Non-Abelian phenomena arise when the sequence of operations on physical systems
influences their behaviors. By possessing internal degrees of freedom such as polarization …

As a fundamental concept of all crystals, space groups are partitioned into symmorphic
groups and nonsymmorphic groups. Each nonsymmorphic group contains glide reflections …

Non-Abelian gauge fields are versatile tools for synthesizing topological phenomena, but
have so far been mostly studied in Hermitian systems, where gauge flux has to be defined …

The topology of the Brillouin zone, foundational in topological physics, is always assumed to
be a torus. We theoretically report the construction of Brillouin real projective plane …

We classify Hermitian tight-binding models describing noninteracting electrons on a one-
dimensional periodic lattice with two energy bands. To do this, we write a generalized Rice …

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

Wigner's seminal work on the Poincaré group revealed one of the fundamental principles of
quantum theory: symmetry groups are projectively represented. The condensed-matter …

We describe the mean-field model of a one-dimensional topological superconductor with
two orbitals per unit cell. Time-reversal symmetry is absent, but a nonsymmorphic symmetry …