The current-voltage characteristics of a new range of devices built around Weyl semimetals has been predicted using the Landauer formalism. The potential step and barrier have been reconsidered for three-dimensional Weyl semimetals, with analogies to the two-dimensional material graphene and to optics. With the use of our results we also show how a Veselago lens can be made from Weyl semimetals, e.g., from NbAs and NbP. Such a lens may have many practical applications and can be used as a probing tip in a scanning tunneling microscope (STM). The ballistic character of Weyl fermion transport inside the semimetal tip, combined with the ideal focusing of the Weyl fermions (by Veselago lens) on the surface of the tip may create a very narrow electron beam from the tip to the surface of the studied material. With a Weyl semimetal probing tip the resolution of the present STMs can be improved significantly, and one may image not only individual atoms but also individual electron orbitals or chemical bonding and therewith to resolve the long-term issue of chemical and hydrogen bond formation. We show that applying a pressure to the Weyl semimental, having no center of spatial inversion, one may model matter at extreme conditions, such as those arising in the vicinity of a black hole. As the materials Cd 3 As 2 and Na 3 Bi show an asymmetry in their Dirac cones, a scaling factor was used to model this asymmetry. The scaling factor created additional regions of no propagation and condensed the appearance of resonances. We argue that under an external pressure there may arise a topological phase transition in Weyl semimetals, where the electron transport changes character and becomes anisotropic. There a hyperbolic Dirac phase occurs where there is a strong light absorption and photocurrent generation.

Here we present a short introduction into physics of Dirac materials. In particular we review main physical properties of various two-dimensional crystals such as graphene, silicene, germanene and others. We comment on the origin of their buckled two-dimensional shape, and address the issues created by Mermin-Wagner theorem prohibiting the existence of strictly two-dimensional, flat crystals. Then we describe main ideas which were leading to the discovery of two and three-dimensional topological insulators and Weyl fermions. We describe some of their outstanding electronic properties which have been originating due to the existence of the Dirac gapless spectrum. We also compare simplest devices made of Dirac materials. Analogies and differences between Dirac materials and optics are also discussed.

By considering the direction of charge carriers and the conservation of probablity current the transmission properties of graphene Zener tunnelling nano-devices were obtained. The scattering properties were then used with an adaptation of the Landauer formalism to calculate an analytical expression for current and conductance. The numerical results of the IV characteristics were then briefly discussed for the graphene step and Zener barrier. A comparison between the theoretical model and experimental results shows the similarities of graphene nanoribbons and infinite sheet graphene. This work has been published as [41].