Phases and phase transitions in restricted systems

Abstract

This thesis is a review of five publications in which some effects characteristic to systems with restricted dimensions are emphasised. These effects are the Bose-like condensation, the divergency of the specific heat at zero temperature in Fermi systems, the diffusion of nonequilibrium quasiparticles in mesoscopic superconductors, and the existence of the core-melted cluster. The first of these effects, the Bose-like condensation, arises from the freezing out of one or more degrees of freedom of particles in a mesoscopic system. During this process, the dimensionality of the particle distribution is changing and analogies can be made with the multiple-step Bose-Einstein condensation. The Bose-like condensation was first observed in the phonon gas inside an ultrathin dielectric membrane at low temperatures. Nevertheless, it can be extended to systems of massive particles and it occurs for both bosons and fermions. In the case of fermions, for certain types of single particle hamiltonians, the specific heat has asymptotically a divergent behavior at zero temperature, as the Fermi energy Ep approaches any value from an infinite discrete set of energies: {Єi}i≥1. The divergent behavior for ЄF = Єi, for any i, is specific to infinite systems. If the system is finite, the specific heat converges to zero at zero temperature, for any ЄF, as expected. All the results are particularized for particles trapped inside parallelepipedic boxes and harmonic potentials. The diffusion of nonequilibrium quasi particles injected into mesoscopic superconducting wires was analyzed in connection with the cooling properties of normal metal-insulator-superconductor tunnel junctions. It turns out that due to the superconducting energy gap, the diffusion in bare superconducting wires is poor, but it can be very much enhanced by depositing a normal metal film in contact with this nano-sized wire. If there is an insulating oxide layer between the normal metal and the superconductor, the quasiparticles from the superconductor can tunnel into the normal metal, reducing in this way the electronic temperature of the superconductor. If the normal metal is in good metal-to-metal contact with the superconductor, the spatial variation of the energy gap strongly enhances the quasiparticle current. Finally, the possibility of the existence of a core-melted cluster was investigated. A pair potential was introduced, with the property that the solid state of the cluster is less dense than the liquid state. With this kind of potential the cluster exhibits quite an unusual behavior. In addition to the known states, solid, liquid and surface-melted, it can also be found in a "dense liquid" phase (a disordered state appearing at low temperatures), a "core-melted" phase and a "core-surface-melted" phase. In the core-melted phase the external part of the cluster consists of atoms that vibrate around regular crystalline sites, while the core atoms have much bigger mobility and sometimes exhibit diffusive motion.