Quantum phase transition in the chirality of the (2+1)-dimensional Dirac oscillator

We study the (2+1)-dimensional Dirac oscillator in the presence of an external uniform magnetic field ($B$). We show how the change of the strength of $B$ leads to the existence of a quantum phase transition in the chirality of the system. A criticalvalue of the strength of the external magnetic field ($B_c$) can be naturally defined in terms of physical parameters of the system. While for $B=B_c$ the fermion can be considered as a free particle without defined chirality, for $B<B_c$ ($B>B_c$) the chirality is left (right) and there exist a net potential acting on the fermion. For the three regimes defined in the quantum phase transition of chirality, we observe that the energy spectra for each regime is drastically different. Then, we consider the $z$-component of the orbital angular momentum as an order parameter that characterizes the quantum phase transition.

Graphene physics via the Dirac oscillator in (2+1) dimensions

We show how the two-dimensional Dirac oscillator model can describe some properties of electrons in graphene. This model explains the origin of the left-handed chirality observed for charge carriers in monolayer and bilayer graphene. The relativisticdispersion relation observed for monolayer graphene is obtained directly from the energy spectrum, while the parabolic dispersion relation observed for the case of bilayer graphene is obtained in the non-relativistic limit. Additionally, if an external magnetic field is applied, the unusual Landau-level spectrum for monolayer graphene is obtained, but for bilayer graphene the model predicts the existence of a magnetic field-dependent gap. Finally, this model also leads to the existence of a chiral phase transition.

Dipolar excitations at the LIII x-ray absorption edges of the heavy rare earth metals

We report measured dipolar asymmetry ratios at the LIII edges of the heavy rare earth metals. The results are compared with a first principles calculation and excellent agreement is found. A simple model of the scattering is developed, enabling us tore-interpret the resonant x-ray scattering in these materials and to identify the peaks in the asymmetry ratios with features in the spin and orbital moment densities.