ZQ Berry phase for higher-order symmetry-protected topological phases
@article{Araki2020ZQB, title={ZQ Berry phase for higher-order symmetry-protected topological phases}, author={Hiromu Araki and Tomonari Mizoguchi and Yasuhiro Hatsugai}, journal={Physical Review Research}, year={2020} }
We propose the $\mathbb{Z}_Q$ Berry phase as a topological invariant for higher-order symmetry-protected topological (HOSPT) phases for two- and three-dimensional systems. It is topologically stable for electron-electron interactions assuming the gap remains open. As a concrete example, we show that the Berry phase is quantized in $\mathbb{Z}_4$ and characterizes the HOSPT phase of the extended Benalcazar-Bernevig-Hughes (BBH) model, which contains the next-nearest neighbor hopping and the…
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References
SHOWING 1-10 OF 99 REFERENCES
Z_{N} Berry Phases in Symmetry Protected Topological Phases.
- PhysicsPhysical review letters
- 2018
We show that the Z_{N} Berry phase (Berry phase quantized into 2π/N) provides a useful tool to characterize symmetry protected topological phases with correlation that can be directly computed…
Higher-order bosonic topological phases in spin models
- PhysicsPhysical Review B
- 2019
We discuss an extension of higher-order topological phases to include bosonic systems. We present two spin models for a second-order topological phase protected by a global…
ZN
Berry phase and symmetry-protected topological phases of the SU(
N
) antiferromagnetic Heisenberg chain
- PhysicsPhysical Review B
- 2018
The local Z_N quantized Berry phase for the SU(N) antiferromagnetic Heisenberg spin model is formulated. This quantity, which is a generalization of the local Z_2 Berry phase for SU(2) symmetry, has…
Möbius topological superconductivity in UPt 3
- Physics
- 2017
Intensive studies for more than three decades have elucidated multiple superconducting phases and odd-parity Cooper pairs in a heavy fermion superconductor UPt$_3$. We identify a time-reversal…
Higher-order symmetry-protected topological states for interacting bosons and fermions
- PhysicsPhysical Review B
- 2018
Higher-order topological insulators have a modified bulk-boundary correspondence compared to other topological phases: instead of gapless edge or surface states, they have gapped edges and surfaces,…
Symmetry protection of topological phases in one-dimensional quantum spin systems
- Physics
- 2012
We discuss the characterization and stability of the Haldane phase in integer spin chains on the basis of simple, physical arguments. We find that an odd-S Haldane phase is a topologically nontrivial…
Classification of topological insulators and superconductors in three spatial dimensions
- Physics
- 2008
We systematically study topological phases of insulators and superconductors (or superfluids) in three spatial dimensions. We find that there exist three-dimensional (3D) topologically nontrivial…
Colloquium : Topological insulators
- Physics
- 2010
Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. These states are possible due to…
Higher-Order Topology in Bismuth
- PhysicsNature physics
- 2018
It is established that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk–boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes.
Quantization of fractional corner charge in
Cn
-symmetric higher-order topological crystalline insulators
- PhysicsPhysical Review B
- 2019
In the presence of crystalline symmetries, certain topological insulators present a filling anomaly: a mismatch between the number of electrons in an energy band and the number of electrons required…