Time-Reversal Soliton Pairs In Even Spin-Chern-Number Higher-Order Topological Insulators

Abstract

Solitons formed through the one-dimensional mass-kink mechanism on the edges of two-dimensional systems with non-trivial topology play an important role in the emergence of higher-order (HO) topological phases. In this connection, the existing work in time-reversal symmetric systems has focused on gapping the edge Dirac cones in the presence of particle-hole symmetry, which is not suited to the common spin-Chern insulators. Here, we address the emergence of edge solitons in spin-Chern number of $2$ insulators, in which the edge Dirac cones are gapped by perturbations preserving time-reversal symmetry but breaking spin-$U(1)$ symmetry. Through the mass-kink mechanism, we thus explain the appearance of pairwise corner modes and predict the emergence of extra charges around the corners. By tracing the evolution of the mass term along the edge, we demonstrate that the in-gap corner modes and the associated extra charges can be generated through the $S_z$-mixing spin-orbit coupling via the mass-kink mechanism. We thus provide strong evidence that an even spin-Chern-number insulator is an HO topological insulator with protected corner charges.

References in corpus (32)

• Classification of topological quantum matter with symmetries
• Bosonization and Strongly Correlated Systems
• Spin-filtered Edge States with an Electrically Tunable Gap in a Two-Dimensional Topological Crystalline Insulator
• Robustness of the Spin-Chern number
• The Fractional Quantum Hall effect in an array of quantum wires
• Topological Mirror Superconductivity
• Majorana Kramers pairs in higher-order topological insulators
• Tunable Majorana corner states in a two-dimensional second-order topological superconductor induced by magnetic fields
• Electric-Field Induced Majorana Fermions in Armchair Carbon Nanotubes
• Spin Charge Separation in the Quantum Spin Hall State
• Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop
• Spin-orbit coupling in interacting quasi-one-dimensional electron systems
• Majorana Kramers pairs in Rashba double nanowires with interactions and disorder
• Filling anomaly for general 2D and 3D $C_4$ symmetric lattices
• Kane-Mele with a twist: Quasicrystalline higher-order topological insulators with fractional mass kinks
• Emergent topological properties in interacting one-dimensional systems with spin-orbit coupling
• Helical Liquids in Semiconductors
• Antiferromagnetic nuclear spin helix and topological superconductivity in ${}^{13}$C nanotubes
• Generation of spin-polarized currents in Zeeman-split Tomonaga-Luttinger models
• Topological Zero-Dimensional Defect and Flux States in Three-Dimensional Insulators
• Fractional Conductance in Strongly Interacting 1D Systems
• Helical nuclear spin order in two-subband quantum wires
• Interaction induced topological protection in one-dimensional conductors
• Boundary edge networks induced by bulk topology
• Quantum spin Hall effect in rutile-based oxide multilayers
• Phase diagram of two interacting helical states
• Double-gap superconducting proximity effect in nanotubes
• Charge transport of a spin-orbit-coupled Luttinger liquid
• Fractional hinge and corner charges in various crystal shapes with cubic symmetry
• General scatterings and electronic states in the quantum-wire network of moiré systems
• Interplay between intrinsic and emergent topological protection on interacting helical modes
• General corner charge formulas in various tetrahedral and cubic space groups

Cited by in corpus (5)

• Two-Dimensional Higher-Order Topological Metals
• Orbital doublet driven even-spin Chern insulators
• Interaction- and phonon-induced topological phase transitions in double helical liquids
• Tunable Competing Electronic Orders in Double Quantum Spin Hall Superlattices
• Engineering Majorana Kramers Pairs In Synthetic High Spin Chern Insulators