Interlayer Josephson Coupling Research Articles

Field-Direction Dependence of the Upper Critical Field in Organic Superconductors

In this work, we investigate the anisotropy of the in-plane critical field in conventional and spatially modulated phases of layered superconductors within the quasi-classical approach, taking into account the interlayer Josephson coupling. We show that the anisotropy of the onset of superconductivity may change dramatically in the FFLO state as compared with the conventional superconducting phase.

Transport properties of stripe-ordered high Tc cuprates

Transport measurements provide important characterizations of the nature of stripe order in the cuprates. Initial studies of systems such as La1.6−xNd0.4SrxCuO4 demonstrated the strong anisotropy between in-plane and c-axis resistivities, but also suggested that stripe order results in a tendency towards insulating behavior within the planes at low temperature. More recent work on La2−xBaxCuO4 with x=1/8 has revealed the occurrence of quasi-two-dimensional superconductivity that onsets with spin-stripe order. The suppression of three-dimensional superconductivity indicates a frustration of the interlayer Josephson coupling, motivating a proposal that superconductivity and stripe order are intertwined in a pair-density-wave state. Complementary characterizations of the low-energy states near the Fermi level are provided by measurements of the Hall and Nernst effects, each revealing intriguing signatures of stripe correlations and ordering. We review and discuss this work.

Correlation between the interlayer Josephson coupling strength and an enhanced superconducting transition temperature of multilayer cuprate superconductors

Infrared reflectivity spectra of multilayered HgBa${}_{2}$Ca${}_{n\ensuremath{-}1}$Cu${}_{n}$O${}_{2n+2+\ensuremath{\delta}}$ ($n=2$, 3, 4, and 5) are measured. Optical plasma modes associated with the Josephson coupling between CuO${}_{2}$ planes within a multilayer appear below ${T}_{c}$ in the $c$-axis component of the reflectivity spectrum. The result allows for quantitative estimation of the interlayer Josephson coupling strength within a multilayer. It is found that the change of the Josephson coupling strength correlates with the increase of ${T}_{c}$ up to $n=3$ and the subsequent decrease for $n\ensuremath{\ge}4$.

The anomalous anisotropy in the ac susceptibility of La1.45Nd0.4Sr0.15CuO4 single crystal

The dependencies of ac susceptibility on the superimposed dc magnetic fields for the stripe-ordered La1.45Nd0.4Sr0.15CuO4 single crystal with two superconducting transitions have been studied in the 3D and 2D superconducting ranges for the fields along different orientations of the crystal. The results show that with increasing fields the interlayer Josephson coupling and the in-plane superconductivity are suppressed orderly for the fields perpendicular to CuO2 planes. The influences of the field parallel to CuO2 planes on the 3D and 2D superconductivity are much weaker than those of the field parallel to the c-axis. The irreversibility lines for the 3D and 2D superconducting states are also studied.

Interlayer Josephson couplings in Hg-based multi-layered cuprates

Infrared reflectivity spectra of the multilayered HgBa2Can-1CunO2n+2+δ(n=2,3,4,and5) are measured. Optical plasma modes associated with the Josephson coupling between CuO2 planes within a multilayer appear below Tc in the c-axis component of the reflectivity spectrum. For the bilayer and trilayer compound an optical Josephson plasma mode appears at unprecedentedly high frequency, ∼700–800cm-1, below Tc. The plasma frequencies appreciably decrease in four- and five-layer compounds which indicates the suppression of superconducting order in the inner CuO2 planes, consistent with the result of NMR experiment.

Interlayer Josephson coupling in stripe-ordered superconducting cuprates

Motivated by experiments on ${\text{La}}_{2\ensuremath{-}x}{\text{Ba}}_{x}{\text{CuO}}_{4}$ which suggest that stripe order coexists with two-dimensional pairing without interlayer phase coherence, we determine the interlayer Josephson coupling in the presence of stripe order. We employ a mean-field description of bond-centered stripes, with a zero-momentum superconducting condensate and alternating stripe directions pinned by the low-temperature tetragonal (LTT) lattice structure. We show that the Fermi-surface reconstruction arising from strong stripe order can suppress the Josephson coupling between adjacent layers by more than an order of magnitude.

Nature of stripes in the generalized t–J model applied to the cuprate superconductors

A recent study of the transport properties on the stripe phase in La1.875Ba01.25CuO4 by Li et al (2007 Phys. Rev. Lett. 99 067001) found two-dimensional (2D) superconductivity over a wide temperature range including a Berezinski–Kosterlitz–Thouless transition at a temperature T=16 K, with 3D superconducting (SC) ordering only at T=4 K. These results contradict the long standing belief that the onset of superconductivity is suppressed by stripe ordering and suggest coexistence of stripe and SC phases. The lack of 3D SC order above T=4 K requires an antiphase ordering in the SC state to suppress the interlayer Josephson coupling as proposed by Berg et al (2007 Phys. Rev. Lett. 99 127003). Here, we use a renormalized mean field theory for a generalized t–J model to examine in detail the energetics of the spin and charge stripe ordered SC states including possible antiphase domains in the SC order. We find that the energies of these modulated states are very close to each other and that the anisotropy present in the low temperature tetragonal crystal structure favors stripe resonating valence bond states. The stripe antiphase SC states are found to have energies very close to, but always above, the ground state energy, which suggests additional physical effects are responsible for their stability.

