Statistical Mechanics of Vortices in Type-II Superconductors

Huse, David A.; Radzihovsky, Leo

doi:10.1016/b978-0-444-81591-0.50007-9

Cited by 4 publications

(3 citation statements)

References 56 publications

(95 reference statements)

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“…These include flux lattices in type-II superconductors 2,3 , charge density waves (CDWs) in anisotropic conductors 4 , magnetic bubble arrays 5 , and the magnetically-induced Wigner crystal in a two-dimensional electron gas 6,7 . In all these systems the relevant degrees of freedom -be they vortices in superconductors or electrons in metals -form a lattice inside a solid matrix, provided by the superconducting or conducting material.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium steady states of driven periodic media

1998

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We study a periodic medium driven over a random or periodic substrate, characterizing the nonequilibrium phases which occur by dynamic order parameters and their correlations. Starting with a microscopic lattice Hamiltonian, we perform a careful coarse-graining procedure to derive continuum hydrodynamic equations of motion in the laboratory frame. This procedure induces nonequilibrium effects (e.g. convective terms, KPZ nonlinearities, and non-conservative forces) which cannot be derived by a naive Galileian boost. Rather than attempting a general analysis of these equations of motion, we argue that in the random case instabilities will always destroy the LRO of the lattice. We suggest that the only periodicity that can survive in the driven state is that of a transverse smectic, with ordering wavevector perpendicular to the direction of motion. This conjecture is supported by an analysis of the linearized equations of motion showing that the induced nonequilibrium component of the force leads to displacements parallel to the mean velocity that diverge with the system size. In two dimensions, this divergence is extremely strong and can drive a melting of the crystal along the direction of motion. The resulting driven smectic phase should also occur in three dimensions at intermediate driving. It consists of a periodic array of flowing liquid channels, with transverse displacements and density ("permeation mode") as hydrodynamic variables. We study the hydrodynamics of the driven smectic within the dynamic functional renormalization group in two and three dimensions. The finite temperature behavior is much less glassy than in equilibrium, owing to a disorder-driven effective "heating" (allowed by the absence of the fluctuation-dissipation theorem). This, in conjunction with the permeation mode, leads to a fundamentally analytic transverse response for T > 0.

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Section: Introductionmentioning

confidence: 99%

Nonequilibrium steady states of driven periodic media

1998

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“…The discovery of high-temperature superconductivity in materials with strong planar anisotropy has led to renewed experimental [1][2][3][4] and theoretical [5][6][7][8][9] interest in the properties of two-dimensional and strongly anisotropic three-dimensional type-II superconductors at fields near H c2 (T ) where thermal fluctuations are important. Phase transitions of type-II superconductors in a magnetic field are unusual because of the Landau level degeneracy of Cooper-pair states in a magnetic field [10].…”

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confidence: 99%

Participation-ratio entropy and critical fluctuations in the thermodynamics of pancake vortices

