Localized Flux Lines and the Bose Glass

Columnar defects provide effective pinning centers for magnetic flux lines in high--$T_{\rm c}$ superconductors. Utilizing a mapping of the statistical mechanics of directed lines to the quantum mechanics of two--dimensional bosons, one expects an entangled flux liquid phase at high temperatures, separated by a second--order localization transition from a low--temperature ``Bose glass'' phase with infinite tilt modulus. Recent decoration experiments have demonstrated that below the matching field the repulsive forces between the vortices may be sufficiently large to produce strong spatial correlations in the Bose glass. This is confirmed by numerical simulations, and a remarkably wide soft ``Coulomb gap'' at the chemical potential is found in the distribution of pinning energies. At low currents, the dominant transport mechanism in the Bose glass phase proceeds via the formation of double kinks between not necessarily adjacent columnar pins, similar to variable--range hopping in disordered semiconductors. The strong correlation effects originating in the long--range vortex interactions drastically reduce variable--range hopping transport.Comment: 10 pages, latex ("lamuphys.sty" file included), 6 figures can be obtained from the author ([email protected]); to appear in Proc. XIV Sitges conference on "Complex Behaviour of Glassy Systems" (Springer--Verlag

On the Coexistence of Diagonal and off-Diagonal Long-Range Order, a Monte Carlo Study

The zero temperature properties of interacting 2 dimensional lattice bosons are investigated. We present Monte Carlo data for soft-core bosons that demonstrate the existence of a phase in which crystalline long-range order and off-diagonal long-range order (superfluidity) coexist. We comment on the difference between hard and soft-core bosons and compare our data to mean-field results that predict a larger coexistence region. Furthermore, we determine the critical exponents for the various phase transitions.Comment: 7 pages and 8 figures appended in postscript, KA-TFP-93-0

Crossover and scaling in a two-dimensional field-tuned superconductor

Using an analysis similar to that of Imry and Wortis, it is shown that the apparent first order superconductor to metal transition, which has been claimed to exist at low values of the magnetic field in a two-dimensional field-tuned system at zero temperature,can be consistentlyinterpreted as a sharp crossover from a strong superconductor to an inhomogeneous state, which is a weak superconductor. The true zero-temperature superconductor to insulator transition within the inhomogenous state is conjectured to be that of randomly diluted XY model. An explaination of the observed finite temperature approximate scaling of resistivity close to the critical point is speculated within this model.Comment: 5 pages, 2 figures, corrected and modified according to referee Report

Quantum vortex fluctuations in cuprate superconductors

We study the effects of quantum vortex fluctuations in two-dimensional superconductors using a dual theory of vortices, and investigate the relevance to underdoped cuprates where the superconductor-insulator transition (SIT) is possibly driven by quantum vortex proliferation. We find that a broad enough phase fluctuation regime may exist for experimental observation of the quantum vortex fluctuations near SIT in underdoped cuprates. We propose that this scenario can be tested via pair-tunneling experiments which measure the characteristic resonances in the zero-temperature pair-field susceptibility in the vortex-proliferated insulating phase.Comment: RevTex 5 pages, 2 eps figures; expanded; to appear in Phys. Rev.

Quantum Phase Transitions and Conserved Charges

The constraints on the scaling properties of conserved charge densities in the vicinity of a zero temperature ($T$), second-order quantum phase transition are studied. We introduce a generalized Wilson ratio, characterizing the non-linear response to an external field, $H$, coupling to any conserved charge, and argue that it is a completely universal function of $H/T$: this is illustrated by computations on model systems. We also note implications for transitions where the order parameter is a conserved charge (as in a $T=0$ ferromagnet-paramagnet transition).Comment: 19 pages, REVTEX 3.0, 8 uuencoded Postscript figues appended, YCTP-xxx

Superconductor-Insulator Transition in a Capacitively Coupled Dissipative Environment

We present results on disordered amorphous films which are expected to undergo a field-tuned Superconductor-Insulator Transition.The addition of a parallel ground plane in proximity to the film changes the character of the transition.Although the screening effects expected from "dirty-boson" theories are not evident,there is evidence that the ground plane couples a certain type of dissipation into the system,causing a dissipation-induced phase transition.The dissipation due to the phase transition couples similarly into quantum phase transition systems such as superconductor-insulator transitions and Josephson junction arrays.Comment: 4 pages, 4 figure

Off-Diagonal Long Range Order and Scaling in a Disordered Quantum Hall System

We have numerically studied the bosonic off-diagonal long range order, introduced by Read to describe the ordering in ideal quantum Hall states, for noninteracting electrons in random potentials confined to the lowest Landau level. We find that it also describes the ordering in disordered quantum Hall states: the proposed order parameter vanishes in the disordered ($\sigma_{xy}=0$) phase and increases continuously from zero in the ordered ($\sigma_{xy}=e^2/h$) phase. We study the scaling of the order parameter and find that it is consistent with that of the one-electron Green's function.Comment: 10 pages and 4 figures, Revtex v3.0, UIUC preprint P-94-03-02

Critical Exponents for Three-Dimensional Superfluid--Bose-Glass Phase Transition

The critical phenomenon of the zero temperature superfluid--Bose-glass phase transition for hard-core bosons on a three-dimensional disordered lattice is studied using a quantum real-space renormalization-group method. The correlation-length exponent $\nu$ and the dynamic exponent z are computed. The critical exponent z is found to be 2.5 for compressible states and 1.3 for incompressible states. The exponent $\nu$ is shown to be insensitive to z as that in the two-dimensional case, and has value roughly equal to 1.Comment: 11 pages, REVTE

Ring exchange, the Bose metal, and bosonization in two dimensions

Motivated by the high-T_c cuprates, we consider a model of bosonic Cooper pairs moving on a square lattice via ring exchange. We show that this model offers a natural middle ground between a conventional antiferromagnetic Mott insulator and the fully deconfined fractionalized phase which underlies the spin-charge separation scenario for high-T_c superconductivity. We show that such ring models sustain a stable critical phase in two dimensions, the *Bose metal*. The Bose metal is a compressible state, with gapless but uncondensed boson and ``vortex'' excitations, power-law superconducting and charge-ordering correlations, and broad spectral functions. We characterize the Bose metal with the aid of an exact plaquette duality transformation, which motivates a universal low energy description of the Bose metal. This description is in terms of a pair of dual bosonic phase fields, and is a direct analog of the well-known one-dimensional bosonization approach. We verify the validity of the low energy description by numerical simulations of the ring model in its exact dual form. The relevance to the high-T_c superconductors and a variety of extensions to other systems are discussed, including the bosonization of a two dimensional fermionic ring model

Soluble `Supersymmetric' Quantum XY Model

We present a `supersymmetric' modification of the $d$-dimensional quantum rotor model whose ground state is exactly soluble. The model undergoes a vortex-binding transition from insulator to metal as the rotor coupling is varied. The Hamiltonian contains three-site terms which are relevant: they change the universality class of the transition from that of the ($d+1$)--- to the $d$-dimensional classical XY model. The metallic phase has algebraic ODLRO but the superfluid density is identically zero. Variational wave functions for single-particle and collective excitations are presented.Comment: 12 pages, REVTEX 3.0, IUCM93-00