Topological zero-dimensional defect and flux states in three-dimensional insulators

Abstract

In insulating crystals, it was previously shown that defects with two fewer dimensions than the bulk can bind topological electronic states. We here further extend the classification of topological defect states by demonstrating that the corners of crystalline defects with integer Burgers vectors can bind 0D higher-order end (HEND) states with anomalous charge and spin. We demonstrate that HEND states are intrinsic topological consequences of the bulk electronic structure and introduce new bulk topological invariants that are predictive of HEND dislocation states in solid-state materials. We demonstrate the presence of first-order 0D defect states in PbTe monolayers and HEND states in 3D SnTe crystals. We relate our analysis to magnetic flux insertion in insulating crystals. We find that π-flux tubes in inversion- and time-reversal-symmetric (helical) higher-order topological insulators bind Kramers pairs of spin-charge-separated HEND states, which represent observable signatures of anomalous surface half quantum spin Hall states.

Effective action approach to the filling anomaly in crystalline topological matter

“…IV. Our work can also be extended to (interacting and noninteracting) time-reversal invariant HOTI phases in 2D, where we expect to find spinresolved responses [112][113][114] and charge-neutral defect states [56,69]. Such an extension would be particularly relevant to experimental searches for non-magnetic obstructed atomic limit phases [115][116][117].…”

“…At the same time, recent work has indicated thatin addition to quantized multipole moments-twodimensional HOTIs can host nontrivial excitations on lattice defects in the bulk [65][66][67][68][69][70][71]. Particularly relevant for this work, it has been shown that for magnetic (timereversal breaking) C 2n -symmetric HOTIs, disclination defects in the bulk with deficit angle π/n bind fractional electric charge (fractional fermion number).…”

Continuously tunable topological defects and topological edge states in dielectric photonic crystals

“…where P plays a role similar to the weak index of 3D topological insulators [62]. Finite ν introduces an effective equivalent flux around the defect core according to the K − B − t rule [36,65].…”

“…) in terms of b 1 and b 2 effectively. For the nontrivial phase where topological edge states appear, we have P = 1 2 (b 1 + b 2 ), similar to the weak index of three-dimensional topological insulators [62]. Alternatively, the nest-Wilson loop can also be used for characterizing the obstructed atomic phase of the designed photonic crystal [63,64].…”

Anomalous flux state in higher-order topological superconductors

“…Previous works have established that higher-order topological insulators and superconductors can be probed by their geometric responses, such as the creation of lattice defects like dislocations or disclinations. By creating these defects, one can observe Majorana zero modes inside the disclination point in two dimensions or chiral fermion modes localized at the dislocation/disclination lines in three dimensions [9,[33][34][35][36][37][38][39]. In contrast to these approaches, which are primarily based on the non-interacting limit, we aim to identify the universal fingerprints and topological responses specifically for strongly interacting higher-order topological superconductor (HOTSC) phases.…”