Band-Structure-Independent Topology from Nonsymmorphic Wannier Complexes

TL;DR

This paper introduces a new topological classification of Wannier complexes arising from nonsymmorphic symmetries, revealing robust boundary phenomena and polarization quantization independent of band structure details.

Contribution

It develops a real-space topological classification of Wannier complexes influenced by nonsymmorphic symmetries and fractional translations, highlighting their universal boundary signatures.

Findings

Wannier complexes require multiband descriptions due to nonsymmorphic symmetries.

All allowed Wannier complexes with certain symmetries have quantized electric polarization.

Boundary phenomena persist across various Hamiltonian deformations, including gapless regimes.

Abstract

Nonsymmorphic symmetries can enforce band connectivity that obstructs a single-band Wannier description. We show that a fractional translation $\mathcal{L}$ connecting distinct high-symmetry Wyckoff positions generically renders the Wannier center of an individual band gauge ill-defined, requiring a symmetry-enforced multiband object -- a Wannier complex. We formulate a real-space topological classification of Wannier complexes and show that, when $\mathcal{L}$ is combined with certain point-group symmetries (notably $C_4$ and $C_3$), all symmetry-allowed Wannier-complex configurations carry a nontrivial quantized total electric polarization. This yields boundary phenomena that persist across symmetry-preserving deformations of the Hamiltonian, including parameter regimes with and without bulk gaps. We demonstrate the mechanism in minimal tight-binding models exhibiting M{\"o}bius-twisted Wilson-loop structures and higher-order corner modes, and propose experimental signatures in a dielectric photonic crystal and a first-principles electronic platform octa-graphene, accompanied by a three-dimensional extension.