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We propose a scheme to realize a new Z_2 topological insulator in a square optical lattice. Different from the conventional topological insulator protected by the time-reversal symmetry, here, the optical lattice possesses a novel hidden…
Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a…
We investigate theoretically properties of two-dimensional topological insulator constrictions both in the integer and fractional regimes. In the presence of a perpedicular magnetic field, the constriction functions as a spin filter with…
Recently, the notion of topological phases of matter has been extended to higher-order incarnations, supporting gapless modes on even lower dimensional boundaries, such as corners and hinges. We here identify a collection of cubic spin-3/2…
We consider a chiral spin liquid constructed using the parton theory. This state supports non-Abelian anyons and neutral fermions, which share some similarities with the celebrated Moore-Read state. The edge physics of the parton state and…
Magnetic spin topological textures recently found their electrical counterparts in polar topologies emerging from the condensation of inhomogeneous polar atomic distortions. Here, we further extend the concept to other non-polar atomic…
The twist-2 contributions to the polarized structure functions in deep inelastic lepton--hadron scattering are calculated including the exchange of weak bosons and using both the operator product expansion and the covariant parton model. A…
Adding a second Kondo channel to heavy fermion materials reveals new exotic symmetry breaking phases associated with the development of Kondo coherence. In this paper, we review two such phases, the "hastatic order" associated with…
In this Letter, we study a previously unexplored class of topological states protected by hidden chiral symmetries that are local, that is, that protect against any off-diagonal disorder. We derive their related topological invariant for…
We present an exactly solvable spin-3/2 model defined on a pentacoordinated three-dimensional graphite lattice, which realizes a novel quantum spin liquid with second-order topology. The exact solutions are described by Majorana fermions…
We demonstrate formation of hierarchical structures in two-dimensional systems with multiple length scales in the inter-particle interaction. These include states such as clusters of clusters, concentric rings, clusters inside a ring, and…
High-order topological phases host robust boundary states at the boundary of the boundary, which can be interpreted from their boundary topology. In this work, considering the interplay between superconductors and magnetic fields to gap the…
Higher-order topological insulators, which support lower-dimensional topological boundary states than the first-order topological insulators, have been intensely investigated in the integer dimensional systems. Here, we provide a new…
The Rauzy fractal is a domain in the two-dimensional plane constructed by the Rauzy substitution, a substitution rule on three letters. The Rauzy fractal has a fractal-like boundary, and the currently known its constructions is not only for…
Symmetry and topology are essential principles in topological physics. Recently, the idea of sub-symmetry-protected topology -- where some of the original symmetries are broken while a remaining subset, called sub-symmetries, continues to…
Second order topological insulator can be engineered from two-dimensional materials with strong spin-orbit coupling and in-plane Zeeman field. In proximity to superconductor, topological superconducting phase could be induced in the…
Coupled-wire constructions have proven to be useful tools to characterize Abelian and non-Abelian topological states of matter in two spatial dimensions. In many cases, their success has been complemented by the vast arsenal of other…
We give a systematic approach to constructing non-reduced, locally Cohen-Macaulay schemes with reduced support a smooth projective variety. The hierarchy of such structures includes a lot of information about the underlying variety, its…
Hopfions, as three-dimensional topologically nontrivial structures described by poloidal and toroidal winding numbers, hold promise as robust information carriers in spintronics, functional materials, and optical communications. Although…
The pyrochlore materials have long been predicted to harbor a quantum spin liquid, an intrinsic long-range-entangled state supporting fractionalized excitations. Existing pyrochlore experiments, on the other hand, have discovered several…