Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems

Abstract

A criterion to determine the existence of zero-energy edge states is discussed for a class of particle-hole symmetric Hamiltonians. A ``loop'' in a parameter space is assigned for each one-dimensional bulk Hamiltonian, and its topological properties, combined with the chiral symmetry, play an essential role. It provides a unified framework to discuss zero-energy edge modes for several systems such as fully gapped superconductors, two-dimensional d-wave superconductors, and graphite ribbons. A variants of the Peierls instability caused by the presence of edges is also discussed.

Completely rewritten. Discussions on coexistence of is- or id_{xy}-wave order parameter near edges in d_{x^{2}-y^{2}}-wave superconductors are added; 4 pages, 3 figures

References in corpus (1)

• Topological Quantum Phase Transitions in Superconductivity on Lattices

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• Tunable zero modes and quantum interferences in flat-band topological insulators
• Topology and $\mathcal{P}\mathcal{T}$ Symmetry in a Non-Hermitian Su-Schrieffer-Heeger Chain with Periodic Hopping Modulation
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping
• Gauge fields induced by curved spacetime
• Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators
• Non-Hermitian topological filters
• Dynamic Moiré-like pattern in non-Hermitian Wannier-Stark ladder system
• Anomalous Bloch oscillation and electrical switching of edge magnetization in bilayer graphene nanoribbon
• Topological quantum slinky motion in resonant extended Bose-Hubbard model
• Impurity strength-temperature phase diagram with phase crystals and competing time-reversal symmetry breaking states in nodal $d$-wave superconductors
• Van Hove Singularities and Excited-State Quantum Phase Transitions in Graphene-like Microwave Billiards
• Strengthened correlations near [110] edges of $d$-wave superconductors in the t-J model with the Gutzwiller approximation
• Zero energy modes with Gaussian, exponential, or polynomial decay: Exact solutions in hermitian and nonhermitian regimes
• Floquet topological phases with high Chern numbers in a periodically driven extended Su-Schrieffer-Heeger model
• Surface Structure and Surface State of a Tight-Binding Model on a Diamond Lattice
• Shannon Entropy and Diffusion Coeffcient in Parity-Time Symmetric Quantum Walks
• Spatiotemporal chaos in the interface growth of topological insulators
• Josephson junctions of topological nodal superconductors
• Detecting ground-state degeneracy in many-body systems through qubit decoherence
• Zero-Field Surface Charge Due to the Gap Suppression in $d$-Wave Superconductors
• Direct Observation of the Zigzag Edge States of a Supramolecular Diatomic Kagome Lattice
• Quantized Spin Hall Effect in Three-Dimensional Nodal-Ring Semimetal: Geometric Scaling and Symmetry-Engineered Spin Response
• The fate of disorder in twisted bilayer graphene near the magic angle
• Surface states of gapped electron systems and semi-metals
• Hidden chiral symmetry protected $\mathbb{Z}\oplus \mathbb{Z}$ topological insulators in a ladder dimer model
• Exact solutions for topological surface states of three-dimensional lattice models
• Bound-like State in a 1D Self-Similar Delta-Barrier Array
• Higher-order topological quantum paramagnets
• Position space formulation for Dirac fermions on honeycomb lattice
• Topologically nontrivial multicritical points