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arXiv:cond-mat/0111361 · Physical review. B, Condensed matter

Competition between columnar pins and vortex screening: A doubly reentrant phase diagram

Ajay Nandgaonkar, D. G. Kanhere, Nandini Trivedi

Published Sep 30, 2002• 6 citations
arXivHTMLPDF

Abstract

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 ${T}_{\mathrm{BG}}$ 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.

DOI
10.1103/physrevb.66.104527

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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\ensuremathφ.{B=B}_{\ensuremath{\varphi}}.B=B\ensuremathφ​. We also find a transition from a strongly pinned Bose glass for B<B\ensuremathφB<{B}_{\ensuremath{\varphi}}B<B\ensuremathφ​ to a weakly pinned Bose glass for B>B\ensuremathφB>{B}_{\ensuremath{\varphi}}B>B\ensuremathφ​ 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 phase diagram of two bosonic chains coupled by interchain hopping and interchain boson-boson repulsion is investigated by means of bosonization and renormalization-group techniques. It comprises two types of charge-density waves, a conventional superfluid phase, and a superfluid phase made of condensed boson pairs. The effect of a random potential on that system is also derived. Compared with the one-chain case, interchain hopping strongly stabilizes the conventional superfluid phase with respect to Anderson localization. By contrast, the superfluid phase made of condensed boson pairs is much more unstable with respect to Anderson localization than the superfluid phase of the one-chain system. An exact mapping of the two strongly correlated bosonic chains onto two coupled vortex planes gives us the phase diagram of the latter system without any further calculation. The vortex system exhibits two types of vortex lattice phase (one with entanglement and another one without entanglement), a normal phase and a phase with bound pairs of vortices. The results for Anderson localization of the bosons allow us to study vortex pinning by columnar defects or twin boundaries and obtain the correlation length of the pinned vortex lattice. We show that interplane vortex hopping strongly reduces vortex pinning by columnar defects but not by twin boundaries. We obtain the melting temperature of the entangled solid. We also derive the critical current by modified Larkin-Ovchinnikov arguments and find a very sharp decrease of critical currents when the system moves into the entangled phase in the case of columnar pins. For strong columnar pins, there is a transition into a pinned solid phase with dislocations. We argue that two multicritical points may exist in the phase diagram.
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 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.
We study vortex lines in high-temperature superconductors with columnar defects produced by heavy-ion irradiation. We reconsider scaling theory for the Bose-glass transition with tilted magnetic fields, and propose, e.g. , a new scaling form for the shape of the Bose glass phase boundary, which is relevant for experiments. We also consider Monte Carlo simulations for a vortex model with a screened interaction. Critical exponents are determined from scaling analysis of Monte Carlo data for current-voltage characteristics and other quantities. The dynamic critical exponent is found to be z = 4.6 ± 0.3.
We present simulations of flux-gradient-driven superconducting vortices interacting with strong columnar pinning defects as an external field H(t)H(t)H(t) is quasistatically swept from zero through a matching field ${B}_{\ensuremath{\varphi}}$. We analyze several measurable quantities, including the local flux density B(x,y,H(t))B(x, y, H(t))B(x,y,H(t)), magnetization M(H(t))M(H(t))M(H(t)), critical current Jc(B(t)){J}_{c}(B(t))Jc​(B(t)), and the individual vortex flow paths. We find a significant change in the behavior of these quantities as the local flux density crosses ${B}_{\ensuremath{\varphi}}$, and quantify it for many microscopic pinning parameters. Further, we find that for a given pin density Jc(B){J}_{c}(B)Jc​(B) can be enhanced by maximizing the distance between the pins for $B<{B}_{\ensuremath{\varphi}}$.