Re-entry in ferromagnetic superconductors

The re-entry phenomenon in magnetic superconductors is studied using the generalized Ginzburg-Landau free energy introduced by Blount and Varma. The re-entry temperature T_c2 is simply that temperature at which the magnetization acts as a source of induction strong enough to destroy superconductivity. Above T_c2 ferromagnetism and superconductivity coexist. The structure is an Abrikosov vortex lattice, with ferromagnetic magnetization spreading widely around the vortex cores. Within our approximations, the phase transition at T_c2 is of second order.     

The effective activation energy Ueff(T,B,J) in Hg-1223 single phase superconductors

We review the methods of calculating the effective activation energy U_eff(T,B,J) for both transport measurements and magnetic decay, together with some theoretical models. Then, we apply these methods to our Hg-1223 single-phase superconductor to obtain the activation energy. Transport results give that the magnetic field and temperature dependence of the U_eff can be well described as U₀B^−α(1−T/T_c)^m. Magnetic relaxation shows that the current density dependence of U(J) can be scaled onto a single curve, which can be considered as the activation energy at some temperature T₀. The pinning mechanism in the measured temperature range does not change, and the activation energy depends separately on the three variables: T, B, and J, are responsible for the magnetic decay data scaling onto a single curve at various temperatures. As temperatures close to zero and near T_c, thermally assisted flux motion model is no longer valid since other processes dominate.     

Disorder effects in the BCS-BEC crossover region of the attractive Hubbard model

We study the disorder effects upon superconducting transition temperature T _c and the number of local pairs within the attractive Hubbard model in the combined Nozieres-Schmitt-Rink and DMFT + Σ approximations. We analyze the wide range of attractive interaction U, from the weak coupling region, where instability of the normal phase and superconductivity are well described by the BCS model, to the limit of strong coupling, where superconducting transition is determined by Bose-Einstein condensation of compact Cooper pairs, forming at temperatures much higher than superconducting transition temperature. It is shown that disorder can either suppress T _c in the weak coupling limit, or significantly enhance T _c in the case of strong coupling. However, in all cases we actually prove the validity of generalized Anderson theorem, so that all changes in T _c are related to change in the effective bandwidth due to disorder. Similarly, disorder effects on the number of local pairs are only due to these band-broadening effects.     

Josephson vortex lattice melting in Bi-2212 probed by commensurate oscillations of Josephson flux-flow

We studied the commensurate semifluxon oscillations of Josephson flux-flow in Bi-2212 stacked structures near T_c as a probe of melting of a Josephson vortex lattice. We found that oscillations exist above 0.5 T. The amplitude of the oscillations is found to decrease gradually with the temperature and to turn to zero without any jump at T = T₀ (3.5 K below the resistive transition temperature T_c), thus, indicating a phase transition of the second order. This characteristic temperature T₀ is identified as the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature, T_BKT, in the elementary superconducting layers of Bi-2212 at zero magnetic field. On the basis of these facts, we infer that melting of a triangular Josephson vortex lattice occurs via the BKT phase with formation of characteristic flux loops containing pancake vortices and antivortices. The B-T phase diagram of the BKT phase found from our experiment is consistent with theoretical predictions.     

Correlated pairs in the attractive Hubbard model

The attractive Hubbard Model is considered in the strong coupling limits (U?t) by treating the hopping integral, t, as a perturbation. A phase diagram emerges with two critical temperatures: itk_BitT_ct²/U and itk_BT_UU/4. For T<T_c, there is regime of strongly correlated pairs reminescent of superconductivity. For T_c<T<T_U, there is a domain of uncorrelated pairs. For T>T_U, one has a normal metal.     

Vortex lattice in Bi2Sr2CaCu2O8+δ well above the first-order phase-transition boundary

Measurements of non-local in-plane resistance originating from transverse vortex-vortex correlations have been performed on a Bi₂Sr₂CaCu₂O_8+δ high-T_c superconductor in a magnetic field up to 9 T applied along the crystal c-axis. Our results demonstrate that a rigid vortex lattice does exist over a broad portion of the magnetic field-temperature (H-T) phase diagram, well above the first-order transition (FOT) boundary H_FOT(T). The results also provide evidence for the vortex lattice melting and vortex liquid decoupling phase transitions, occurring above the H_FOT(T).     

Width of the zero-field superconducting resistive transition in the vicinity of the localization threshold

Resistive superconducting zero-field transition in amorphous In-O films in the states in the vicinity of the insulator-superconductor transition is analyzed in terms of two characteristic temperatures: the upper T _c0 , where the finite amplitude of the order parameter is established, and the lower T _c , where the phase ordering takes place. It follows from the magnetoresistance measurements that the resistance in between, T _c <T< T _c0 , cannot be ascribed to the dissipation by thermally dissociated vortex pairs. So, it is not a Kosterlitz-Thouless-Berezinskii transition that occurs at T _c .     

