Semiconductor cavity QED: Bandgap induced by vacuum fluctuations

We consider theoretically a semiconductor nanostructure embedded in one-dimensional microcavity and study the modification of its electron energy spectrum by the vacuum fluctuations of the electromagnetic field. To solve the problem, a non-perturbative diagrammatic approach based on the Green's function formalism is developed. It is shown that the interaction of the system with the vacuum fluctuations of the optical cavity opens gaps within the valence band of the semiconductor. The approach is verified for the case of large photon occupation numbers, proving the validity of the model by comparing to previous studies of the semiconductor system excited by a classical electromagnetic field. The developed theory is of general character and allows for unification of quantum and classical descriptions of the strong light-matter interaction in semiconductor structures

BCS pairing in fully repulsive fermion mixtures

We consider a mixture of two neutral cold Fermi gases with repulsive interactions. We show that in some region of the parameter space of the system the effective attraction between fermions of the same type can appear due to the exchange of collective excitations. This leads to the formation of BCS pairing in the case where bare inter-atomic interactions are repulsive

Electronic and magnetic properties of graphite quantum dots

We study the electronic and magnetic properties of multilayer quantum dots (MQDs) of graphite in the nearest-neighbor approximation of tight-binding model. We calculate the electronic density of states and orbital susceptibility of the system as function of the Fermi level location. We demonstrate that properties of MQD depend strongly on the shape of the system, on the parity of the layer number and on the form of the cluster edge. The special emphasis is given to reveal the new properties with respect to the monolayer graphene quantum dots. The most interesting results are obtained for the triangular MQD with zig-zag edge at near-zero energies. The asymmetrically smeared multipeak feature is observed at Dirac point within the size-quantized energy gap region, where monolayer graphene flakes demonstrate the highly-degenerate zero-energy state. This feature, provided by the edge-localized electronic states results in the splash-wavelet behavior in diamagnetic orbital susceptibility as function of energy