Characteristics of two-dimensional vortex dynamics from XY-type models with Ginzburg-Landau dynamics

Jönsson, Anna; Minnhagen, Petter

doi:10.1103/physrevb.55.9035

Cited by 34 publications

(50 citation statements)

References 14 publications

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“…Bound motion is still dominant up to T /T BKT = 1.1, since its weight is larger, although the free mobility itself exceeds the one of bound pairs. Combining the two contributions (figure 4) yields a rather extended flat region of Im(1/ǫ(ω)) for intermediate frequencies, which is another signature of ≪anomalous≫ vortex dynamics found also in numerical simulations [24].…”

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confidence: 69%

Vortex dynamics in two-dimensional Josephson junction arrays

2003

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The dynamic response of unfrustrated two-dimensional Josephson junction arrays close to, but above the Kosterlitz-Thouless(KT ) transition temperature is described in terms of the vortex dielectric function ǫ(ω). The latter is calculated by considering separately the contribution of ≪free≫ vortices interacting by a screened Coulomb potential, and the ≪pair motion≫ of vortices that are closer to each other than the KT correlation length. This procedure allows to understand various anomalous features in ǫ(ω) and in the flux noise spectra that have been observed experimentally and in dynamic simulations. The dynamics of JJAs is less well understood. For the equations of motion for the superconducting phases the ≪resistively shunted junction model≫ (RSJ) can be used for arrays in which electrostatic charging effects may be neglected. Based on this model an equation of motion for the vortex excitations can be derived [3], describing them as massless point particles, subject to a friction force coming from normal current losses and interacting via the 2d Coulomb interaction, varying essentially with the logarithm of their distance. The dynamics of such a system is usually treated by considering separately the motion of bound pairs and of free particles. The simplest picture for free motion is given by the Drude form of the dynamic dielectric function ǫ(ω), expressed in terms of the friction constant. Minnhagen [4] has developed a more sophisticated expression for ǫ(ω) by assuming that this quantity can be derived from the static wave number dependent dielectric function, taken to have a Debye screening form, by replacing the wave number by frequency. The result -usually referred to as ≪Minnhagen phenomenology≫ (M P ) -differs in an essential way from Drude's (D) behaviour. In particular Re(1/ǫ D (ω)) ∝ ω 2 , whereas Re(1/ǫ MP (ω)) ∝ |ω|, and the so-called ≪peak-ratio≫ r, given by (1) where ω max is the frequency at which Im(1/ǫ) has its maximum, is r D = 1, whereas r MP = 2/π is smaller.The dynamics below T BKT is usually treated by averaging the dynamic response of a pair of separation d over a probability distribution for d [5,6].Three main types of experiments aim at elucidating dynamical properties of JJAs. The exponent of the non-linear current-voltage characteristics is related to the dynamic critical exponent describing the critical slowing down of the 2d CG near the BKT transition (see [1]). The dynamic conductance G(ω) of the array can be inferred from measuring the dynamic response of the array to a time dependent current in a two-coil experiment [1,2,7]. Measurements on frustrated arrays [8] have produced results that are closer to the M P prediction than to the simple Drude form, in particular as far as the above-mentioned peak-ratio and the frequency dependence of 1/ǫ(ω) are concerned: Re(1/ǫ(ω)) ∝ |ω| over a sizable range of frequencies, which is a signature of anomalous M P dynamics. Similar results have been obtained by analytical calculations [6,9,10].Measuring the temporal fluctuations of the magneti...

