Onset of flux penetration into a type-I superconductor disk

Кузнецов, А. В.; Eremenko, D. V.; Trofimov, V. N.

doi:10.1103/physrevb.57.5412

Cited by 18 publications

(8 citation statements)

References 26 publications

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“…This approximation is possible, over a suitably small bias range, if the reorganization energy is much larger than the reaction free energy for the given ET reaction and leads to rates with exponential dependence on both the reorganization and reaction free energies. 20,21,41,44 All these approximations are, indeed, special cases of eqs 7a, which can be exploited to obtain further useful approximations (see, e.g., Figure S1 in the Supporting Information). We shall see that eqs 7a-d provide convenient ET rate expressions also for describing the I-φ ∆ characteristics of electrochemical molecular conduction junctions.…”

Section: Theoretical Modelsmentioning

confidence: 97%

“…Expressions (6) have been extensively used in theoretical analyses of electrochemical processes, 43 including electron transport in electrochemical molecular junctions. 20,21,44 In this work, in departure from standard treatments we consider the general expressions obtained from evaluating these integrals (see Appendix A):…”

Section: Theoretical Modelsmentioning

confidence: 99%

“…Extensive modeling studies are needed to guide such inquiries. 1 In recent years, redox molecular junctions, that is junctions whose operation involves reversible transitions 12 between two or more oxidation states of the molecular bridge, have been the focus of many experimental 2,11,[13][14][15][16][17][18] and theoretical 5,7,9,[19][20][21] studies, motivated by important features of nonlinear charge transport in such junctions and the control mechanisms offered by the correlation between their charging state and conductive properties. 2,13 The ability of a molecular junction to switch between redox states is synonymous with the ability of the bridging molecule to localize an electron during the transmission process, which in turn depends on the relative alignment of the electrode Fermi levels and molecular energy levels (usually, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO)) and on the interaction between the molecule and its thermal environment.…”

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confidence: 99%

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Nonlinear Charge Transport in Redox Molecular Junctions: A Marcus Perspective

2011

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Redox molecular junctions are molecular conduction junctions that involve more than one oxidation state of the molecular bridge. This property is derived from the ability of the molecule to transiently localize transmitting electrons, implying relatively weak molecule-leads coupling and, in many cases, the validity of the Marcus theory of electron transfer. Here we study the implications of this property on the nonlinear transport properties of such junctions. We obtain an analytical solution of the integral equations that describe molecular conduction in the Marcus kinetic regime and use it in different physical limits to predict some important features of nonlinear transport in metal-molecule-metal junctions. In particular, conduction, rectification, and negative differential resistance can be obtained in different regimes of interplay between two different conduction channels associated with different localization properties of the excess molecular charge, without specific assumptions about the electronic structure of the molecular bridge. The predicted behaviors show temperature dependences typically observed in the experiment. The validity of the proposed model and ways to test its predictions and implement the implied control strategies are discussed.

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Section: Theoretical Modelsmentioning

confidence: 97%

Section: Theoretical Modelsmentioning

confidence: 99%

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confidence: 99%

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Nonlinear Charge Transport in Redox Molecular Junctions: A Marcus Perspective

2011

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“…However, to determine precisely when a vortex enters or exits at the edge is a difficult problem, because these processes are sensitive to details such as the shape and perfection of the edge. 7,8,11,12,19,20,21,22,24,28,29,30,31,32,33,34,35,36,37,38 When H a is just above H 0 , vortices enter a pin-free disk and collect in a flux dome at the center, driven by the Lorentz force,…”

Section: Initial Growth Of Small Flux Domesmentioning

confidence: 99%

Geometrical Barriers and the Growth of Flux Domes in Thin Ideal Superconducting Disks

Clem

2008

J Supercond Nov Magn

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When an ideal (no bulk pinning) flat type-II superconducting disk is subjected to a perpendicular magnetic field Ha, the first vortex nucleates at the rim when Ha = H0, the threshold field, and moves quickly to the center of the disk. As Ha increases above H0, additional vortices join the others, and together they produce a domelike field distribution of radius b. In this paper I present analytic solutions for the resulting magnetic-field and sheet-current-density distributions. I show how these distributions vary as b increases with Ha, and I calculate the corresponding field-increasing magnetization.

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“…Instead, they exhibit intermediate state in which the sample splits into normal and superconducting regions separated by planar interfaces of positive energy [12][13][14]. Recently, there has been a renewed interest to the equilibrium structure, pinning, and dynamics of interfaces in type-I superconductors [15][16][17][18][19][20]. Pure lead has been mostly used as a prototypical experimental system.…”

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Quantum tunneling of the interfaces between normal-metal and superconducting regions of a type-I Pb superconductor

et al. 2011

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Evidence of a non-thermal magnetic relaxation in the intermediate state of a type-I superconducor is presented. It is attributed to quantum tunneling of interfaces separating normal and superconducting regions. Tunneling barriers are estimated and temperature of the crossover from thermal to quantum regime is obtained from Caldeira-Leggett theory. Comparison between theory and experiment points to tunneling of interface segments of size comparable to the coherence length, by steps of order one nanometer. When placed in the magnetic field, type-I superconductors do not develop flux lines. Instead, they exhibit intermediate state in which the sample splits into normal and superconducting regions separated by planar interfaces of positive energy [12][13][14]. Recently, there has been a renewed interest to the equilibrium structure, pinning, and dynamics of interfaces in type-I superconductors [15][16][17][18][19][20]. Pure lead has been mostly used as a prototypical experimental system. In the presence of pinning centers the interfaces adjust to the pinning potential by developing curvature as is schematically shown in Fig. 1. Pinning by point or small-volume defects should result in a broad distribution of energy barriers. It is, therefore, plausible that at low temperature type-I superconductors continue to relax towards equilibrium via quantum diffusion of interfaces. This situation is similar to the diffusion of domain walls in disordered ferromagnets with one essential difference. Contrary to a ferromagnetic domain wall, the dynamics of the planar interface in a superconductor should be dominated by dissipation.At low temperature the decay of metastable states created by pinning provides slow relaxation of magnets and superconductors towards thermal equilibrium. This relaxation is known as magnetic after-effect. At finite temperature it may occur via thermal activation with a probability proportional to exp(−U B /T ) where U B is the energy barrier. As T → 0 thermal processes die out and the only channel of escape from the metastable state becomes underbarrier quantum tunneling. Its probability is proportional to exp(−I ef f /h) where I ef f is the effective action associated with tunneling. The pre-exponential factors in the two expressions are of lesser importance because the dependence of the probability on the parameters is dominated by the exponents. Equating the two exponents, one finds that the crossover from thermal activation to quantum tunneling occurs at T Q ≈hU B /I ef f . Experimental evidence of such a crossover in type-II su-

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Onset of flux penetration into a type-I superconductor disk

Cited by 18 publications

References 26 publications

Nonlinear Charge Transport in Redox Molecular Junctions: A Marcus Perspective

Nonlinear Charge Transport in Redox Molecular Junctions: A Marcus Perspective

Geometrical Barriers and the Growth of Flux Domes in Thin Ideal Superconducting Disks

Quantum tunneling of the interfaces between normal-metal and superconducting regions of a type-I Pb superconductor

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