Related papers: Surface chiral Abelian topological order on multil…
We show that there exist flat surface bundles with closed leaves having non-trivial normal bundles. This leads us to compute the Abelianisation of surface diffeomorphism groups with marked points. We also extend a formula of Tsuboi that…
In many materials, ordered phases and their order parameters are easily characterized by standard experimental methods. "Hidden order" refers to a phase transition in which an ordered state emerges without such an easily detectable order…
We propose the concept of 2D non-Abelian topological insulator which can explain the energy distributions of the edge states and corner states in systems with parity-time symmetry. From the viewpoint of non-Abelian band topology, we…
Employing the $\mathbf{k}\cdot\mathbf{p}$ expansion for a family of tight-binding models for SmB$_6$, we analytically compute topological surface states on a generic $(lmn)$ surface. We show how the Dirac-cone spin structure depends on…
We discuss the proximate phases of a three-dimensional system with Dirac-like dispersion. Using the cubic lattice with plaquette $\pi$-flux as a model, we find, among others phases, a chiral topological insulator and singlet topological…
We study a class of translational-invariant insulators with discrete rotational symmetry. These insulators have no spin-orbit coupling, and in some cases have no time-reversal symmetry as well, i.e., the relevant symmetries are purely…
Three-dimensional topological (crystalline) insulators are materials with an insulating bulk, but conducting surface states which are topologically protected by time-reversal (or spatial) symmetries. Here, we extend the notion of…
Weyl nodal loop semimetals are gapless topological phases that, unlike their insulator counterparts, may be unstable to small perturbations that respect their topology-protecting symmetries. Here, we analyze a clean system perturbed by…
We report the electronic structure of YbB6, a recently predicted moderately correlated topological insulator, measured by angle-resolved photoemission spectroscopy. We directly observed linearly dispersive bands around the time-reversal…
We present detailed data on the unusual angular-dependent magnetoresistance oscillation phenomenon recently discovered in a topological insulator Bi_{0.91}Sb_{0.09}. Direct comparison of the data taken before and after etching the sample…
We show that abelian surfaces (and consequently curves of genus 2) over totally real fields are potentially modular. As a consequence, we obtain the expected meromorphic continuation and functional equations of their Hasse--Weil zeta…
We explore the phase diagrams of moir\'e materials in search of a new class of intervalley-coherent correlated insulating state: the Chern texture insulator (CTI). This phase of matter, proposed in a companion paper, breaks valley $U(1)$…
Topology of Foliations of the Riemann Surfaces given by the real part of generic holomorphic 1-forms, is studied. Our approach is based on the notion of Transversal Canonical Basis of Cycles (TCB) instead of using just one closed…
We investigate the ground-state properties of the one-dimensional two-band Hubbard model with different bandwidths. The density-matrix renormalization group method is applied to calculate the averaged electron occupancies $n$ as a function…
We study three dimensional systems where strong repulsion leads to an insulating state via spontaneously generated spin-orbit interactions. We discuss a microscopic model where the resulting state is topological. Such topological `Mott'…
We investigate the electronic structures of the alloyed Bi$_{1-x}$Sb$_x$ compounds based on first-principle calculations including spin-orbit coupling (SOC), and calculate the surface states of semi-infinite systems using maximally…
We study the finite temperature nature of a quantum phase transition between an Abelian and a non-Abelian topological phase in an exactly solvable model of a chiral spin liquid. By virtue of the exact solvability, this model can serve as a…
Using the theory of cohomology support locus, we give a necessary condition for the Albanese map of a smooth projective surface being a submersion. More precisely, assuming the cohomology support locus of any finite abelian cover of a…
Topological crystalline insulators (TCI) possess electronic states protected by crystal symmetries, rather than time-reversal symmetry. We show that the transition metal oxides with heavy transition metals are able to support nontrivial…
Anyons have recently received great attention due to their promising application in topological quantum computation. The best validated system that enjoys the anyonic excitations are the Laughlin states. The quasi-particles in Laughlin…