Related papers: Brillouin Klein Bottle From Artificial Gauge Field…
Many magnetic point-group symmetries induce a topological classification on crystalline insulators, dividing them into those that have a nonzero quantized Chern-Simons magnetoelectric coupling ("axion-odd" or "topological"), and those that…
In this lecture for the Nobel symposium, we review previous research on a class of translational-invariant insulators without spin-orbit coupling. These may be realized in intrinsically spinless systems such as photonic crystals and…
Dimensionality plays a fundamental role in the classification of novel phases and their responses. In generic lattices of 2D and beyond, however, we found that non-Hermitian couplings do not merely distort the Brillouin zone (BZ), but can…
As recent additions to the catalog of 2D crystals, silicene and other silicene-class crystals have numerous unique properties currently being investigated and considered for use in novel device applications. In this paper, we investigate…
In crystalline systems with a superstructure, the electron dispersion can form a nontrivial covering of the Brillouin zone. It is proved that the number of sheets in this covering and its monodromy are topological invariants under ambient…
Skyrmions are spatially localized magnetic swirls which carry a nonzero integer topological charge. We study crystals of skyrmions in a two-dimensional ferromagnet model with chiral interactions induced by the presence of broken inversion…
To realize band structures with non-trivial topological properties in an optical lattice is an exciting topic in current studies on ultra cold atoms. Here we point out that this lofty goal can be achieved by using a simple scheme of shaking…
Topological quantum phase transition in electron gas systems is an enthralling phenomena. This phase transition has a unique property in that it is associated with a quantum phase transition point, which separates different regions with…
The study of band topology in photonic crystals was primarily focused on near-field effects, including edge states and high order corner states. However, this work investigated the polarization distribution of radiated fields for photonic…
The generalized Brillouin zone (GBZ) has been highly successful in characterizing the topology and band structure of non-Hermitian systems. However, its applicability has been challenged in spatially inhomogeneous settings, where the…
We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure. The algorithm applies to crystals with broken time-reversal, particle-hole, and chiral…
The concept of the Brillouin zone (BZ) in relation to a photonic crystal fabricated in an optically anisotropic material is explored both experimentally and theoretically. In experiment, we used femtosecond laser pulses to excite THz…
In two-dimensional systems with space-time inversion symmetry, such as $C_{2z}T$, the reality condition on wave functions gives rise to real band topology characterized by the Euler class, a $\mathbb{Z}$-valued topological invariant for a…
Topological phases in (2+1)-dimensions are frequently equipped with global symmetries, like conjugation, bilayer or electric-magnetic duality, that relabel anyons without affecting the topological structures. Twist defects are static…
Topological insulators are characterized by insulating bulk states and robust metallic surface states. Band inversion is a hallmark of topological insulators: at time-reversal invariant points in the Brillouin zone, spin-orbit coupling…
We show that the $Z_N$ Berry phase (Berry phase quantized into $2\pi/N$) provides a useful tool to characterize symmetry protected topological phases with correlation that can be directly computed through numerics of a relatively small…
Topological semimetals are under intensive theoretical and experimental studies. The first step of these studies is always the theoretical (numerical) predication of one of several candidate materials, starting from first principles. In…
In recent years, there have been rapid advances in the parallel fields of electronic and photonic topological crystals. Topological photonic crystals in particular show promise for coherent transport of light and quantum information at…
We introduce topological phases of matter defined by skyrmions in the ground state spin -- or pseudospin -- expectation value textures in the Brillouin zone, the chiral and helical topological skyrmion phases of matter. These phases are…
We study the emergence of non-Hermitian band topology in a two-dimensional metal with planar spiral magnetism due to a momentum-dependent relaxation rate. A sufficiently strong momentum dependence of the relaxation rate leads to exceptional…