Related papers: D-Algebra Structure of Topological Insulators
Monte Carlo studies of pure glue SU(3) gauge theory using the overlap-based topological charge operator have revealed a laminar structure in the QCD vacuum consisting of extended, thin, coherent, locally 3-dimensional sheets of topological…
Topological insulators in odd dimensions are characterized by topological numbers. We prove the well-known relation between the topological number given by the Chern character of the Berry curvature and the Chern-Simons level of the low…
Drinfeld showed that any finite dimensional Hopf algebra \G extends to a quasitriangular Hopf algebra \D(\G), the quantum double of \G. Based on the construction of a so--called diagonal crossed product developed by the authors, we…
We consider the combined effect of a gap and a Zeeman interaction on the helical Dirac fermions which exist on the surface of a topological insulator. Magneto-optical properties, the magnetization, Hall effect and the density of states are…
One of us (L.S.) and H. Verlinde independently conjectured a holographic duality between the double-scaled SYK model at infinite temperature and dimensionally reduced $(2+1)$-dimensional de Sitter space [1]-[8]. Beyond the statement that…
It is shown that the generalized (with nonpolynomial Lagrangian) Chern-Simons membranes and in general $p$-branes moving in $D$-dimensional target space admit an infinite set of secondary constraints. With respect to the Poisson bracket…
We study a general problem how the gap in a nonmagnetic band insulator closes by tuning a parameter. We review our recent results on the classification of all the possible gap closing in two and three dimensions. We show that they accompany…
A topological theory of d-wave superconductors is derived in this thesis. Ginzburg-Landau theory describes superconductivity by defining a complex order parameter and applying Landau's theory for phase transitions. However, there is no…
We study the quantum Hall effect in the surface states of topological insulator in the presence of a perpendicular magnetic field in the framework of edge states. Motion of Dirac fermions will form descrete Landau levels, among which a…
We study the algebraic structure of electron density operators in gapless Weyl fermion systems in $d=3,5,7,\cdots$ spatial dimensions and in topological insulators (without any protecting symmetry) in $d=4,6,8,\cdots$ spatial dimensions.…
Topological insulators are new class of materials which are characterized by a bulk band gap like ordinary band insulator but have protected conducting states on their edge or surface. These states emerge out due to the combination of…
The D3-probe-D7 brane system, oriented so as to have 2+1-dimensional Poincare symmetry, is argued to be the holographic representation of a strongly correlated fractional topological insulator which exhibits a zero-field quantized Hall…
An exhaustive classification scheme of topological insulators and superconductors is presented. The key property of topological insulators (superconductors) is the appearance of gapless degrees of freedom at the interface/boundary between a…
Two-dimensional (2D) topological insulators (TIs) hold promise for applications in spintronics based on the fact that the propagation direction of edge electrons of a 2D TI is robustly linked to their spin origination. Here, with the use of…
This is a noncommutative-geometric study of the semiclassical dynamics of finite topological D-brane systems. Starting from the formulation in terms of A -infinity categories, I show that such systems can be described by the noncommutative…
In this work, we supply an engineering solution that paves the way to the implementation of the full classification table of topological insulators with passive acoustic crystals. As an example, we design an acoustic crystal displaying the…
Quantized responses are important tools for understanding and characterizing the universal features of topological phases of matter. In this work, we consider a class of topological crystalline insulators in $3$D with $C_n$ lattice rotation…
We examine Chern-Simons theory written on a noncommutative plane with a `hole', and show that the algebra of observables is a nonlinear deformation of the $w_\infty$ algebra. The deformation depends on the level (the coefficient in the…
We construct continuum models of 3D and 4D topological insulators by coupling spin-1/2 fermions to an SU(2) background gauge field, which is equivalent to a spatially dependent spin-orbit coupling. Higher dimensional generalizations of flat…
Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and…