Static high-field vortex phase of disordered high-Tc superconductors: equilibrium elastic vortex glass or current-induced ordering of a plastically pinned state?

In disordered high-temperature superconductors (HTS), standard transport measurements show electric-field/current-density scaling collapses widely interpreted as a vortex-glass transition, whereas dc magnetization relaxation on the same materials reveals finite, plastic pinning barriers at the small current densities representative of static conditions. L. Miu (Physica C 468, 1254 (2008)) proposed that this tension is resolved by current-induced ordering: the large currents needed for transport dynamically heal vortex-lattice dislocations and order the creeping vortex assembly, so the apparent elastic vortex glass is a measurement artifact and the static $J\to 0$ phase is intrinsically plastic. The open problem is to determine the true nature of the static high-field vortex phase of disordered HTS: whether an equilibrium elastic vortex glass, in which the vortex pinning barriers diverge at low current densities, exists in the zero-current limit at high field, or whether the static phase is intrinsically plastically pinned with nondiverging barriers over the wide $H$-$T$ domain revealed by dc magnetization relaxation, so that the elastic-vortex-glass signature of standard $E$-$J$ transport scaling is instead produced by the ordering effect of the driving force (current-induced dynamic ordering of the creeping vortex assembly) present in the transport experiments.

Background

In a type-II superconductor in a magnetic field, flux penetrates as quantized vortex lines (flux quantum $\Phi_0=h/2e$) that form the Abrikosov vortex lattice and are pinned by material defects. In high-temperature superconductors (HTS), chiefly cuprates such as $YBa_2Cu_3O_{7-\delta}$ (YBCO) and $Bi_2Sr_2CaCu_2O_{8+\delta}$ (Bi-2212), thermal fluctuations let vortices hop over pinning barriers in a process called thermally activated flux creep, which slowly decays the persistent currents. In the Bean critical-state model the irreversible magnetic moment $M$ is proportional to the macroscopic current density $J$ circulating in the sample, so the time decay of $M$ in a dc magnetization-relaxation experiment measures creep at $J$ values far below those of transport measurements. Two standard diagnostics are the normalized relaxation rate $S=-\Delta\ln|M|/\Delta\ln t$ (evaluated over a time window) and the normalized vortex-creep activation energy $U^*=T/S$, where $T$ is temperature.

Creep is called elastic (or collective) when vortices move as an elastically distorted, topologically ordered manifold, so the pinning barrier $U$ grows without bound as $J\to 0$; in the weak-disorder limit this ordered disordered phase is the Bragg glass. Creep is called plastic when vortex-lattice defects, chiefly dislocations, mediate motion and the effective barrier stays finite. The vortex-glass model of Fisher, Fisher, and Huse predicted that strong quenched disorder freezes the vortex system at a finite glass temperature $T_g$ into a true thermodynamic phase with zero linear resistivity and diverging activation barriers, and Koch et al. reported scaling collapses of the electric-field-versus-current-density ($E$-$J$) isotherms of YBCO films consistent with such a transition. This framework became the standard reading of high-field transport data in disordered HTS.