Effective pinning barriers of NdFeAsO0.88F0.12 superconductor

Resistivities of polycrystalline iron-based NdFeAsO_0.88F_0.12 superconductors prepared via solid-state reaction in ambient pressure (AP) and high pressure (HP) were measured in various magnetic fields ranging from 0 to 9 T. Different resistivity broadening behaviors of the AP and HP samples, which may originate from the anisotropic superconductivity, the vortex motion, or the connectivity, were investigated in detail. The effective pinning barriers of both the AP and HP samples were obtained from the Arrhenius plot of the resistivity data by two analytic methods of which one assuming the prefactor 2ρ_cU/T of the thermally activated ?ux ?ow (TAFF) resistivity ρ=(2ρ_cU/T)exp(−U/T) is a constant, while the other assuming the prefactor is temperature dependent. The results determined from the two methods were compared and analysed, and the true effective pinning barriers were obtained. The origin of different pinning barriers of the AP and HP samples is discussed.     

μSR studies of heavy fermion systems

We have performed both zero field and high transverse field measurements at dilution refrigerator temperatures on a number of heavy electron systems, examining the superconducting and magnetic properties of these interesting materials. Among the materials studied to date are UBe₁₃, URu₂Si₂ and U₆Fe. The magnetic field penetration depth in the superconducting state of UBe₁₃ is greater than 10000 Å, as no increase in the transverse field relaxation rate is observed belowT _c . A sharp increase in the precession frequency is seen, starting atT _c . This frequency shift shows little temperature dependence at low temperature; we found no clear evidence for unconventional superconductivity in this material. Zero field measurements in URu₂Si₂ show the weak antiferromagnetic transition at 17.5 K. Finally, we we found no clear evidence for unconventional superconductivity in this material. Zero field measurements in URu₂Si₂ show the weak antiferromagnetic transition at 17.5 K. Finally, we have observed relaxation in high transverse field due to the formation of a flux lattice in U₆Fe, a material where the electron effective mass is rather lighter than in other heavy fermion systems. The relaxation exhibits a sharp onset atT _c=3.9 K, and is flat at low temperatures as expected for a conventional superconductor.     

Effect of charging energy on transition temperature of granular superconductors

The effect of the zero-point fluctuations of the phase on the transition temperature T_c of a granular superconductor is calculated using a model which takes into account the short-range part of the charging energy. A self-consistent mean field theory predicts a critical value of the ratio of the Josephson coupling constant to the charging energy and the existence of two values of T_c, indicating the possibility of reentrance into normal state at the lower one.     

Vortex core shapes measured by STM

We have studied vortex core shapes in superconducting NbSe₂ by STM, as function of temperature and bias voltage. The experimentally measured tunnel current profiles are compared with the results of calculations using microscopic theory. We find that, at low temperatures (T/T _c ? 0.25), the apparent vortex core radius strongly depends on the bias voltage, which demonstrates the energy dependence of the scale for spatial variation of the quasiparticle density of states. Good quantitative agreement between measured and calculated profiles is found by using the accepted value for the superconducting coherence length Ξ_S, without further adjustable parameters. This shows that the bias dependence is a useful extra tool in the interpretation of local density of states measurements.     

Dynamics of vortices in type-II superconductors with periodic square columnar pins

The dynamics of a two-dimensional vortex system with strong periodic square columnar pins is investigated. For the case vortex number matching pinning number, we find that the vortex liquid is frozen into square lattice via a continuous transition, and the freezing (melting) temperature T_m is the same as the thermal depinning temperature of vortices, which are different from the first-order phase transition at weak pinning. The zero-temperature critical depinning force F_c0 is exactly the same as the maximum pinning force, and the depinning property at T = 0 can be expressed by scaling v ～ (F ? F_c0)^β with the exponent β close to 0.5. The v–F curves at temperatures below T_m show that vortices are pinned at small driving force.     

Helical instability of a straight Abrikosov vortex in an anisotropic superconductor

Because of attraction of the parallel currents forming an Abrikosov vortex, the vortex energy per unit length decreases, under bending of the vortex, by a quantity proportional to the square of the curvature. Solving the London equation in an approximation allowing for this effect makes it possible to calculate the energy of an Abrikosov vortex in the form of a helix whose length and pitch are much larger than the correlation length, whose curvature is small compared to the reciprocal London length, and whose slope in relation to an axis coinciding with the direction in which the vortex energy is the highest is also small. When the anisotropy is large, which is characteristic of high-T _c superconductors, the energy of such an Abrikosov vortex is lower than that of a straight Abrikosov vortex. Certain consequences of the fact that the Abrikosov vortices in a high-T _c superconductor are helical are discussed. Among these is a phase transition that breaks the symmetry between Abrikosov vortices shaped like right-and left-hand helixes in relation to the magnetic field. Zh. éksp. Teor. Fiz. 111, 1869–1878 (May 1997)     

Dynamic melting of driven vortex matter below 1 K

We report on measurements of a mode-locking resonance in amorphous Mo_xGe_1?x films at different temperatures T down to 0.8 K, which is well below the superconducting transition (6 K). We observe dynamic ordering of driven vortex matter for all the temperatures studied. As the field exceeds a certain critical field B_c,dyn at fixed T, moving vortices do not exhibit dynamic ordering. At high T, this field B_c,dyn(T), so-called dynamic melting, nearly coincides with a characteristic field B_c(T) where the linear resistivity vanishes. At low T, however, B_c,dyn(T) is significantly suppressed compared to B_c(T), suggesting intrinsic quantum melting in the absence of pinning.     

