# Topology invisible to eigenvalues in obstructed atomic insulators

@article{Cano2022TopologyIT, title={Topology invisible to eigenvalues in obstructed atomic insulators}, author={Jennifer Cano and Luis Elcoro and Mira Aroyo and Bogdan Andrei Bernevig and Barry Bradlyn}, journal={Physical Review B}, year={2022} }

Jennifer Cano, 2 L. Elcoro, M. I. Aroyo, B. Andrei Bernevig, and Barry Bradlyn Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11974, USA Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA Department of Condensed Matter Physics, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain Department of Physics, Princeton University, Princeton, New Jersey 08544, USA Department of Physics and Institute for…

## Figures and Tables from this paper

## 6 Citations

### Pfaffian invariant identifies magnetic obstructed atomic insulators

- Physics, Mathematics
- 2022

We derive a (cid:90) 4 topological invariant that extends beyond symmetry eigenvalues and Wilson loops and classiﬁes two-dimensional insulators with a C 4 T symmetry. To formulate this invariant, we…

### Orbital Shift‐Induced Boundary Obstructed Topological Materials with a Large Energy Gap

- PhysicsAdvanced science
- 2022

Boundary obstructed topological phases caused by Wannier orbital shift between ordinary atomic sites are proposed, which, however, cannot be indicated by symmetry eigenvalues at high symmetry momenta…

### Topological materials discovery from crystal symmetry

- Materials ScienceNature Reviews Materials
- 2021

Topological materials discovery has evolved at a rapid pace over the past 15 years following the identification of the first nonmagnetic topological insulators (TIs), topological crystalline…

### Interacting topological quantum chemistry of Mott atomic limits

- Physics
- 2022

Topological quantum chemistry (TQC) is a successful framework for identifying (non-interacting) topological materials. Based on the symmetry eigenvalues of Bloch eigenstates at high symmetry momenta,…

### Obstructed insulators and flat bands in topological phase-change materials

- Physics
- 2022

Phase-change materials are ubiquitous in technology because of their ability to transition between amorphous and crystalline phases fast and reversibly, upon shining light or passing a current. Here…

### General theory of Josephson Diodes

- Physics
- 2021

Motivated by recent progress in the superconductivity nonreciprocal phenomena, we study the general theory of Josephson diodes. The central ingredient for Josephson diodes is the asymmetric proximity…

## References

SHOWING 1-10 OF 27 REFERENCES

### Experimental Discovery of the First Nonsymmorphic Topological Insulator KHgSb

- Physics
- 2016

Topological Insulator KHgSb J.-Z. Ma, C.-J. Yi, B. Q. Lv, Z. J. Wang, S.-M. Nie, L. Wang, L.-Y. Kong, Y.-B. Huang, P. Richard, H.-M. Weng, B. A. Bernevig, Y.-G. Shi, T. Qian, and H. Ding 1 Beijing…

### Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals

- PhysicsScience
- 2016

The guiding principle of the classification is to find irreducible representations of the little group of lattice symmetries at high-symmetry points in the Brillouin zone for each of the 230 space groups (SGs), the dimension of which corresponds to the number of bands that meet at the high-Symmetry point.

### Quantized electric multipole insulators

- PhysicsScience
- 2017

This work introduces a paradigm in which “nested” Wilson loops give rise to topological invariants that have been overlooked and opens a venue for the expansion of the classification of topological phases of matter.

### Magnetic topological quantum chemistry

- Materials ScienceNature communications
- 2021

This work completes the 100-year-old problem of crystalline group theory by deriving the small core presentations, momentum stars, compatibility relations, and magnetic elementary band corepresentations of the 1,421 magnetic space groups (MSGs), which are made freely accessible through tools on the Bilbao Crystallographic Server.

### Wallpaper fermions and the nonsymmorphic Dirac insulator

- PhysicsScience
- 2018

It is shown that a consideration of symmetry-allowed band degeneracies in the wallpaper groups can be used to understand previously described topological crystalline insulators and to predict phenomenologically distinct examples.

### Hourglass fermions

- PhysicsNature
- 2016

This work finds that non-symmorphic symmetries protect an exotic surface fermion whose dispersion relation is shaped like an hourglass; surface bands connect one hourglass to the next in an unbreakable zigzag pattern.

### Topological quantum chemistry

- PhysicsNature
- 2017

A complete electronic band theory is proposed, which builds on the conventional band theory of electrons, highlighting the link between the topology and local chemical bonding and can be used to predict many more topological insulators.

### Topological crystalline insulators in the SnTe material class.

- Physics, Materials ScienceNature communications
- 2012

This work predicts the first material realization of topological crystalline insulator in the semiconductor SnTe by identifying its non-zero topological index and predicts that as a manifestation of this non-trivial topology, SnTe has metallic surface states with an even number of Dirac cones on high-symmetry crystal surfaces.

### Catalogue of topological electronic materials

- Materials ScienceNature
- 2019

An effective, efficient and fully automated algorithm that diagnoses the nontrivial band topology in a large fraction of nonmagnetic materials is introduced, based on recently developed exhaustive mappings between the symmetry representations of occupied bands and topological invariants.

### New classes of topological crystalline insulators having surface rotation anomaly

- 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.