L. Miu (2008) challenged this reading with dc magnetization relaxation (zero-field-cooled, first data point near $t\approx 100$ s) on optimally doped YBCO films of three thicknesses ($\approx 200$, $250$, and $1000$ nm, $T_c\approx 91.5$ K), compared with published Bi-2212 results. The temperature of the $U^*(T)$ maximum, taken as the elastic-to-plastic creep crossover, lies far below the transport $T_g$ (about 20 K versus $T_g\approx 85.3$ K at $H=25$ kOe for the 200 nm film, where the $E$-$J$ collapse yields $z\approx 6.1$, $\nu\approx 1.55$) and shifts to still lower $T$ when the relaxation window samples smaller $J$. The crossover points define a current-induced order-disorder line in the $H$-$T$ plane, empirically $H\propto T^{-2}$ at low $T$ with prefactor $a\approx 1.2$-$1.5\times 10^4$ kOe$\cdot$K$^2$, essentially thickness-independent across the three films. Miu proposed that extrapolating the monotonic shift of the crossover to $J\to 0$ indicates non-diverging plastic barriers, i.e. no elastic vortex glass in the static limit; the glass-like transport signature is then attributed to current-induced ordering: the comparatively large current densities required in transport reduce the pinning energy relative to the vortex elastic energy, allow some lattice dislocations to heal, and dynamically order the creeping vortex assembly. Dynamic ordering of driven vortex matter under strong drive is an established phenomenon in other superconductors (dynamic melting of the moving lattice and flow-induced lattice organization), which makes the mechanism plausible, but it has not been tested in disordered cuprates at the relevant current densities, and the role of surface barriers (barriers to vortex entry at the sample surface, which in Bi-2212 were proposed to inject disordered vortices through nonuniform surface regions) remains unsettled. A full microscopic theory tying the measured relaxation maximum, the drive-induced ordering, and the dislocation structure of the disordered phase together does not exist.

Problem Statement

Determine the nature of the static, zero-current-limit high-field vortex phase in disordered high-temperature superconductors, and the origin of its apparent glassy transport signatures: do disordered HTS develop diverging elastic (collective) pinning barriers as the driving current density $J\to 0$ at high magnetic field, i.e. does an equilibrium elastic vortex glass exist in the static limit, or is the static disordered phase intrinsically plastically pinned, with nondiverging (plastic) pinning barriers over the wide $H$-$T$ domain revealed by dc magnetization relaxation, and the vortex-glass signature of standard $E$-$J$ transport scaling instead produced by the ordering effect of the driving force, i.e. by current-induced dynamic ordering of the vortex assembly at the large current densities transport requires?

