Three-dimensional (3D) topological Dirac semimetals (TDSs) represent an unusual state of quantum matter that can be viewed as "3D graphene." In contrast to 2D Dirac fermions in graphene or on the surface of 3D topological insulators, TDSs possess 3D Dirac fermions in the bulk. By investigating the electronic structure of Na3Bi with angle-resolved photoemission spectroscopy, we detected 3D Dirac...

The role of the Killing–Yano tensors in the construction of the Dirac-type operators is pointed out. The general results are applied to the case of the four-dimensional Euclidean Taub–Newman–Unti–Tamburino space. Three new Dirac-type operators, equivalent to the standard Dirac operator, are constructed from the covariantly constant Killing–Yano tensors of this space. Finally the Runge–Lenz oper...

We performed low temperature scanning tunneling microscopy (STM) and spectroscopy (STS) studies on the electronic properties of (√3 × √3)R30° phase of silicene on Ag(111) surface. We found the existence of Dirac Fermion chirality through the observation of -1.5 and -1.0 power law decay of quasiparticle interference (QPI) patterns. Moreover, in contrast to the trigonal warping of Dirac cone in g...

We present the first experimental microwave realization of the one-dimensional Dirac oscillator, a paradigm in exactly solvable relativistic systems. The experiment relies on a relation of the Dirac oscillator to a corresponding tight-binding system. This tight-binding system is implemented as a microwave system by a chain of coupled dielectric disks, where the coupling is evanescent and can be...

We show that any closed spin manifold not diffeomorphic to the two-sphere admits a sequence of volume-one-Riemannian metrics for which the smallest non-zero Dirac eigenvalue tends to zero. As an application, we compare the Dirac spectrum with the conformal volume. Spineurs presque harmoniques Résumé. Nous montrons que, sur toute variété spinorielle compacte sans bord non difféomorphe à la sphèr...

We study with first-principles methods the interplay between bulk and surface Dirac fermions in three dimensional Dirac semimetals. By combining density functional theory with the coherent potential approximation, we reveal a topological phase transition in Na_{3}Bi_{1-x}Sb_{x} and Cd_{3}[As_{1-x}P_{x}]_{2} alloys, where the material goes from a Dirac semimetal to a trivial insulator upon chang...

We present a formalism to calculate the orbital magnetization of interacting Dirac fermions under a magnetic field. In this approach, the divergence difficulty is overcome with a special limit of the derivative of the thermodynamic potential with respect to the magnetic field. The formalism satisfies the particle-hole symmetry of the Dirac fermions system. We apply the formalism to the interact...

Given a one-dimensional weighted Dirac operator we can define a spectral measure by virtue of singular Weyl–Titchmarsh–Kodaira theory. Using the theory of de Branges spaces we show that the spectral measure uniquely determines the Dirac operator up to a gauge transformation. Our result applies in particular to radial Dirac operators and extends the classical results for Dirac operators with one...

Dirac cohomology is a new tool to study unitary and admissible representations of semisimple Lie groups. It was introduced by Vogan and further studied by Kostant and ourselves [V2], [HP1], [K4]. The aim of this paper is to study the Dirac cohomology for the Kostant cubic Dirac operator and its relation to Lie algebra cohomology. We show that the Dirac cohomology coincides with the correspondin...

The magnetic field of an infinitely long solenoid is immensely important for various reasons. For example, it is used to study the Aharanov-Bohm [1] effect. Similarity with this field also helps one to understand the physics of cosmic strings [2]. It is therefore important to study the quantum mechanics of a Dirac fermion in the field of an infinitely long solenoid, which is what we do in the p...