Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors

Abstract

We study a link between the ground-state topology and the topology of the lattice via the presence of anomalous states at disclinations -- topological lattice defects that violate a rotation symmetry only locally. We first show the existence of anomalous disclination states, such as Majorana zero-modes or helical electronic states, in second-order topological phases by means of Volterra processes. Using the framework of topological crystals to construct $d$-dimensional crystalline topological phases with rotation and translation symmetry, we then identify all contributions to $(d-2)$-dimensional anomalous disclination states from weak and first-order topological phases. We perform this procedure for all Cartan symmetry classes of topological insulators and superconductors in two and three dimensions and determine whether the correspondence between bulk topology, boundary signatures, and disclination anomaly is unique.

v3: 45 + 26 pages, 16 + 7 figures, minor revision for clarifications and improved readability. v2: 38 + 25 pages, 15 + 7 figures, format for scipost submission, updated references. v1: 19 + 15 pages, 15 + 7 figures

References in corpus (16)

• 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
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Topology of crystalline insulators and superconductors
• Helical Metal Inside a Topological Band Insulator
• Experimental discovery of bulk-disclination correspondence
• Genons, twist defects, and projective non-Abelian braiding statistics
• Disclinations, dislocations and continuous defects: a reappraisal
• Refined symmetry indicators for topological superconductors in all space groups
• Symmetry-based indicators for topological Bogoliubov-de Gennes Hamiltonians
• Higher-order topological band structures
• Dynamical solitons and boson fractionalization in cold-atom topological insulators
• Second-Order Bulk-Boundary Correspondence in Rotationally Symmetric Topological Superconductors from Stacked Dirac Hamiltonians
• Construction and classification of point group symmetry protected topological phases in 2D interacting fermionic systems
• Unconventional Majorana fermions on the surface of topological superconductors protected by rotational symmetry

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• Quasicrystalline second-order topological semimetals
• Effective field theories of topological crystalline insulators and topological crystals
• Higher-order topological semimetals and nodal superconductors with an order-two crystalline symmetry
• Cataloging topological phases of $N$-stacked Su-Schrieffer-Heeger chains by a systematic breaking of symmetries
• Thermodynamic transitions and topology of spin-triplet superconductivity: Application to UTe${}_2$
• Effective action approach to the filling anomaly in crystalline topological matter
• Emergent metallicity at the grain boundaries of higher-order topological insulators
• Additive rule of real and reciprocal space topologies at disclinations
• Pentagonal nanowires from topological crystalline insulators: a platform for intrinsic core-shell nanowires and higher-order topology
• Topological electronic structure of twin boundaries and twinning superlattices in the SnTe material class
• Scattering theory of higher order topological phases
• Topological magnonic dislocations modes
• Impurity-induced Mott ring states and Mott zeros ring states in the Hubbard operator formalism
• Electronic structure and hinge states of strained half-Heusler compounds LiSbZn and LiBiZn