The higher-order topological phases have attracted intense attention in the past years,
which reveals various intriguing topological properties. Meanwhile, the enrichment of group …

We present impelling evidence of topological phase transitions induced by electron-phonon
(e-ph) coupling in an α-T 3 Haldane-Holstein model that facilitates smooth tunability …

Internal and crystalline symmetries play critical roles in the classification of topological
materials. Recently, the crystalline symmetries are found to allow projective representations …

The Bloch band theory and Brillouin zone (BZ) that characterize wave-like behaviors in
periodic mediums are two cornerstones of contemporary physics, ranging from condensed …

The topological simulation of acoustic waves has induced unconventional propagation
characteristics, thereby offering extensive application potential in the field of acoustics. In …

Braiding is a geometric concept that manifests itself in a variety of scientific contexts from
biology to physics, and has been employed to classify bulk band topology in topological …

In the field of symmetry-protected topological phases, a common wisdom is that the
symmetries may fix the nontrivial topological classifications, but they alone cannot determine …

We theoretically construct a higher-order topological insulator (HOTI) on a Brillouin real
projective plane enabled by momentum-space nonsymmorphic (k-NS) symmetries from …

Spin angular momentum (SAM) and orbital angular momentum (OAM) are fundamental
physical characteristics described by polarization and spatial degrees of freedom …

The manifold of the fundamental domain of the Brillouin zone is always considered to be a
torus. However, under the synthetic gauge field, the Brillouin manifold can be modified by …