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confidence: 69%

Vortex dynamics in two-dimensional Josephson junction arrays

2003

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“…32: ξ is obtained from the wavevector dependence of the static dielectric function 1/ǫ(0) introduced in Eq. (24).…”

Section: High-temperature Phasementioning

confidence: 99%

Dynamic critical exponent of two-, three-, and four-dimensionalXYmodels with relaxational and resistively shunted junction dynamics

2000

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The dynamic critical exponent z is determined numerically for the d-dimensional XY model (d = 2, 3, and 4) subject to relaxational dynamics and resistively shunted junction dynamics. We investigate both the equilibrium fluctuation and the relaxation behavior from nonequilibrium towards equilibrium, using the finite-size scaling method. The resulting values of z are shown to depend on the boundary conditions used, the periodic boundary condition, and fluctuating twist boundary condition (FTBC), which implies that the different treatments of the boundary in some cases give rise to different critical dynamics. It is also found that the equilibrium scaling and the approach to equilibrium scaling for the the same boundary condition do not always give the same value of z. The FTBC in conjunction with the finite-size scaling of the linear resistance for both type of dynamics yields values of z consistent with expectations for superfluids and superconductors: z = 2, 3/2, and 2 for d = 2, 3, and 4, respectively.

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“…The real "smoking gun" experimental signature is a sharp drop to zero of the superfluid density when it crosses the universal BKT line, at the temperature T BKT and experimentally that does not happen in HTS films even when they are merely one unit cell (1 UC) thick. 8 Nevertheless, Minnhagen 5,6,9 suggested that at high frequencies it should still be possible to observe the BKT transition-like response from the bound pairs with the vortex separation length r < λ eff . This predicted "dynamic BKT transition" has been indeed observed by detecting the response of vortex-antivortex pairs with short separation lengths at radio, microwave, and terahertz frequencies in very thin HTS films.…”

Section: Critical Behavior In Two-dimensional Superconductorsmentioning

confidence: 99%

“…[3][4][5][6][7][8][9][10][11][12][13] At large distance, the vortex-antivortex interaction is screened, and hence BKT transition cannot be seen unless the sample size L s is smaller than the effective (Pearl) penetration depth λ eff = 2λ −2 /d, where λ is the usual (London) magnetic penetration depth and d is the film thickness. 4,5 On the other hand, in small samples, the edge effects dominate and wipe out the transition.…”

Section: Critical Behavior In Two-dimensional Superconductorsmentioning

confidence: 99%

Study of high-Tc interface superconductivity in La1.55Sr0.45CuO₄/La₂CuO₄ heterostructures at high magnetic fields and frequencies

Gasparov

Audouard

Drigo

et al. 2017

Int. J. Mod. Phys. B

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We have synthesized heterostructures that consist of a layer of a cuprate insulator, La 2 CuO 4 , and a layer of a nonsuperconducting cuprate metal, La 1.55 Sr 0.45 CuO 4 . Such bilayers show high-Tc interface superconductivity confined within a single CuO 2 plane. Here, we explore the behavior of interface superconductivity at high frequencies (up to 50 MHz) under high magnetic fields (up to 56 T). We find that interface superconductivity persists up to very high perpendicular fields (exceeding 40 T). The critical magnetic field Hm(T ) shows an upward divergence with decreasing temperature suggestive of vortex-lattice melting, similar to what is observed in bulk superconducting cuprates.

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Characteristics of two-dimensional vortex dynamics from XY-type models with Ginzburg-Landau dynamics

Cited by 34 publications

References 14 publications

Vortex dynamics in two-dimensional Josephson junction arrays

Vortex dynamics in two-dimensional Josephson junction arrays

Dynamic critical exponent of two-, three-, and four-dimensionalXYmodels with relaxational and resistively shunted junction dynamics

Study of high-Tc interface superconductivity in La1.55Sr0.45CuO₄/La₂CuO₄ heterostructures at high magnetic fields and frequencies

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Characteristics of two-dimensional vortex dynamics from XY-type models with Ginzburg-Landau dynamics

Cited by 34 publications

References 14 publications

Vortex dynamics in two-dimensional Josephson junction arrays

Vortex dynamics in two-dimensional Josephson junction arrays

Dynamic critical exponent of two-, three-, and four-dimensionalXYmodels with relaxational and resistively shunted junction dynamics

Study of high-Tc interface superconductivity in La1.55Sr0.45CuO4/La2CuO4 heterostructures at high magnetic fields and frequencies

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Study of high-Tc interface superconductivity in La1.55Sr0.45CuO₄/La₂CuO₄ heterostructures at high magnetic fields and frequencies