Disclination classes, fractional excitations, and the melting of quantum liquid crystals

Abstract

We consider how fractional excitations bound to a dislocation evolve as the dislocation is separated into a pair of disclinations. We show that some dislocation-bound excitations (such as Majorana modes and half-quantum vortices) are possible only if the elementary dislocation consists of two inequivalent disclinations, as is the case for stripes or square lattices but not for triangular lattices. The existence of multiple inequivalent disclination classes governs the two-dimensional melting of quantum liquid crystals (i.e., nematics and hexatics), determining whether superfluidity and orientational order can simultaneously vanish at a continuous transition.

6 pages, 5 figures

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• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Fracton-Elasticity Duality
• Classification of Two Dimensional Topological Crystalline Superconductors and Majorana Bound States at Disclinations
• Higher order symmetry-protected topological states for interacting bosons and fermions
• Quantum quasicrystals of spin-orbit coupled dipolar bosons
• Torsion, Parity-odd Response and Anomalies in Topological States
• Crystal-to-Fracton Tensor Gauge Theory Dualities
• Fractonic line excitations : an inroad from 3d elasticity theory
• Unconventional Fusion and Braiding of Topological Defects in a Lattice Model
• Majorana modes in emergent-wire phases of helical and cycloidal magnet-superconductor hybrids
• Possible quantum liquid crystal phases of helium monolayers
• Microscopic prediction of skyrmion lattice state in clean interface superconductors
• Corner states of topological fullerenes
• Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors
• Interaction Enabled Topological Crystalline Phases
• Stripe melting, a transition between weak and strong symmetry protected topological phases
• Intertwined and vestigial order with ultracold atoms in multiple cavity modes
• Boundary edge networks induced by bulk topology
• Condensation of Lattice Defects and Melting Transitions in Quantum Hall phases
• Geometry defects in Bosonic symmetry protected topological phases
• Universal quantum computing with parafermions assisted by a half fluxon
• Gravitational Response of Topological Quantum States of Matter
• Additive rule of real and reciprocal space topologies at disclinations
• Topological Field Theories of Three-Dimensional Rotation Symmetric Insulators: Coupling Curvature and Electromagnetism