TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.3.114
TI  - Pfaffian invariant identifies magnetic obstructed atomic insulators
PY  - 2023/09/25
UR  - https://scipost.org/SciPostPhys.15.3.114
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 3
SP  - 114
A1  - Araya Day, Isidora
AU  - Varentcova, Anastasiia
AU  - Varjas, Daniel
AU  - Akhmerov, Anton R.
AB  - We derive a $\mathbb{Z}_4$ topological invariant that extends beyond symmetry eigenvalues and Wilson loops and classifies two-dimensional insulators with a $C_4 \mathcal{T}$ symmetry. To formulate this invariant, we consider an irreducible Brillouin zone and constrain the spectrum of the open Wilson lines that compose its boundary. We fix the gauge ambiguity of the Wilson lines by using the Pfaffian at high symmetry momenta. As a result, we distinguish the four $C_4 \mathcal{T}$-protected atomic insulators, each of which is adiabatically connected to a different atomic limit. We establish the correspondence between the invariant and the obstructed phases by constructing both the atomic limit Hamiltonians and a $C_4 \mathcal{T}$-symmetric model that interpolates between them. The phase diagram shows that $C_4 \mathcal{T}$ insulators allow $\pm 1$ and $2$ changes of the invariant, where the latter is overlooked by symmetry indicators.
ER  -

@Article{10.21468/SciPostPhys.15.3.114,
	title={{Pfaffian invariant identifies magnetic obstructed atomic insulators}},
	author={Isidora Araya Day and Anastasiia Varentcova and Daniel Varjas and Anton R. Akhmerov},
	journal={SciPost Phys.},
	volume={15},
	pages={114},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.3.114},
	url={https://scipost.org/10.21468/SciPostPhys.15.3.114},
}