# Hybrid-order topology of weak topological insulators

@article{Kooi2020HybridorderTO, title={Hybrid-order topology of weak topological insulators}, author={Sander H. Kooi and Guido van Miert and Carmine Ortix}, journal={Physical Review B}, year={2020}, volume={102}, pages={041122} }

We consider weak topological insulators with a twofold rotation symmetry around the 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…

## 5 Citations

The bulk-corner correspondence of time-reversal symmetric insulators

- 2021

The topology of insulators is usually revealed through the presence of gapless boundary modes: this is the so-called bulk-boundary correspondence. However, the many-body wavefunction of a crystalline…

Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals

- Physics
- 2021

We give a bulk-hinge correspondence for higher-order topological phases protected by rotoinversion C4I symmetry in magnetic systems. Our approach allows us to show the emergence of the chiral hinge…

Homotopy invariant in time-reversal and twofold rotation symmetric systems

- Physics
- 2021

The primary goal of this paper is to study topological invariants in two dimensional twofold rotation and time-reversal symmetric spinful systems. In this paper, firstly we build a new homotopy…

Higher-Order Weyl Semimetals.

- Physics, MedicinePhysical review letters
- 2020

A new type of Weyl node is identified that can be identified as a transition in momentum space in which both the Chern number and a higher order topological invariant change are identified.

Higher-Order Weyl Semimetals.

- Physics, MedicinePhysical review letters
- 2020

Higher-order Weyl semimetals manifest themselves uniquely by exhibiting concurrent chiral Fermi-arc surface states, topological hinge states, and the momentum-dependent fractional hinge charge, revealing a novel class of higher-order topological phases.

## References

SHOWING 1-10 OF 71 REFERENCES

Topological crystalline insulators.

- Physics, MedicinePhysical review letters
- 2011

A class of three-dimensional "topological crystalline insulators" which have metallic surface states with quadratic band degeneracy on high symmetry crystal surfaces is found.

Higher-order topological insulators protected by inversion and rotoinversion symmetries

- PhysicsPhysical Review B
- 2018

We provide the bulk topological invariant for chiral higher-order topological insulators in (i) fourfold rotoinversion invariant bulk crystals, and (ii) inversion-symmetric systems with or without an…

Higher-order topological insulators

- Physics, MedicineScience Advances
- 2018

The notion of three-dimensional topological insulators is extended to systems that host no gapless surface states but exhibit topologically protected gapless hinge states and it is shown that SnTe as well as surface-modified Bi2TeI, BiSe, and BiTe are helical higher-order topology insulators.

New classes of topological crystalline insulators having surface rotation anomaly

- Medicine, PhysicsScience Advances
- 2019

It is shown that these anomalous states are physically realized on the surface of new classes of topological crystalline insulators, normal to the rotation axis, connecting the anomalous two-dimensional states on the top and bottom surfaces.

Inversion-symmetric topological insulators

- Physics
- 2011

We analyze translationally invariant insulators with inversion symmetry that fall outside the current established classification of topological insulators. These insulators exhibit no edge or surface…

One-dimensional Dirac electrons on the surface of weak topological insulators

- Physics
- 2015

We show that a class of weak three-dimensional topological insulators feature one-dimensional Dirac electrons on their surfaces. Their hallmark is a linelike energy dispersion along certain…

Topological mirror insulators in one dimension

- Physics
- 2016

We demonstrate the existence of topological insulators in one dimension (1D) protected by mirror and time-reversal symmetries. They are characterized by a nontrivial ${\mathbb{Z}}_{2}$ topological…

Purely rotational symmetry-protected topological crystalline insulator $\alpha$ -Bi
4
Br
4

- Materials Science, Physics2D Materials
- 2019

Recent theoretical advances have proposed a new class of topological crystalline insulator (TCI) phases protected by rotational symmetries. Distinct from topological insulators (TIs), rotational…

Topological insulators with inversion symmetry

- Physics
- 2007

Topological insulators are materials with a bulk excitation gap generated by the spin-orbit interaction that are different from conventional insulators. This distinction is characterized by ${Z}_{2}$…

Topology in time-reversal symmetric crystals

- PhysicsPhysical Review B
- 2019

The discovery of topological insulators has reformed modern materials science, promising to be a platform for tabletop relativistic physics, electronic transport without scattering, and stable…