Hybrid-order topology of weak topological insulators

Abstract

We consider weak topological insulators with a twofold rotation symmetry around their "dark" direction and show that these systems can be endowed with the topological crystalline structure of a higher-order topological insulator protected by rotation symmetry. These hybrid-order weak topological insulators display surface Dirac cones on all surfaces. Translational symmetry breaking perturbations gap the Dirac cones on the side surfaces leaving anomalous helical hinge modes behind. We also prove that the existence of this topological phase comes about due to a novel crystalline topological invariant of quantum spin-Hall insulators that can neither be revealed by symmetry indicators nor using Wilson loop invariants. Considering the minimal symmetry requirements, we anticipate that our findings could apply to a large number of weak topological insulators.

Unit cell distortion and surface morphology diversification in a SnTe/CdTe(001) topological crystalline insulator heterostructure: influence of defect azimuthal distribution

“…In the specific case of SnTe it is largely known both from theoretical modelling 16,17 and from experiment. 18 Theoretical analysis of the influence of crystal lattice distortions of various symmetries is shown, e.g. in the seminal paper by M. Serbyn and L. Fu.…”

The bulk-corner correspondence of time-reversal symmetric insulators

“…As shown in ref. 39, however, quantum spin-Hall phases in twofold rotation symmetric crystals are endowed with an additional topological Z 2 invariant, which cannot be probed at these topological defects. We will now show that the corner charge in the geometry of Fig.…”

“…However, for the physically relevant case of materials with spin-orbit coupling and timereversal symmetry eigenvalues-based schemes do suffer of intrinsic limitations. Topological crystalline phases with robust boundary modes may pass completely undetected 39 using the current classification schemes based on symmetry indicators [40][41][42][43][44] . Likewise, the real-space invariants originally introduced in ref.…”

Transport and spectral properties of magic angle twisted bilayer graphene junctions based on local orbital models

“…Lattice models suffer, however, of the so-called Wannier obstructions [21][22][23][24][25][26] which prevent the description of topological bands in terms of local orbitals. While simple low energy two bands models were proposed which avoid this problem by neglecting certain symmetries [27], so called "faithful" tight-binding (TB) models including higher energy bands are able to account properly for the fragile topology [28][29][30][31][32][33][34] of the low energy bands [24,35]. Other models have been proposed mixing real and momentum space descriptions [36], or including both valleys in a two-band description [37].…”