2024/05/23 by Q. He, Zhang, Jie, He, Qinghua +5
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Photorefractive and Nonlinear Optics #Superconductivity (cond-mat.supr-con) #Topological Materials and Phenomena #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2405.14165
openalex publication_date 2024/05/23 · openalex created_date 2024/05/25 · openalex updated_date 2026/07/31
Nonsymmorphic symmetries can enforce band connectivity that obstructs a single-band Wannier description. We show that a fractional translation 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 L is combined with certain point-group symmetries (notably C4 and C3), 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 Möbius-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.