We perform a complete classification of two-band k·p theories at band crossing points in 3D semimetals with n-fold rotation symmetry and broken time-reversal symmetry. Using this classification, we show the existence of new 3D topological semimetals characterized by C(4,6)-protected double-Weyl nodes with quadratic in-plane (along k(x,y)) dispersion or C(6)-protected triple-Weyl nodes with cubi...

The Weyl semimetal phase is a recently discovered topological quantum state of matter characterized by the presence of topologically protected degeneracies near the Fermi level. These degeneracies are the source of exotic phenomena, including the realization of chiral Weyl fermions as quasiparticles in the bulk and the formation of Fermi arc states on the surfaces. Here, we demonstrate that the...

Weyl fermions, first proposed for describing massless chiral Dirac fermions in particle physics, have not been observed yet in experiments. Recently, much effort has been devoted to explore Weyl fermions around band touching points of single-particle energy dispersions in certain solid state materials (named Weyl semimetals), similar as graphene for Dirac fermions. Here we show that such Weyl s...

In this paper, we have studied the connectedness of the graphs on the direct product of the Weyl groups. We have shown that the number of the connected components of the graph on the direct product of the Weyl groups is equal to the product of the numbers of the connected components of the graphs on the factors of the direct product. In particular, we show that the graph on the direct product o...

We consider the semigroup $S$ of highest weights appearing in tensor powers $V^{otimes k}$ of a finite dimensional representation $V$ of a connected reductive group. We describe the cone generated by $S$ as the cone over the weight polytope of $V$ intersected with the positive Weyl chamber. From this we get a description for the asymptotic of the number of highest weights appearing in $V^{otime...

A pseudoclassical model to describe Weyl particle in 10 dimensions is proposed. In course of quantization both the massless Dirac equation and the Weyl condition are reproduced automatically. The construction can be relevant to Ramond-Neveu-Schwarz strings where the Weyl reduction in the Ramond sector has to be made by hands.

A non-classical Weyl theory is developed for Dirac systems with rectangular matrix potentials. The notion of the Weyl function is introduced and the corresponding direct problem is treated. Furthermore , explicit solutions of the direct and inverse problems are obtained for the case of rational Weyl matrix functions.

We define a Weyl group action on quiver varieties using reflection functors, which resemble ones introduced by Bernstein-Gelfand-Ponomarev [1]. As an application, we define Weyl group representations of homology groups of quiver varieties. They are analogues of Slodowy’s construction of Springer representations of the Weyl group.

A non-classical Weyl theory is developed for Dirac systems with rectangular matrix potentials. The notion of the Weyl function is introduced and the corresponding direct problem is solved. Furthermore, explicit solutions of the direct and inverse problems are obtained for the case of rational Weyl matrix functions. Mathematics subject classification (2010): 34B20, 34L40, 15A15, 93B15.

In this paper, we study the actions of the Weyl groups of the U duality groups for type IIA string theory toroidally compactified to all dimensions D ≥ 3. We show how these Weyl groups implement permutations of the field strengths, and we discuss the Weyl group multiplets of all supersymmetric p-brane solitons.