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Physical Review Letters

Random disorder in a model vortex liquid

Asle Sudbø

Published May 3, 1993• 6 citations
Publisher

Abstract

A model system of impenetrable vortex lines with short range interactions is considered on a cylindrical superconducting film with random disorder at a temperature T\ensuremath{\ge}0. The system is dual to spinless fermions in a dynamic random external potential. Replicaton and Bethe ansatz calculations yield a finite charge stiffness for the fermions, which are thus not localized. Some amount of correlation of the disorder appears necessary to produce a vortex-glass phase in the simple model vortex-pin system considered.

DOI
10.1103/physrevlett.70.2758

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A model system of impenetrable vortex lines with short range interactions is considered on a cylindrical superconducting film with random disorder at a temperature T\ensuremath{\ge}0. The system is dual to spinless fermions in a dynamic random external potential. Replicaton and Bethe ansatz calculations yield a finite charge stiffness for the fermions, which are thus not localized. Some amount of correlation of the disorder appears necessary to produce a vortex-glass phase in the simple model vortex-pin system considered.
We study the vortex glass transition in disordered high temperature superconductors using Monte Carlo simulations. We use a random pinning model with strong point-correlated quenched disorder, a net applied magnetic field, long-range vortex interactions, and periodic boundary conditions. From a finite size scaling study of the helicity modulus, the rms current, and the resistivity, we obtain critical exponents at the phase transition. The new exponents differ substantially from those of the gauge glass model, but are close to those of the pure three-dimensional XY model.
We analyze finite-temperature classical phase transitions that a two-dimensional collection of directed line objects placed in various external potentials may undergo. We find the conditions for a spin-glass-like transition in a disordered material and show that the collection of flux lines in dirty two-dimensional superconductors always stays in a vortex-glass phase. In addition, we resolve some of the controversies on the subject existing in the literature. We also look at a related problem of zero-temperature quantum phase transitions that a one-dimensional many-body system placed in various external potentials may undergo. In particular we predict that short-range repulsive bosons with sufficiently strong interaction will be pinned by a single impurity while translational symmetry is not broken for weakly repulsive particles; there is a phase transition between the indicated regimes. Taking into account the effects of commensurability, we construct the phase diagram for the conductive properties of a one-dimensional quantum liquid in the presence of a single impurity.
We study the phase diagram of flux lines in superconductors with columnar pins. Based on numerical exact diagonalization simulations on small clusters, we get two phases of vortices: A low-temperature pinned glass with diverging tilt modulus and a high-temperature delocalized entangled vortex liquid. For random potential disorder we find a new phase transition temperature TBG{T}_{\mathrm{BG}}TBG​ from a pinned Bose glass to an entangled liquid that reduces with increasing vortex density. This occurs primarily because vortices screen the disorder potential and generate an effective weaker random potential with increasing vortex density. For a fixed fraction of randomly placed attractive columnar pins, we find a Mott-insulating phase when the vortex density exactly matches the density of pins at the matching field ${B=B}_{\ensuremath{\varphi}}.$ We also find a transition from a strongly pinned Bose glass for $B<{B}_{\ensuremath{\varphi}}$ to a weakly pinned Bose glass for $B>{B}_{\ensuremath{\varphi}}$ as the vortex density is varied.
We study the ground state of a two-dimensional vortex system with random pinnings by cooling the vortex system to zero temperature. The peak of structure factor S ( k ) of vortices increases with vortex density B but decreases with pin density B ϕ , indicating that the vortex lattice becomes better and better ordered with increasing B . When B > B ϕ , the triangular vortex lattice is observed away from the pins. Repulsive vortex interactions destroy the Mott insulator phase which is predicted to occur at B = B ϕ . The crossover line between the strong Bose glass and the weak Bose glass is nearly independent of B ϕ for small B ϕ .
The XY\mathrm{XY}XY model with quenched random disorder is studied by a zero-temperature domain wall renormalization group method in two dimensions (2D) and three dimensions (3D). Instead of the usual phase representation we use the charge (vortex) representation to compute the domain wall, or defect, energy. For the gauge glass corresponding to the maximum disorder we reconfirm earlier predictions that there is no ordered phase in 2D but an ordered phase can exist in 3D at low temperature. However, our simulations yield spin stiffness exponents ${\ensuremath{\theta}}_{s}\ensuremath{\approx}\ensuremath{-}0.36$ in 2D and ${\ensuremath{\theta}}_{s}\ensuremath{\approx}+0.31$ in 3D, which are considerably larger than previous estimates and strongly suggest that the lower critical dimension is less than three. For the $\ifmmode\pm\else\textpm\fi{}J \mathrm{XY}$ spin glass in 3D, we obtain a spin stiffness exponent ${\ensuremath{\theta}}_{s}\ensuremath{\approx}+0.10$ which supports the existence of spin glass order at finite temperature in contrast with previous estimates which obtain ${\ensuremath{\theta}}_{s}<0.$ Our method also allows us to study renormalization group flows of both the coupling constant and the disorder strength with a length scale L. Our results are consistent with recent analytic and numerical studies suggesting the absence of a reentrant transition in 2D at low temperature. Some possible consequences and connections with real vortex systems are discussed.
We present 3D numerical simulation results for driven vortex lattices in presence of weak random columnar disorder at finite temperature and high driving force. A moving Bose glass phase is expected theoretically, characterized by a flow along rough static channels and dynamical transverse Meissner effect, the moving flux lines being localized along the correlated disorder direction. We find the moving Bose glass phase to be stable in a large range of temperature and velocity. Moreover, we confirm the existence of an effective static pinning potential in the tranverse direction, previously observed in zero temperature simulations, and leading to a "kink" structure of the vortex lines beyond a critical transverse field.