References

1. L. Miu, 'Absence of an elastic vortex glass in disordered HTS', Physica C: Superconductivity 468, 1254-1257 (2008). DOI: 10.1016/j.physc.2008.05.008, https://doi.org/10.1016/j.physc.2008.05.008
2. R. H. Koch, V. Foglietti, W. J. Gallagher, G. Koren, A. Gupta, M. P. A. Fisher, 'Experimental evidence for vortex-glass superconductivity in Y-Ba-Cu-O', Physical Review Letters 63, 1511-1514 (1989). DOI: 10.1103/PhysRevLett.63.1511, https://doi.org/10.1103/PhysRevLett.63.1511
3. D. S. Fisher, M. P. A. Fisher, D. A. Huse, 'Thermal fluctuations, quenched disorder, phase transitions, and transport in type-II superconductors', Physical Review B 43, 130-159 (1991). DOI: 10.1103/PhysRevB.43.130, https://doi.org/10.1103/PhysRevB.43.130
4. Y. Yeshurun, A. P. Malozemoff, A. Shaulov, 'Magnetic relaxation in high-temperature superconductors', Reviews of Modern Physics 68, 911-949 (1996). DOI: 10.1103/RevModPhys.68.911, https://doi.org/10.1103/RevModPhys.68.911
5. T. Giamarchi, P. Le Doussal, 'Elastic theory of flux lattices in the presence of weak disorder', Physical Review B 52, 1242-1270 (1995). DOI: 10.1103/PhysRevB.52.1242, https://doi.org/10.1103/PhysRevB.52.1242
6. A. E. Koshelev, V. M. Vinokur, 'Dynamic melting of the vortex lattice', Physical Review Letters 73, 3580-3583 (1994). DOI: 10.1103/PhysRevLett.73.3580, https://doi.org/10.1103/PhysRevLett.73.3580
7. W. Henderson, E. Y. Andrei, M. J. Higgins, 'Plastic motion of a vortex lattice driven by alternating current', Physical Review Letters 81, 2352-2355 (1998). DOI: 10.1103/PhysRevLett.81.2352, https://doi.org/10.1103/PhysRevLett.81.2352
8. Z. L. Xiao, E. Y. Andrei, M. J. Higgins, 'Flow induced organization and memory of a vortex lattice', Physical Review Letters 83, 1664-1667 (1999). DOI: 10.1103/PhysRevLett.83.1664, https://doi.org/10.1103/PhysRevLett.83.1664
9. L. Miu, T. Noji, Y. Koike, E. Cimpoiasu, T. Stein, C. C. Almasan, 'Crossover from elastic to plastic vortex creep across the second magnetization peak of high-temperature superconductors', Physical Review B 62, 15172-15176 (2000). DOI: 10.1103/PhysRevB.62.15172, https://doi.org/10.1103/PhysRevB.62.15172
10. Y. Paltiel, E. Zeldov, Y. Myasoedov, M. L. Rappaport, G. Jung, S. Bhattacharya, M. J. Higgins, Z. L. Xiao, E. Y. Andrei, P. L. Gammel, D. J. Bishop, 'Instabilities and disorder-driven first-order transition of the vortex lattice', Physical Review Letters 85, 3712-3715 (2000). DOI: 10.1103/PhysRevLett.85.3712, https://doi.org/10.1103/PhysRevLett.85.3712
11. D. R. Strachan, M. C. Sullivan, P. Fournier, S. P. Pai, T. Venkatesan, C. J. Lobb, 'Do superconductors have zero resistance in a magnetic field?', Physical Review Letters 87, 067007 (2001); preprint 'Is there a vortex-glass transition in high-temperature superconductors?', arXiv:cond-mat/0011014. DOI: 10.1103/PhysRevLett.87.067007, https://arxiv.org/abs/cond-mat/0011014
12. S. L. Li, H. H. Wen, 'Absence of a true vortex-glass phase above the Bragg glass line in Bi2Sr2CaCu2O8+delta', Physica C: Superconductivity 390, 107-112 (2003). DOI: 10.1016/S0921-4534(03)00622-1, https://doi.org/10.1016/S0921-4534(03)00622-1
13. L. Miu, S. Popa, T. Noji, Y. Koike, D. Miu, S. Diaz, G. Chouteau, 'Nonmonotonic temperature dependence of the experimentally determined vortex-creep activation energy in disordered high-temperature superconductors', Physical Review B 70, 134523 (2004). DOI: 10.1103/PhysRevB.70.134523, https://doi.org/10.1103/PhysRevB.70.134523
14. L. Miu, 'Ordering of the creeping vortex system in Bi2Sr2CaCu2O8+delta single crystals at low temperatures', Physical Review B 72, 132502 (2005). DOI: 10.1103/PhysRevB.72.132502, https://doi.org/10.1103/PhysRevB.72.132502
15. L. Miu, D. Miu, G. Jakob, H. Adrian, 'Vortex-system ordering during magnetisation measurements in YBa2Cu3O7-delta films at low temperatures', Physica C: Superconductivity 460-462, 1206-1207 (2007). DOI: 10.1016/j.physc.2007.04.050, https://doi.org/10.1016/j.physc.2007.04.050
