Magnetic Penetration Length Research Articles

Shift of the critical temperature in superconductors: a self-consistent approach

Within the Ginzburg-Landau functional framework for the superconducting transition, we analyze the fluctuation-driven shift of the critical temperature. In addition to the order parameter fluctuations, we also take into account the fluctuations of the vector potential above its vacuum. We detail the approximation scheme to include the fluctuating fields contribution, based on the Hartree-Fock-Bogoliubov-Popov framework. We give explicit results for d = 2 and d = 3 spatial dimensions, in terms of easily accessible experimental parameters such as the Ginzburg-Levanyuk number Gi(d), which is related to the width of the critical region where fluctuations cannot be neglected, and the Ginzburg-Landau parameter κ, defined as the ratio between the magnetic penetration length and the coherence one.

Vortex in holographic two-band superfluid/superconductor

We construct numerically static vortex solutions in a holographic model of two-band superconductor with an interband Josephson coupling in both the superfluid and superconductor regime. We investigate the effects of the interband coupling on the order parameter of each superconducting band in the vortex solution, and we find that it is different for each of the two bands. We compute also the free energy, critical magnetic field, magnetic penetration length and coherence lengths for the two bands, and we study their dependence on the interband coupling and temperature. Interestingly, we find that the coherence lengths of the two bands are close to identical.

Coherence length and magnetic penetration depth of the s-wave holographic superconductor model in Lifshitz spacetime

The AdS/CFT duality provides us a powerful guidance to study the strong-coupled conformal field theory by using its dual weak-coupled gravity. One of the interesting applications of the duality is to study high temperature superconductors, which are supposed to be a strongly coupled system. According to Ginzburg-Landau theory, a superconductor can be characterized by only two parameters, coherence length and the magnetic penetration length ; therefore, it is important to determine the two parameters. In this paper in the D=d+2-dimensional Lifshitz black hole, we analytically study the static fluctuation of the scalar field with nonzero spatial momentum along one spatial coordinate of the boundary, and investigate the perturbation of the gravitational system near the critical temperature Tc. Working in the probe limit (the gauge field and scalar field do not backreact on the original metric), we obtain the superconducting coherence length via AdS/CFT (anti-de Sitter/conformal field theory) correspondence, which is (1/Tc)(1-(T/Tc)-1/2. Moreover, in the probe limit (the magnetic field does not backreact to the background spacetime), we have calculated the diamagnetic current induced by a homogeneous external magnetic field perpendicular to the surface of the superconductor. Then, we obtain the magnetic penetration depth (Tc-T)-1/2, which agrees with the result in Ginzburg-Landau theory. And these results strongly support the idea that a superconductor can be described by a charged scalar field on the Lifshitz black hole via AdS/CFT (anti-de Sitter/conformal field theory) duality.

Supersymmetric BCS: effects of an external magnetic field and spatial fluctuations of the gap

Recently an N=1 supersymmetric model of BCS superconductivity was proposed realizing spontaneous symmetry breaking of a U(1)_R symmetry. Due to scalar contributions the superconducting phase transition turned out to be first order rather than second order as in standard BCS theory. Here we consider the effects of an external magnetic field and spatial fluctuations of the gap in that model. This allows us to compute the magnetic penetration length and the coherence length, and also to distinguish between type I and type II superconductors. We compare the supersymmetric and standard relativistic BCS results, where the main differences come from the different orders of the phase transition.

Single vortex fluctuations in a superconducting chip as generating dephasing and spin flips in cold atom traps

We study trapping of a cold atom by a single vortex line in an extreme type-II superconducting chip, allowing for pinning and friction. We evaluate the atom's spin flip rate and its dephasing due to the vortex fluctuations in equilibrium and find that they decay rapidly when the distance to the vortex exceeds the magnetic penetration length. We find that there are special spin orientations, depending on the spin location relative to the vortex, at which spin dephasing is considerably reduced while perpendicular directions have a reduced spin flip rate.

Superconducting characteristics of 4-A carbon nanotube-zeolite composite.

We have fabricated nanocomposites consisting of 4-A carbon nanotubes embedded in the 0.7-nm pores of aluminophosphate-five (AFI) zeolite that display a superconducting specific heat transition at 15 K. MicroRaman spectra of the samples show strong and spatially uniform radial breathing mode (RBM) signals at 510 cm(-1) and 550 cm(-1), characteristic of the (4, 2) and (5, 0) nanotubes, respectively. The specific heat transition is suppressed at >2 T, with a temperature dependence characteristic of finite-size effects. Comparison with theory shows the behavior to be consistent with that of a type II BCS superconductor, characterized by a coherence length of 14 +/- 2 nm and a magnetic penetration length of 1.5 +/- 0.7 mum. Four probe and differential resistance measurements have also indicated a superconducting transition initiating at 15 K, but the magnetoresistance data indicate the superconducting network to be inhomogeneous, with a component being susceptible to magnetic fields below 3 T and other parts capable of withstanding a magnetic field of 5 T or beyond.

