Abstract: Recent technological advances resulted in high-quality superconducting metallic nanofilms and nanowires. The physical properties of such nanostructures are governed by the size-quantization of the transverse electron spectrum. This has a substantial impact on the basic superconducting characteristics, e.g., the order parameter, the critical temperature and the critical magnetic field. In the present paper we give an overview of our theoretical results on this subject. Based on a numerical self-consistent solution of the Bogoliubov-de Gennes equations, we investigate how the superconducting properties are modified in the quantum-size regime.

Abstract: Molecular dynamic simulations are performed to investigate the melting process of small three-dimensional clusters (i.e., systems with one and two shells) of classical charged particles trapped in an isotropic parabolic potential. The confined particles interact through a repulsive potential. We find that the ground-state configurations for systems with N=6, 12, 13, and 38 particles interacting through a Coulomb potential are magic clusters. Such magic clusters have an octahedral or icosahedral symmetry and are found to have a large stability against intrashell diffusion leading to an intershell melting transition prior to the intrashell and radial melting process. For systems with two shells a local radial melting of subshells is found at low temperatures resulting in a structural transition leading to an increased symmetry of the ordered system. Using Lindemanns criterion the different melting temperatures are determined and the influence of the screening of the interparticle interaction was investigated. A normal mode analysis is performed and some of the normal modes are found to be determinantal for the melting process.

Abstract: We model the fluorescence spectra of planar spin oscillators to find conditions that maximize spin resonance fluorescence. Spin oscillators perform Rabi oscillations under the effect of a periodic effective magnetic field caused by the winding motion of an electron in a gradient of magnetic field. We show that, despite the weak coupling of the spin magnetic dipole to the vacuum, spin oscillators excited by a direct current output a few nanowatts of microwave power, which is comparable to the best microwave sources. The large quantum efficiency relies on the combination of two effects. On the one hand, the spontaneous emission rate is enhanced by the synchronization of spin oscillators, which interact through the microwave field that they emit. On the other hand, the huge Rabi frequencies experienced by spin oscillators promote spins into upper levels of Zeeman transitions, from which a radiative cascade is triggered. We demonstrate different regimes of fluorescence which correspond to different values of the Rabi period relative to the spontaneous decay time and to the oscillator dwell time in the gradient of magnetic field. We investigate the device parameters which make these regimes experimentally accessible and find conditions that optimize microwave output. We find that microwave emission is centered around the cutoff frequency of spin oscillators. This has the advantage that the peak emission frequency may be tuned from zero continuously up to a few hundred gigahertz using an electrostatic gate. Quite remarkably for a spintronics effect, electrically induced spin resonance fluorescence does not require the injection of a spin polarized current. In fact, we show that microwave spectra are mostly independent of the incoming spin polarization except for magnetic waveguides which are shorter than a certain critical length, which we will specify.