Vortex-creep activation energy in YBa2Cu3O7/PrBa2Cu3O7 superlattices

YBa₂Cu₃O₇/PrBa₂Cu₃O₇ (YBCO/PBCO) superlattices with a different ratio of the superconducting and insulating layer thicknesses were prepared by high pressure dc sputtering. The vortex-creep activation energy U₀ was determined by analyzing the in-plane resistive transition of 200 μm wide bridges with the external magnetic field B oriented along the c axis. It was found that U₀ is proportional to the thickness of the YBCO layers, and does only weakly depend on the PBCO layer thickness, when the latter exceeds two unit cells. We observed a change in the variation of U₀ with the current I in the specimen: U₀ exhibits a plateau in the low-I region, then decreases significantly with increasing I. This behaviour is explained in terms of a crossover plastic vortex creep – elastic (collective) creep induced by the transport current.     

Superconductivity and Peierls instability in coupled linear chain systems

We study the superconducting transition temperature (T_c) and the Peierls instability temperature (T_p) using Eliashberg type equations for both T_c and T_p self consistently with finite interchain coupling. We show that T_c > T_p below a critical electron-phonon coupling constant which depends on the bare phonon frequency. This determines an upper bound on T_c so that for higher transition temperatures T_p > T_c and superconductivity is unlikely. Higher values of T_c are possible if the interchain coupling is increased above a critical value where the Peierls instability is suppressed.     

Influence of an adsorbing gas on the layering transitions in crystal growth

The influence of an adsorbing gas on the layering transition of a film is studied. In agreement with an earlier publication, we find that the adsorbate lowers the critical temperature T_c(n) for the nth layer. We also find that a system which is dry near T = 0 may undergo an apparent wetting transition due to the adsorbate. Indirect evidence is given that the sequence T_c(n) ends at T_R, the roughening temperature, as conjectured by de Oliviera and Griffiths. Re-entrant behavior in the layering transitions is observed for sufficiently strong adsorption energy; similar behavior also appears in the roughening transition, for which there exists some experimental evidence.     

On possibility of the spontaneous magnetic flux in a Josephson junction containing magnetic impurities

The Josephson junction containing localized magnetic moments in a dielectric layer between two superconductors is considered. Conditions are studied under which the phase difference between superconductors in the state with energy minimum is equal to π (such a junction we call π-junction). In addition we consider “one-dimensional” Josephson junction one part (2) of which is π-junction, the other (1) being the usual Josephson junction ( 0 - junction). Conditions are found under which in such a system there is a spontaneous vortex with the centre at the boundary between the parts 1 and 2 and magnetic flux associated with this vortex. The vortex appears by second order phase transition as temperature decreases for T_c.     

Effect of structural relaxation on low energy excitations in amorphous Zr x Cu1−x

We report on an investigation of the liquid-quenched metallic glass Zr _x Cu_1?x (0.6≦x≦0.74) subjected to heat treatments below the glass transition temperatureT _g. Annealing temperatures up to 200°C (<0.8T _g) were chosen as to achieve topological relaxation only. The superconducting transition temperaturesT _c are lowered, as already observed for other metallic glasses. Low temperature measurements of the thermal conductivity (0.5 K≦T≦15 K) and of the specific heat (0.1 K≦T≦3 K) were carried out in order to determine the effect of structural relaxation on the low energy configurational excitations characteristic of the amorphous state. The annealed samples show no detectable (<20%) change in the specific heat forT?T _c, but an increase of the thermal conductivity by a factor of 2 forT?T _c is observed. Within the tunneling model of two level systems (TLS) for the low energy excitations, this behavior can be qualitatively understood in terms of a change of the TLS relaxation time distribution upon annealing. This distribution differs from that of the commonly used standard tunneling model. The change of the phonon scattering by TLS directly observed forT?T_c is largely responsible for the enhancement of the thermal conductivity found also aboveT _c.     

Time dependence of isothermal magnetization in single-phase B1 MoCy encapsulated in multiwall carbon nanocages

Isothermal magnetization M(t) in nanocrystalline single-phase B1 MoC_y encapsulated in multiwall carbon nanocages is studied within the time window of 100 < t < 5000 s. The current density J exhibits a linear logarithmic time decay. The effective activation energy U_eff increases linearly with increasing temperature T, and decreases linearly with increasing J. The behaviors of J(t), U_eff(T), and U_eff(J) can be described by the Anderson–Kim flux-creep model for thermally activated motion of uncorrelated vortices or vortex bundles over a net potential barrier U_eff. The slower relaxation of current density above the broad peak field in the isothermal magnetization curves suggests that the peak is a result of vortex dynamics.