The massless Dirac–Weyl equation with deformed extended complex potentials

Basically (2 + 1)-dimensional Dirac equation with real deformed Lorentz scalar potential is investigated in this study. The position-dependent Fermi velocity function transforms Dirac Hamiltonian into a Klein–Gordon-like effective Hamiltonian system. The complex Hamiltonian and its real energy spectrum and eigenvectors are obtained analytically. Moreover, the Lie algebraic analysis is also performed.

Trapping electrons in a circular graphene quantum dot with Gaussian potential

We study the dependence of trapping time of an electron in a circular graphene quantum dot depends on the electron's angular momentum and on the parameters of the external Gaussian potential used to induce the dot. The trapping times are calculated through a numerical determination of the quasi-bound states of electron from the two-dimensional Dirac-Weyl equation. It is shown that on increasing the angular momentum, not only does the trapping time decreases but also the trend of how the trapping time depends on the effective radius of the dot changes. In particular, as the dot radius increases, the trapping time increases for m<3 but decreases for m > 3. The trapping time however always decreases upon increasing the potential height. It is also found that the wave functions corresponding to the states of larger trapping times or higher m are more localized in space.

Weyl fermions in a family of Gödel-type geometries with a topological defect

In this paper, we study Weyl fermions in a family of Gödel-type geometries in Einstein general relativity. We also consider that these solutions are embedded in a topological defect background. We solve the Weyl equation and find the energy eigenvalues and eigenspinors for all three cases of Gödel-type geometries where a topological defect is passing through them. We show that the presence of a topological defect in these geometries contributes to the modification of the spectrum of energy. The energy zero modes for all three cases of the Gödel geometries are discussed.