# 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…

## 21 Citations

Symmetry-Protected Zero Modes in Metamaterials Based on Topological Spin Texture

- Physics
- 2020

We predict the emergence of second-order topological insulators in the dynamics of spin-texture-based metamaterials. We propose that the quantized Chern number and the ${\mathbb{Z}}_{6}$ Berry phase…

Higher-order topological phases in a spring-mass model on a breathing kagome lattice

- PhysicsPhysical Review B
- 2020

We propose a realization of higher-order topological phases in a spring-mass model with a breathing kagome structure. To demonstrate the existence of the higher-order topological phases, we…

Second-order topological solitonic insulator in a breathing square lattice of magnetic vortices

- PhysicsPhysical Review B
- 2020

We study the topological phase in a dipolar-coupled two-dimensional breathing square lattice of magnetic vortices. By evaluating the quantized Chern number and ${\mathbb{Z}}_{4}$ Berry phase, we…

Floquet Second-Order Topological Phases in Momentum Space

- PhysicsNanomaterials
- 2021

A momentum-space counterpart of HOTPs is revealed in time-periodic driven systems, which is demonstrated in a two-dimensional extension of the quantum double-kicked rotor and protected by chiral symmetry and characterized by a pair of topological invariants.

Orbital corner states on breathing kagome lattices

- Physics
- 2020

We investigate the higher-order topological insulators on the breathing kagome lattices with $p$-orbital freedom. The bulk topological phase diagram is obtained by calculating the ${Z}_{3}$ Berry…

Higher-order topological Mott insulator on the pyrochlore lattice

- PhysicsScientific reports
- 2021

The first unbiased evidence for a higher-order topological Mott insulator in three dimensions is provided by numerically exact quantum Monte Carlo simulations and it is shown that the topological phase transition from the third-orderTopological MOTT insulator to the usual Mottinsulator occurs when the bulk spin gap solely closes.

First and second order topological phases on ferromagnetic breathing kagome lattice.

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2020

Topological properties of a ferromagnetic Heisenberg model on a breathing kagome lattice are investigated extensively in the presence of Dzyaloshinskii-Moriya interaction to identify several first and second order phases as well as their overlap.

Higher-order band topology

- Physics
- 2021

A conventional topological insulator (TI) has gapped bulk states but gapless edge states. The emergence of the gapless edge states is dictated by the bulk topological invariant of the insulator and…

Classical higher-order topological insulators.

- Physics
- 2020

Topological states nurtures the emergence of devices with unprecedented functions in photonics, plasmonics, acoustics and phononics. As one of the recently discovered members, higher-order…

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