Effect of columnar disorder on the superconducting transition of a type-II superconductor in zero applied magnetic field

We investigate the effect of random columnar disorder on the superconducting phase transition of a type-II superconductor in zero applied magnetic field using numerical simulations of three dimensional XY and vortex loop models. We consider both an unscreened model, in which the bare magnetic penetration length is approximated as infinite, and a strongly screened model, in which the magnetic penetration length is of order the vortex core radius. We consider both equilibrium and dynamic critical exponents. We show that, as in the disorder free case, the equilibrium transitions of the unscreened and strongly screened models lie in the same universality class, however scaling is now anisotropic. We find for the correlation length exponent $\nu=1.2\pm 0.1$, and for the anisotropy exponent $\zeta=1.3\pm 0.1$. We find different dynamic critical exponents for the unscreened and strongly screened models.

STANDARD MANUFACTURE AND PROPERTIES OF ARRAYS OF Pb AND Sn NANOWIRES

Nanowires grown by electrodeposition using nanoporous template have attracted much attention due to the simplicity of this technique for preparing nano-scaled materials. We present here a standard way to fabricate lead or tin nanowire arrays. We also present some of their superconducting properties directly affected by the reduced dimensions; these are the magnetic flux penetration and confinement in nanowires having a diameter only a few times the magnetic penetration length, as well as the formation of phase-slips centres in nanowires having a diameter smaller than the coherence length.

Vortex Molecule in Unconventional Superconductor

In this study we calculate numerically the vortex structure for a two-component Ginzburg-Landau functional in the regime when time-reversal symmetry is not spontaneously broken. In a wide range of parameters a single-quantum vortex dissociates into a bound pair (molecule) of half-quantum vortices. We determine the phase diagram of different types of vortices in the space of parameters of the Ginzburg-Landau functional. A novel characteristic length which is related to the vortex molecule size is found. The characteristic length is longer than the coherence length and shorter than the magnetic penetration length.

The novel characteristic length of dissociated vortex in an unconventional superconductor

We investigate numerically structure of a single vortex for a vector superconducting order parameter. In the case of time-reversal preserving Meisner phase we find instability of a one-quantum vortex towards dissociation into a bound pair of half-quantum vortices. A novel characteristic length different from the coherence length and the magnetic penetration length determines size of the vortex molecule.

Vortex phases of an unconventional superconductor with two components order parameter

We examined the single vortex structure of superconductor with the order parameter of two components by numerical calculation. Under certain conditions in the case of time-reversal preserving phase a single vortex dissociates into a pair of half-quantum vortices. We determine the phase diagram for these vortices in the space of parameters of the Ginzburg–Landau functional. A novel characteristic length which is longer than the coherence length ξ and shorter than the magnetic penetration length λ London is introduced.

Magnetic penetration length and irreversibility of a disordered granular superconductor withπjunctions

We calculate the magnetic penetration length $\ensuremath{\lambda}(T)$ of a disordered granular superconductor with $\ensuremath{\pi}$ junctions in zero magnetic field, using a mean-field replica method. The superconductor is modeled by an array of Josephson junctions whose couplings are drawn randomly from a Gaussian distribution centered at ${J}_{0}g0,$ with width J. For disorder strength $\ensuremath{\delta}\ensuremath{\equiv}{J/J}_{0}l1$ there are three thermodynamical phases of the array separated by continuous transitions: (i) the high-temperature normal phase, (ii) the reversible superconducting phase, and (iii) the low-temperature superconducting glass phase with broken ergodicity. For a range of disorder $\ensuremath{\delta}$ near 1 there is a further possibility of reentry into a low-temperature normal glass phase. For $\ensuremath{\delta}g~1$ there are only two phases: (i) the high-temperature normal phase and (ii) the low-temperature normal glass phase with broken ergodicity. In the superconducting glass phase we calculate both the Gibbs averaged and the single-state-averaged magnetic penetration lengths.

Strong axial anisotropy of the magnetic penetration length in superconducting

We report muon spin rotation measurements of the temperature dependence and anisotropy of the magnetic field penetration lengths in the heavy fermion superconductor . We observe a strong axial anisotropy. At 0.05 K we obtain for the penetration length parallel and perpendicular to the c axis (150) Å and (130) Å, respectively. at low temperatures excludes a superconducting order parameter in the B phase with only a line of nodes in the equatorial plane of the Fermi surface. The combined analysis of and measured in the B phase favours an hybrid order parameter with point nodes at the poles and a line of nodes at the equatorial plane. The A phase is characterized by a larger density of nodes than the B phase.

