Bulk-Defect Correspondence in Particle-Hole Symmetric Insulators and Semimetals

Abstract

Lattices with a basis can host crystallographic defects which share the same topological charge (e.g.~the Burgers vector $\vec{b}$ of a dislocation) but differ in their microscopic structure of the core. We demonstrate that in insulators with particle-hole symmetry and an odd number of orbitals per site, the microscopic details drastically affect the electronic structure: modifications can create or annihilate non-trivial bound states with an associated fractional charge. We show that this observation is related to the behavior of end modes of a dimerized chain and discuss how the end or defect states are predicted from topological invariants in these more complicated cases. Furthermore, using explicit examples on the honeycomb lattice, we explain how bound states in vacancies, dislocations and disclinations are related to each other and to edge modes and how similar features arise in nodal semimetals such as graphene.

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Cited by in corpus (23)

• Fractional disclination charge in two-dimensional $C_n-$symmetric topological crystalline insulators
• Bulk-boundary correspondence from the inter-cellular Zak phase
• Interplay between electronic topology and crystal symmetry: Dislocation-line modes in topological band-insulators
• Experimental realization of single-plaquette gauge flux insertion and topological Wannier cycles
• Topological dislocation modes in three-dimensional acoustic topological insulators
• Partial lattice defects in higher order topological insulators
• Non-Hermitian skin effect of dislocations and its topological origin
• Dislocation charges reveal two-dimensional topological crystalline invariants
• Bulk-edge and bulk-hinge correspondence in inversion-symmetric insulators
• Coexistence of Fermi arcs with two dimensional gapless Dirac states
• Obstructed insulators and flat bands in topological phase-change materials
• Bulk-boundary correspondence in extended trimer Su-Schrieffer-Heeger model
• Space group constraints on weak indices in topological insulators
• Floquet Mode Resonance: Trapping light in the bulk mode of a Floquet topological insulator by quantum self-interference
• Characterizing the weak topological properties: Berry phase point of view
• Field-sensitive dislocation bound states in two-dimensional $d$-wave altermagnets
• Topological Wannier cycles for the bulk and edges
• Additive rule of real and reciprocal space topologies at disclinations
• Observation of trapped fractional charge and topological states at disclination defects in higher-order topological insulators
• Scaling of critical wavefunctions at topological Anderson transitions in 1D
• Confinement-induced Majorana modes in a nodal topological superconductor
• Crystalline Weyl semimetal phase in Quantum Spin Hall systems under magnetic fields
• Designing atomic-scale resistive circuits in topological insulators through vacancy-induced localized modes