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In a Dirac material we investigated the confining properties of massive and massless particles subjected to a potential well generated by a purely electrical potential, that is, an electric quantum dot. To achieve this in the most exhaustive way, we have worked on the aforementioned problem for charged particles with and without mass, limited to moving on a plane and whose dynamics are governed by the Dirac equation. The bound states are studied first and then the resonances, the latter by means of the Wigner time delay of the dispersion states as well as through the complex eigenvalues of the outgoing states, in order to obtain a complete picture of the confinement. One of the main results obtained and described in detail is that electric quantum dots for massless charges seem to act as sinks (or sources in the opposite direction) of resonances, while for massive particles the resonances and bound states are conserved with varying position depending on the depth of the well.
Dirac particles have been notoriously difficult to confine. Implementing a curved space Dirac equation solver based on the quantum Lattice Boltzmann method, we show that curvature in a 2-D space can confine a portion of a charged, mass-less Dirac fer
We study excitonic effects in two-dimensional massless Dirac fermions with Coulomb interactions by solving the ladder approximation to the Bethe-Salpeter equation. It is found that the general 4-leg vertex has a power law behavior with the exponent g
Motivated by the conduction properties of graphene discovered and studied in the last decades, we consider the quantum dynamics of a massless, charged, spin 1/2 relativistic particle in three dimensional space-time, in the presence of an electrostati
Effect of spin-orbit coupling (SOC) on Dirac electrons in the organic conductor $alpha$-(BETS)$_2$I$_3$ [BETS = bis(ethylenedithio)tetraselenafulvalene] has been examined by calculating electric conductivity and spin magnetic susceptibility. A tight-
We consider the Dirac equation on periodic networks (quantum graphs). The self-adjoint quasi periodic boundary conditions are derived. The secular equation allowing us to find the energy spectrum of the Dirac particles on periodic quantum graphs is o