrieffer-Heeger model in a non-Hermitian photonic ring system
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
• Topological properties of a class of generalized Su-Schrieffer-Heeger networks: chains and meshes
• Space-time symmetry and nonreciprocal parametric resonance in mechanical systems
• Kitaev Chain with a Fractional Twist
• A non-Hermitian Su-Schrieffer-Heeger model with the energy levels of free parafermions
• Impurity flat band states in the diamond chain
• Generalized Majorana edge modes in a number-conserving periodically driven $p$-wave superconductor
• Flat bands and topological phase transition in entangled Su-Schrieffer-Heeger chains
• Hidden topology in flat-band topological insulators: Strong, weak and square-root topological states
• High-root topological edge-state bands
• Topological phase transition and its stability against an applied magnetic field in a class of low dimensional decorated lattices
• Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars
• Exceptional horns in $n$-root graphene and Lieb photonic ring lattices
• $q$th-root non-Hermitian Floquet topological insulators
• Realization of second-order photonic square-root topological insulators