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arXiv:supr-con/9602001 · Physical review. B, Condensed matter

Vortex plastic flow, local flux density, magnetization hysteresis loops, and critical current, deep in the Bose-glass and Mott-insulator regimes

Cynthia J. O. Reichhardt, Cynthia J. Olson, Jennifer Groth, Stuart B. Field, Franco Nori

Published Apr 1, 1996• 112 citations
arXivHTMLPDF

Abstract

We present simulations of flux-gradient-driven superconducting vortices interacting with strong columnar pinning defects as an external field $H(t)$ is quasistatically swept from zero through a matching field ${B}_{\ensuremath{\varphi}}$. We analyze several measurable quantities, including the local flux density $B(x, y, H(t))$, magnetization $M(H(t))$, critical current ${J}_{c}(B(t))$, 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 ${J}_{c}(B)$ can be enhanced by maximizing the distance between the pins for $B<{B}_{\ensuremath{\varphi}}$.

DOI
10.1103/physrevb.53.r8898

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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\ensuremathφ{B}_{\ensuremath{\varphi}}B\ensuremathφ​. 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\ensuremathφ{B}_{\ensuremath{\varphi}}B\ensuremathφ​, 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\ensuremathφB<{B}_{\ensuremath{\varphi}}B<B\ensuremathφ​.
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 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.
I show that in a Bose glass superconductor with high jc{j}_{c}jc​ and at low TTT the magnetization relaxation ( SSS), dominated by quantum tunneling, is $\ensuremath{\propto}\sqrt{{j}_{c}}$, which crosses over to the conventional classical rate $\ensuremath{\propto}T/{j}_{c}$ at higher TTT and lower jc{j}_{c}jc​, with the crossover ${T}^{*}\ensuremath{\sim}{j}_{c}^{3/2}$. I argue that due to interactions between flux lines there exist three relaxation regimes, depending on whether $B<{B}_{\ensuremath{\varphi}}$, $B\ensuremath{\approx}{B}_{\ensuremath{\varphi}}$, $B>{B}_{\ensuremath{\varphi}}$, corresponding to strongly pinned Bose glass with large jc2{j}_{c2}jc2​, Mott insulator with vanishing SSS, and weakly pinned Bose glass characterized by small jc1{j}_{c1}jc1​. I discuss the effects of interactions on jc{j}_{c}jc​ and focus attention on a recent experiment which is consistently described by the theory.
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 .
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.
Superconductivity is an electronic state of matter arising from the existence of a common wave function with a coherent phase extending on a truly macroscopic scale. One major manifestation of this striking quantum phenomenon is the dissipationless transport of electrical current, an asset deserving particular attention in the present times where the efficient energy distribution has become of utmost importance. Unfortunately, the motion of quantum units of magnetic flux (so-called vortices or fluxons), which is an unavoidable side-effect found in superconductors in the presence of transport currents and magnetic fields, severely limits the conditions to preserve dissipationless transport. This poses a challenge for achieving the functionalization of superconducting materials and threatens their spectrum of applications. It is widely known that any inhomogeneities (either material imperfections, or ones made artificially), which locally suppress superconductivity on the scale comparable to the core of the vortex, can pin the vortex and delay the onset of the vortex motion to higher applied currents. In recent years a substantial effort has been made to minimize the effects of current-induced vortex motion by tailoring arrays of artificial pinning centers. Besides improving the critical parameters of the superconducting state, a pinning matrix can be used for the manipulation of vortex matter, thus directly affecting the vortex dynamics, such as rectification of vortex motion under an ac drive (vortex diode) by introducing asymmetric pinning landscapes. In the literature one can find that the realization of the anchoring of the vortices can be based on nanostructured arrays of perforations, chemically grown defects, permanent nanomagnets, or even pinning sites produced by heavy ion bombardment. All of those realizations are based on a permanent imprint on the superconductor, without any possibility for subsequent modifications in the distribution and strength of the pinning. The principal objective of this thesis is to investigate the dynamical behavior of vortex matter under an entirely new kind of pinning landscape consisting of spatial and temporal modulation of the superconducting condensate. A particular case of spatial modulation is considered in a constricted structure where current lensing can cause extremely high vortex velocities. Subsequently, a time-dependent thermal potential introduced to the superconducting condensate will cause stroboscopic resonances during the vortex motion - a phenomenon that cannot be observed in the systems with static pinning imprints. Finally, a study of electronic gating is presented, where the local properties of superconductor, such as mean free path, or electronic band structure in general, can be influenced electronically. This is a completely unexplored interdisciplinary research topic, which will eventually allow one to manipulate individual vortices in superconducting materials by means of spatially confined and temporally controlled thermal and electromagnetic excitations. Furthermore, such techniques can provide one fundamental insight in different states of the vortex matter with respect to variation of the transport current, highly relevant for understanding the resistive state of superconducting materials and their applications.