Critical Behavior of the Meissner Transition in the Lattice London Superconductor

We carry out Monte Carlo simulations of the three dimensional (3D) lattice London superconductor in zero applied magnetic field, making a detailed finite size scaling analysis of the Meissner transition. We find that the magnetic penetration length \lambda, and the correlation length \xi, scale as \lambda ~ \xi ~ |t|^{-\nu}, with \nu = 0.66 \pm 0.03, consistent with ordinary 3D XY universality, \nu_XY ~ 2/3. Our results confirm the anomalous scaling dimension of magnetic field correlations at T_c.

Superconducting Coherence in a Vortex Line Liquid: Simulations with Finite lambda.

We carry out simulations of a lattice London superconductor in a magnetic field B, with a finite magnetic penetration length \lambda. We find that superconducting coherence parallel to B persists into the vortex line liquid. We argue that the length scale relevant to this effect is \Lambda=\phi_0^2/8\pi T_m.

Mu SR investigation of anisotropy and temperature dependence of magnetic penetration lengths in crystals of YBa2Cu3O7-d

Pulsed mu SR measurements on an aligned mosaic of single crystals of YBCO are interpreted in terms of an anisotropic magnetic penetration length arising from currents flowing parallel and perpendicular to the CuO2 planes. At low temperatures a mean penetration depth ( lambda 1 lambda 3)1/2 of 502 nm is reduced from measurements in fields parallel to the ab plane. Relaxation rate measurements for fields at angles up to 24 degrees out of the plane exhibit a marked angular anisotropy. The observed anisotropy implies a ratio of effective masses perpendicular and parallel to the CuO2 planes of at least 30. The values obtained are compared with those obtained by other authors and techniques. A different temperature dependence of the relaxation rate is observed for fields parallel and at 24 degrees to the CuO2 planes.

Temperature and field dependence of the magnetic penetration length of c-axis oriented YBa2Cu3O7 films

The penetration depth λ of c-axis oriented thin films of YBa2Cu3O7 in perpendicular magnetic fields up to 14T is determined from complex impedance measurements at 1.25kHz. Vortex core pinning dominates over the condensate term and determines the functional form of λ(T,H). The critical field Hcp(T) identified by λ → ∞ is associated with the vanishing of the curvature of harmonic pinning potentials. The critical temperature at which the pinning potentials vanish is field dependent, in contrast with assumptions elsewhere in the literature.

Critical current limitations in ceramic oxide superconductors

Weak links between grains of ceramic oxide superconductors limit the measured transport critical current density, J c, because of both the weak coupling between grains, and the field caused by the measuring current. The weak links have a critical current density, J w, much less than the intra-grain critical current density J grain. Magnetic fields, specifically the field induced by the measuring current, further reduce J c; a large fraction of the links become resistive at field values, H half (typically 4 to 25 Gauss), which depend only on the magnetic penetration length, λ L, and the grain size, L. As a result of these two effects, the measured critical current in a field-limited sample of cross-section A and circumference C is modelled to be J c = J w for J w < (5/2 π) ( C/ A) H half and J c = (5/2 π) ( C/ A) H half otherwise. In the latter case, J c is independent of J w. Most reported critical currents of ceramic oxide superconductors are apparently field-limited measurements, and therefore depend on the sample dimensions rather than the value of the intergranular limit, J w. One measures J w only for small samples or weakly coupled junctions. The field-limited behaviour disappears only when the grains are coupled well enough that links can carry enough current to shield them from external fields, which occurs when L > λ J =λ L (J grain J w ) 1 2 , this condition having apparently been achieved in some reported samples.

Eddy current damping due to a linear periodic array of magnetic poles

Eddy currents induced in a conductor moving in a magnetic field produce a retarding force proportional to the heat generated in the material. This principle is utilized in the design of magnetic damping or systems for various applications. The problem considered here is that of a conducting sheet adjacent to a periodic array of magnetic poles. Quasistatic magnetic field solutions are derived for a sheet of arbitrary permeability and thickness moving uniformly at a fixed distance from the poles. The fields inside and outside the conducting sheet are computed over the complete range of dynamic conditions in terms of a relative magnetic penetration length. The field solutions are then employed to calculate the induced current density in the case where the conductor thickness is large in comparison with the axial pole length. The resulting braking power is computed for the purpose of establishing design principles for effective damping. The derived results are applied to two possible situations: a high reluctance magnetic circuit which utilizes a nonpermeable conducting sheet, and a low reluctance circuit which requires a highly permeable conductor. Differences in these two approaches are analyzed with respect to braking power and preferred type of permanent magnets for optimum performance.