Vortex phase separation in mesoscopic superconductors

Iaroshenko, Oleksandr; Rybalko, Volodymyr; Vinokur, V. M.; Berlyand, Leonid

doi:10.1038/srep01758

Cited by 11 publications

(11 citation statements)

References 20 publications

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“…Since the spatial scale of the variation of the order parameter ξ is the smallest scale in the problem we can set the dimensionless order parameter | u | = 1 everywhere besides the CDs. Then the problem of minimizing GL functional is formulated as a problem of finding a minimizer for the so-called harmonic map-type functional 25 ,…”

Section: Methodsmentioning

confidence: 99%

“…Since the spatial scale of the variation of the order parameter ξ is the smallest scale in the problem, we can set the order parameter | u | = 1 everywhere besides the CDs. It has been established 25 26 that the distribution of vortices obtained from the minimization of (1) is identical to that obtained by minimizing the energy…”

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confidence: 99%

“…If the array of CDs is regular , the vortex system can assume a terrace-like ground state i.e. form a hierarchical nested domain structure 25 26 .…”

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confidence: 99%

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Rayleigh approximation to ground state of the Bose and Coulomb glasses

Ryan

Mityushev

Vinokur

et al. 2015

Sci Rep

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Glasses are rigid systems in which competing interactions prevent simultaneous minimization of local energies. This leads to frustration and highly degenerate ground states the nature and properties of which are still far from being thoroughly understood. We report an analytical approach based on the method of functional equations that allows us to construct the Rayleigh approximation to the ground state of a two-dimensional (2D) random Coulomb system with logarithmic interactions. We realize a model for 2D Coulomb glass as a cylindrical type II superconductor containing randomly located columnar defects (CD) which trap superconducting vortices induced by applied magnetic field. Our findings break ground for analytical studies of glassy systems, marking an important step towards understanding their properties.

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Section: Methodsmentioning

confidence: 99%

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confidence: 99%

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Rayleigh approximation to ground state of the Bose and Coulomb glasses

Ryan

Mityushev

Vinokur

et al. 2015

Sci Rep

Self Cite

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“…The concept has subsequently been involved in many applications of the model: tribology [3][4][5], charge-density waves conductors [6][7][8][9], charge transport in solids and on crystal surfaces [10], magnetic or ferro-and antiferromagnetic domain walls CONTACT W. Quapp Email: quapp@uni-leipzig.de, J. M. Bofill Email: jmbofill@ub.edu [11], magnetic superlattices [12], superconductivity [13][14][15], vortex matter [16][17][18], fractal spin glasses [19], Josephson junctions [20,21], quantum algorithm [8], and H-bonded chains [1], just to name a few. Nowadays sliding friction forms a broad interdisciplinary research field that often involves the application of the FK model [3,22,23].…”

Section: Introductionmentioning

confidence: 99%

Newton trajectories for the tilted Frenkel–Kontorova model

Quapp

Bofill

2019

Molecular Physics

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Newton trajectories are used for the Frenkel-Kontorova model of a finite chain with free-end boundary conditions. We optimize stationary structures, as well as barrier breakdown points for a critical tilting force were depinning of the chain happens. These special points can be obtained straight forwardly by the tool of Newton trajectories. We explain the theory and add examples for a finite-length chain of a fixed number of 2, 3, 4, 5 and 23 particles.

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“…Using homogenization-type arguments, it was shown in [6] that in the limit of ε → 0 and when the external magnetic field of order O(a −2 ), the minimizers can be characterized by nested subdomains of constant vorticity. The physical nature of this result was discussed in [12]. The analysis in [6] relies on a conjecture that for small ε, the degrees of the hole vortices are the same for both C-and S 1 -valued maps.…”

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On approximation of Ginzburg–Landau minimizers by S1-valued maps in domains with vanishingly small holes

Berlyand

Golovaty

Iaroshenko

et al. 2018

Journal of Differential Equations

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We consider a two-dimensional Ginzburg-Landau problem on an arbitrary domain with a finite number of vanishingly small circular holes. A special choice of scaling relation between the material and geometric parameters (Ginzburg-Landau parameter vs hole radius) is motivated by a recently discovered phenomenon of vortex phase separation in superconducting composites. We show that, for each hole, the degrees of minimizers of the Ginzburg-Landau problems in the classes of S 1 -valued and C-valued maps, respectively, are the same. The presence of two parameters that are widely separated on a logarithmic scale constitutes the principal difficulty of the analysis that is based on energy decomposition techniques.1 have been studied, in particular, in [16,18] where the existence of two critical magnetic fields, H c1 and H c2 , was established rigorously for simply-connected domain when ε > 0 is small. When the external magnetic field is weak (h ext < H c1 ) it is completely expelled from the bulk semiconductor (Meissner effect) and there are no vortices. When the field strength is ramped up from H c1 to H c2 , the magnetic field penetrates the superconductor through an increasing number of isolated vortices while the superconductivity is destroyed everywhere, once the field exceeds H c2 .The pinning phenomenon that we consider in this paper is observed in non-simply-connected domains with holes that may or may not contain another material. If a hole "pins" a vortex, the order parameter u has a nonzero winding number on the boundary of the hole. We refer to this object as a hole vortex. Note that degrees of the hole vortices increase along with the strength of the external magnetic field. This situation is in contrast with the regular bulk vortices that have degree ±1 and increase in number as the field becomes stronger.An alternative way to model the impurities is to consider a potential term (a(x) − |u| 2 ) 2 where a(x) varies throughout the sample. It was proven in [9] that the impurities corresponding to the weakest superconductivity (where a(x) is minimal) pin the vortices first. This model was studied further in [1] and [4] to demonstrate the existence of nontrivial pinning patterns and in [2] to investigate the breakdown of pinning in an increasing external magnetic field, among other issues. A composite consisting of two superconducting samples with different critical temperatures was considered in [5,14] where nucleation of vortices near the interface was shown to occur.In our model we consider a superconductor with holes, similar to the setup in [3]. In that work, the authors considered the asymptotic limits of minimizers of GL ε as ε → 0 and determined that holes act as pinning sites gaining nonzero degree for moderate but bounded magnetic fields. For magnetic fields below the threshold of order | ln ε| the degree of the order parameter on the holes continues to grow without bound, however beyond the critical field strength, the pinning breaks down and vortices appear in the interior of the superconductor. Since...

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Vortex phase separation in mesoscopic superconductors

Cited by 11 publications

References 20 publications

Rayleigh approximation to ground state of the Bose and Coulomb glasses

Rayleigh approximation to ground state of the Bose and Coulomb glasses

Newton trajectories for the tilted Frenkel–Kontorova model

On approximation of Ginzburg–Landau minimizers by S1-valued maps in domains with vanishingly small holes

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