Systematic construction of square-root topological insulators and superconductors

Abstract

We propose a general scheme to construct a Hamiltonian $H_{\text{root}}$ describing a square root of an original Hamiltonian $H_{\text{original}}$ based on the graph theory. The square-root Hamiltonian is defined on the subdivided graph of the original graph of $H_{\text{original}}$, where the subdivided graph is obtained by putting one vertex on each link in the original graph. When $H_{\text{original}}$ describes a topological system, there emerge in-gap edge states at non-zero energy in the spectrum of $H_{\text{root}}$, which are the inherence of the topological edge states at zero energy in $H_{\text{original}}$. In this case, $H_{\text{root}}$ describes a square-root topological insulator or superconductor. Typical examples are square roots of the Su-Schrieffer-Heeger (SSH) model, the Kitaev topological superconductor model and the Haldane model. Our scheme is also applicable to non-Hermitian topological systems, where we study an example of a nonreciprocal non-Hermitian SSH model.

arXiv comment6 pages, 4 figures

References in corpus (32)

• Topological Insulators
• Topological insulators and superconductors
• Unpaired Majorana fermions in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Edge states and topological invariants of non-Hermitian systems
• Quantized Electric Multipole Insulators
• Search for Majorana fermions in superconductors
• Higher-Order Topological Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Anomalous edge state in a non-Hermitian lattice
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topolectrical circuit realization of topological corner modes
• Reflection symmetric second-order topological insulators and superconductors
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Acoustic higher-order topological insulator on a Kagome lattice
• Introduction to topological superconductivity and Majorana fermions
• Topolectrical circuits
• Flat bands and Wigner crystallization in the honeycomb optical lattice
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Topologically protected midgap states in complex photonic lattices
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• Minimal model for higher-order topological insulators and phosphorene
• Exact low-temperature behavior of kagome antiferromagnet at high fields
• Higher-order topological electric circuits and topological corner resonance on the breathing Kagome and pyrochlore lattices
• Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization
• Rotation Anomaly and Topological Crystalline Insulators
• Boundary Green functions of topological insulators and superconductors
• Topological tight-binding models from non-trivial square roots
• Electric-circuit simulation of the Schrödinger equation and non-Hermitian quantum walks
• Electric circuits for universal quantum gates and quantum Fourier transformation

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• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
• Supersymmetry dictated topology in periodic gauge fields and realization in strained and twisted 2D materials
• Topological states constructed by two different trivial quantum wires
• Generalized Majorana edge modes in a number-conserving periodically driven $p$-wave superconductor
• A non-Hermitian Su-Schrieffer-Heeger model with the energy levels of free parafermions
• Exceptionally deficient topological square-root insulators
• High-root topological edge-state bands
• $q$th-root non-Hermitian Floquet topological insulators
• Exceptional horns in $n$-root graphene and Lieb photonic ring lattices
• Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars