Effects of diagonal disorder on Charge Density Wave and Superconductivity in local pair systems

We analyse the influence of diagonal disorder (random site energy) on Charge Density Wave (CDW) and Superconductivity (SS) in local pair systems which are described by the model of hard core charged bosons on a lattice. This problem was previously studied within the mean field approximation for the case of half filled band (n = 1). Here we extend that investigation to the case of arbitrary particle concentration (0 < n < 2) and examine the phase diagrams of the model and the behaviour of superfluid density as a function of n and the increasing disorder. Depending on the strength of random on-site energies, the intersite density-density repulsion and the concentration the model can exhibit several various phases, including homogeneous phases: CDW, SS and Bose-glass (NO) as well as the phase separated states: CDW-SS, CDW-NO and particle droplets. The obtained results for SS phase are in qualitative agreement with the available Monte Carlo calculations for two dimensional lattice. Also, in a definite range of parameters the system exhibits the phenomena which we call a disorder induced superconductivity and a disorder induced charge ordering.Comment: 21 pages, 8 figure

Mean Field Theory of the Localization Transition

A mean field theory of the localization transition for bosonic systems is developed. Localization is shown to be sensitive to the distribution of the random site energies. It occurs in the presence of a triangular distribution, but not a uniform one. The inverse participation ratio, the single site Green's function, the superfluid order parameter and the corresponding susceptibility are calculated, and the appropriate exponents determined. All of these quantities indicate the presence of a new phase, which can be identified as the {\it Bose-glass}.Comment: 4 pages, Revtex, 2 figures appende

A Gaussian Theory of Superfluid--Bose-Glass Phase Transition

We show that gaussian quantum fluctuations, even if infinitesimal, are sufficient to destroy the superfluidity of a disordered boson system in 1D and 2D. The critical disorder is thus finite no matter how small the repulsion is between particles. Within the gaussian approximation, we study the nature of the elementary excitations, including their density of states and mobility edge transition. We give the gaussian exponent $\eta$ at criticality in 1D and show that its ratio to $\eta$ of the pure system is universal.Comment: Revtex 3.0, 11 pages (4 figures will be sent through airmail upon request

Superfluidity vs Bose-Einstein condensation in a Bose gas with disorder

We investigate the phenomenon of Bose-Einstein condensation and superfluidity in a Bose gas at zero temperature with disorder. By using the Diffusion Monte-Carlo method we calculate the superfluid and the condensate fraction of the system as a function of density and strength of disorder. In the regime of weak disorder we find agreement with the analytical results obtained within the Bogoliubov model. For strong disorder the system enters an unusual regime where the superfluid fraction is smaller than the condensate fraction.Comment: 4 pages, 4 Postscript figure

Ground State and Excitations of Disordered Boson Systems

After an introduction to the dirty bosons problem, we present a gaussian theory for the ground state and excitations. This approach is physically equivalent to the Bogoliubov approximation. We find that ODLRO can be destroyed with sufficient disorder. The density of states and localization of the elementary excitations are discussed. (To appear in JLTP Proceedings of the Conference on Condensed Bose Systems at the University of Minnesota, 1993.)Comment: 13 pages. (postscript file because of the figures inserted in the text.

Onset of Superfluidity in 4He Films Adsorbed on Disordered Substrates

We have studied 4He films adsorbed in two porous glasses, aerogel and Vycor, using high precision torsional oscillator and DC calorimetry techniques. Our investigation focused on the onset of superfluidity at low temperatures as the 4He coverage is increased. Torsional oscillator measurements of the 4He-aerogel system were used to determine the superfluid density of films with transition temperatures as low as 20 mK. Heat capacity measurements of the 4He-Vycor system probed the excitation spectrum of both non-superfluid and superfluid films for temperatures down to 10 mK. Both sets of measurements suggest that the critical coverage for the onset of superfluidity corresponds to a mobility edge in the chemical potential, so that the onset transition is the bosonic analog of a superconductor-insulator transition. The superfluid density measurements, however, are not in agreement with the scaling theory of an onset transition from a gapless, Bose glass phase to a superfluid. The heat capacity measurements show that the non-superfluid phase is better characterized as an insulator with a gap.Comment: 15 pages (RevTex), 21 figures (postscript

Interaction effects in non-Hermitian models of vortex physics

Vortex lines in superconductors in an external magnetic field slightly tilted from randomly-distributed parallel columnar defects can be modeled by a system of interacting bosons in a non-Hermitian vector potential and a random scalar potential. We develop a theory of the strongly-disordered non-Hermitian boson Hubbard model using the Hartree-Bogoliubov approximation and apply it to calculate the complex energy spectra, the vortex tilt angle and the tilt modulus of (1+1)-dimensional directed flux line systems. We construct the phase diagram associated with the flux-liquid to Bose-glass transition and find that, close to the phase boundary, the tilted flux liquid phase is characterized by a band of localized excitations, with two mobility edges in its low-energy spectrum.Comment: 19 pages, 19 figures, To appear in Phys. Rev.

Some basic aspects of quantum phase transitions

Several basic problems of the theory of quantum phase transitions are reviewed. The effect of the quantum correlations on the phase transition properties is considered with the help of basic models of statistical physics. The effect of quenched disorder on the quantum phase transitions is also discussed. The review is performed within the framework of the thermodynamic scaling theory and by the most general methods of statistical physics for the treatment of phase transitions: general length-scale arguments, exact solutions, mean field approximation, Hubbard-Stratonovich transformation, Feynman path integral approach, and renormalization group in the field theoretical variant. Some new ideas and results are presented. Outstanding theoretical problems are mentioned.Comment: 81 pages, Latex2e, 8 figures, Phys. Rep.(2003) in pres