MacDonald

1995

Phys. Rev. B

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We report on a study of the thermodynamics of the Ginzburg-Landau model for tmo-dimensional type-II superconductors near the transition from the normal state to the Abrikosov-lattice state. We couch our analysis in terms of the participation-ratio entropy s(P), which completely determines the thermodynamics of the system. We report on results for s(P) obtained analytically using perturbation expansion methods and numerically using Monte Carlo simulation methods and discuss the weak first-order phase transition which occurs in this system in terms of the properties of s(P). The discovery of high-temperature superconductivity in materials with strong planar anisotropy has led to renewed experimental and theoretical interest in the properties of two-dimensional and strongly anisotropic three-dimensional type-II superconductors at fields near H, 2(T). Phase transitions of type-II superconductors in a magnetic Geld are unusual because of the Landau leve1 degeneracy of Cooper-pair states in a magnetic field. In mean-field-theory continuous phase transitions occur simultaneously in a number of channels equal to the Landau level degeneracy and the low-temperature Abrikosov lattice state has both superconducting and positional order. It is well established experimentally and theoretically that the Abrikosov vortex lattice state in D = 3 dimension melts into a vortex liquid state through a weakly Grst-order phase transition. ' ' ' A consensus ' 'has emerged from recent work that a weak first-order phase transition with a latent heat which is 2'Fo of the mean-field condensation energy at the depressed transition temperature also survives in D = 2, although this view is not universally held.The thermodynamics of this system may be expressed in terms of s(P) the participation-ratio entropy. In this paper we report on evaluations of s(P) based on high-temperature and lowtemperature expansions and on Monte Carlo simulations of the Ginzburg-Landau (GL) model.For fields suKciently strong and close to H 2 the order parameter is confined to the lowest Cooper-pair Landau level.The &ee energy density of the lowest-Landaulevel GL (LLL-GL) model is when the order parameter has a smaller participation ratio (2) P[4'] is roughly the fraction of the area A of the sample over which the local superfiuid density (l@l ) is spread. (In LLL-GL theory P [@] is known as the Abrikosov ratio, P~[4]. ) For a given participation ratio the minimum of E&L/A is o. Ir P/2p. -The mean-field-theory order parameter of the LI L-GL model is the LLI. order parameter with the maximum value of P; P is maximized by placing the vortices on a triangular lattice; P~--1/Pgg = 0.862370. . . At finite temperatures the properties of the LLL-GL model are determined by a competition between the thermal weighting factor (exp( -Eci, [4']jkgyT)) which favors large values of P[iII] and the distribution function of P[4] which is peaked at smaller values of P as we discuss below.In the Landau gauge the order parameter can be expanded in the form, where the number of terms in th...

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“…As a result, much has been clarified about the nature of equilibrium and nonequilibrium properties of vortex states in the presence of thermal fluctuations, pinning disorder and electrical ("super"-) current [2][3][4][5][6] , leading to a rich phase diagram. In particular, in contrast to a mean-field phase diagram, thermal fluctuations drive a first-order melting of a vortex lattice over a large portion of the phase diagram into a resistive (although with large conductivity and diamagnetic response) vortex liquid [7][8][9][10] , that, from the symmetry point of view is qualitatively identical to the normal state.…”

Section: Introduction a Background And Motivationmentioning

confidence: 99%

Thermal depinning and transverse-field tilting transitions in a planar vortex array pinned by a columnar defect

Radzihovsky

2006

Phys. Rev. B

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We study thermal and a transverse magnetic field response of a vortex line array confined to a plane with a single columnar pinning defect. By integrating out "bulk" degrees of freedom away from the columnar defect we reduce this two-dimensional problem to a one-dimensional one, localized on the defect and exhibiting a long-range elasticity along the defect. We show that as a function of temperature, for a magnetic field aligned with the defect this system exhibits a one-dimensional analog of a roughening transition, with a low-temperature "smooth" phase corresponding to a vortex array pinned by the defect, and a high-temperature "rough" phase in which at long scales thermal fluctuations effectively average away pinning by the defect. We also find that in the low-temperature pinned phase, the vortex lattice tilt response to a transverse magnetic field proceeds via a soliton proliferation "transition", governed by an integrable sine-Hilbert equation and analogous to the well-known commensurate-incommensurate transition in sine-Gordon systems. The distinguishing feature here is the long-range nature of the one-dimensional elasticity, leading to a logarithmic soliton energy and interaction. We predict the transverse-field-temperature phase diagram and discuss extension of our results to a bulk vortex array in the presence of a dilute concentration of columnar defects.

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Statistical Mechanics of Vortices in Type-II Superconductors

Cited by 4 publications

References 56 publications

Nonequilibrium steady states of driven periodic media

Nonequilibrium steady states of driven periodic media

Participation-ratio entropy and critical fluctuations in the thermodynamics of pancake vortices

Thermal depinning and transverse-field tilting transitions in a planar vortex array pinned by a columnar defect

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