16. N. Kokubo, T. Asada, K. Kadowaki, K. Takita, T. G. Sorop, P. H. Kes, 'Dynamic ordering of driven vortex matter in the peak effect regime of amorphous MoGe films and 2H-NbSe2 crystals', Physical Review B 75, 184512 (2007), arXiv:0706.2047. DOI: 10.1103/PhysRevB.75.184512, https://arxiv.org/abs/0706.2047
17. M. G. Adesso, M. Polichetti, S. Pace, 'A new method to detect the vortex glass phase and its evidence in YBCO', Journal of Physics: Condensed Matter 20, 385211 (2008), arXiv:0807.2260. DOI: 10.1088/0953-8984/20/38/385211, https://doi.org/10.1088/0953-8984/20/38/385211
18. I. Ivan, D. Miu, S. Popa, G. Jakob, L. Miu, 'On the determination of vortex creep parameters in superconductors using standard magnetization relaxation data', Superconductor Science and Technology 24, 095005 (2011). DOI: 10.1088/0953-2048/24/9/095005, https://doi.org/10.1088/0953-2048/24/9/095005
19. A. El Tahan, G. Jakob, D. Miu, I. Ivan, P. Badica, L. Miu, 'Vortex creep crossover in YBCO/PrBCO superlattices during standard magnetization relaxation measurements', Superconductor Science and Technology 24, 045014 (2011). DOI: 10.1088/0953-2048/24/4/045014, https://doi.org/10.1088/0953-2048/24/4/045014
20. L. Miu, P. Mele, A. Crisan, A. Ionescu, D. Miu, 'Evolution of vortex dynamics in YBa2Cu3O7 films with nanorods by adding nanoparticles', Physica C: Superconductivity 500, 40-43 (2014). DOI: 10.1016/j.physc.2014.03.002, https://doi.org/10.1016/j.physc.2014.03.002
21. A. M. Ionescu, D. Miu, A. Crisan, L. Miu, 'Pinning-induced vortex-system disordering at the origin of the second magnetization peak in superconducting single crystals', Journal of Superconductivity and Novel Magnetism 31, 2329-2337 (2017). DOI: 10.1007/s10948-017-4487-5, https://doi.org/10.1007/s10948-017-4487-5
22. L. Miu, A. M. Ionescu, D. Miu, M. Burdusel, P. Badica, D. Batalu, A. Crisan, 'Second magnetization peak, rhombic-to-square Bragg vortex glass transition, and intersecting magnetic hysteresis curves in overdoped BaFe2(As1-xPx)2 single crystals', Scientific Reports 10, 17274 (2020). DOI: 10.1038/s41598-020-74156-z, https://doi.org/10.1038/s41598-020-74156-z
23. I. Ivan, A. M. Ionescu, D. N. Crisan, A. Crisan, 'Vortex glass-vortex liquid transition in BaFe2(As1-xPx)2 and CaKFe4As4 superconductors from multi-harmonic AC magnetic susceptibility studies', International Journal of Molecular Sciences 24, 7896 (2023). DOI: 10.3390/ijms24097896, https://doi.org/10.3390/ijms24097896
24. M. Zehetmayer, 'How the vortex lattice of a superconductor becomes disordered: a study by scanning tunneling spectroscopy', Scientific Reports 5, 9244 (2015). DOI: 10.1038/srep09244, https://doi.org/10.1038/srep09244
25. L. Burlachkov, V. Vinokur, 'Density-gradient mechanism of vortex plastic creep', Physical Review B 106, 094513 (2022). DOI: 10.1103/PhysRevB.106.094513, https://doi.org/10.1103/PhysRevB.106.094513
26. S. Sundar, P. V. Lopes, S. Salem-Sugui Jr., Z.-Z. Li, W.-S. Hong, H.-Q. Luo, S.-L. Li, L. Ghivelder, 'Order-disorder phase transition and elastic-to-plastic vortex creep crossover in a triclinic iron pnictide superconductor (Ca0.85La0.15)10(Pt3As8)(Fe2As2)5', Scientific Reports 13, 16273 (2023). DOI: 10.1038/s41598-023-43424-z, https://doi.org/10.1038/s41598-023-43424-z
27. Z.-Y. Han, T.-Y. Jing, J. Yang, W.-B. Cai, Z.-Q. Li, 'Vortex-glass transition and vortex pinning behavior in three-dimensional NbTiN epitaxial films', Superconductor Science and Technology 37, 055011 (2024). DOI: 10.1088/1361-6668/ad3f82, https://doi.org/10.1088/1361-6668/ad3f82
28. J. Lidmar, 'Amorphous vortex glass phase in strongly disordered superconductors', Physical Review Letters 91, 097001 (2003). DOI: 10.1103/PhysRevLett.91.097001, https://doi.org/10.1103/PhysRevLett.91.097001
29. P. Olsson, 'Depinning of the Bragg glass in a point disordered model superconductor', Physical Review Letters 98, 097001 (2007). DOI: 10.1103/PhysRevLett.98.097001, https://doi.org/10.1103/PhysRevLett.98.097001