A zero-gap state with a Dirac cone type energy dispersion was discovered in an organic conductor α-(BEDT-TTF)2I3 under high hydrostatic pressures. This is the first two-dimensional (2D) zero-gap state discovered in bulk crystals with a layered structure. In contrast to the case of graphene, the Dirac cone in this system is highly anisotropic. The present system, therefore, provides a new type o...

A three-dimensional (3D) Dirac semimetal (SM) is the 3D analogue of graphene having linear energy dispersion around Fermi points. Owing to the nontrivial topology of electronic wave functions, the 3D Dirac SM shows nontrivial physical properties and hosts various exotic quantum states such as Weyl SMs and topological insulators under proper external conditions. There are several kinds of Dirac ...

Fermi-level pinning phenomena due to DX centers in AlGaAs/GaAs HEMT’s are analyzed using two-dimensional numerical simulation based on a drift-diffusion model. A DX center model is introduced assuming Fermi-Dirac statistics for ionized donor density with the aluminum mole fraction dependence of the deep-donor energy level. The calculated results reveal that the decrease in transconductance of A...

We consider a general class of convolution-type nonlocal wave equations modeling bidirectional propagation nonlinear waves in continuous medium. In the limit vanishing nonlocality we study behavior solutions to Cauchy problem. prove that, as kernel functions convolution integral approach Dirac delta function, converge strongly corresponding classical elasticity equation. An energy estimate with...

We derive the noncommutative Dirac-Born-Infeld action for the D-brane, which governs dynamics of D-brane with a NS-NS B-field in the low energy regime. Depending on some details of the path integral prescriptions, both ordinary Dirac-Born-Infeld action and noncommutative one can be obtained by evaluating the same Polyakov string path integral for the open string ending on the D-brane. Thus, it ...

In this paper we prove global-in-time existence of smooth solutions to the homogeneous Landau-Fermi-Dirac equation with Coulomb potential. The initial conditions are nonnegative, bounded and integrable. We also show that any weak solution converges, as time grows, towards steady state given by Fermi-Dirac equilibrium distribution. Furthermore, convergence is exponential, provided datum close in...

In this document we discuss the long time behaviour for homogeneous Landau-Fermi-Dirac equation in hard potential case. Uniform estimates statistical moments and Sobolev regularity are presented used to prove exponential relaxation of non degenerate distributions Fermi-Dirac statistics. All these results valid rather general initial datum. An important feature is independence with respect quant...

Friedel oscillations of the graphene-like materials are investigated theoretically for low and intermediate Fermi energies. Numerical calculations have been performed within the random phase approximation. It was demonstrated that for intra-valley transitions the contribution of the different Dirac points in the wave-number dependent quantities is determined by the orientation of the wave-numbe...

We consider Friedel oscillation in the two-dimensional Dirac materials when the Fermi level is near the van Hove singularity. Twisted graphene bilayer and the surface state of topological crystalline insulator are the representative materials which show low-energy saddle points that are feasible to probe by gating. We approximate the Fermi surface near saddle point with a hyperbola and calculat...

A central mystery in quantum condensed matter physics is the zero temperature quantum phase transition between strongly renormalized Fermi-liquids as found in heavy fermion intermetallics and possibly high Tc superconductors. Field theoretical statistical techniques are useless because of the fermion sign problem, but we will present here results showing that the mathematics of string theory is...