Role of interlayer coupling in cuprate high-T c superconductors

The effect of the interlayer Josephson coupling on the high-Tc superconductors (HTSCs) is re-examined in light of the recent discovery that the critical temperatures, Tc, of the n = 4 members of the HTSC homologous series HgBa 2 Can-1CunO2n+2+ , Tl2Ba2Can-1CunO2n+4+ , and TlBa2Can-1CunO2n+3+ , are lower than those of the n = 3 members of the series. This is in contradiction to the prediction of a Ginzburg-Landau theory that the Tc's of a homologous series of HTSCs would increase monotonically with the number of layers. That theory was based on the assumption that the strengths of the Josephson coupling between the different CuO2 layers within a homologous series are the same. It is shown that the Tc's of the n = 4 member in a series would be lower than those of the n = 3 member if the hole concentrations in the interior CuO2 layers are different from those in the outer layers.

Surface melting of the vortex lattice in layered superconductors: Density functional theory

We study the effects of an $ab$ surface on the vortex-solid to vortex-liquid transition in layered superconductors in the limit of vanishing interlayer Josephson coupling. We derive the interaction between pancake vortices in a semi-infinite sample and adapt the density functional theory of freezing to this system. We obtain an effective one-component order-parameter theory which can be used to describe the effects of the surface on vortex-lattice melting. Due to the absence of protecting layers in the neighborhood of the surface, the vortex lattice formed near the surface is more susceptible to thermal fluctuations. Depending on the value of the magnetic field, we predict either a continuous or a discontinuous surface melting transition. For intermediate values of the magnetic field, the surface melts continuously, assisting the formation of the liquid phase and eliminating the hysteresis above the melting transition, a prediction consistent with experimental results. For very low and very high magnetic fields, the surface melts discontinuously. The two different surface melting scenarios are separated by two surface multicritical points, which we locate on the melting line.

Kosterlitz-Thouless Behavior in Layered Superconductors: The Role of the Vortex Core Energy

In layered superconductors (SC) with small interlayer Josephson coupling vortex-antivortex phase fluctuations characteristic of quasi two-dimensional (2D) Kosterlitz-Thouless behavior are expected to be observable at some energy scale T(d). While in the 2D case T(d) is uniquely identified by the KT temperature T(KT) where the universal value of the superfluid density is reached, we show that in a generic anisotropic 3D system T(d) is controlled by the vortex-core energy, and can be significantly larger than the 2D scale T(KT). These results are discussed in relation to recent experiments in cuprates, which represent a typical experimental realization of layered anisotropic SC.

Effect of the intrinsic Josephson coupling on the pancake lattice in layered superconductors

We study the pancake lattice system induced by the application of transverse magnetic field to the layered superconductor. A simple statistical field theory for the pancake lattice is derived. It incorporates effects of the magnetic interaction between pancakes as well as those of the interlayer Josephson coupling. The proposed description enables us to estimate the pancake crystal melting temperature from above. Also, it allows us to compare directly the effects of the magnetic and Josephson energies on the statistical properties of the pancake lattice. We demonstrate that even for such an anisotropic material as BSCCO the pancake interaction induced by the Josephson coupling is of the same order as the magnetic interaction.

Josephson coupling energy and c-axis sum rules in Bi2Sr2Ca2Cu3O10

Polarized reflectivity measurements were performed on a textured Bi2Sr2Ca2Cu3O10 polycrystal. The far infrared c-axis optical conductivity exhibits similarities with other multilayer superconductors. Namely, a broad band develops around 450cm−1 and nearby phonon anomalies are observed as temperature is decreased. In agreement with lattice dynamics calculation, two oxygen bond-bending modes are found at 362cm−1 and 392cm−1. In contrast with bilayer compounds, this latter phonon mode grows in intensity as temperature decreases. In order to describe quantitatively the appearance of the 450cm−1 peak in the superconducting state, we used the Josephson superlattice model to fit experiments. In this model, the multilayer superconductor is considered as a stack of superconducting layers with non-equivalent intralayer and interlayer Josephson coupling constants. The temperature dependence of the interlayer Josephson coupling energy is extracted from the fit and compared to a possible change in c-axis kinetic energy deduced from an approximate tight-binding sum rule.

Pancake Vortices

I describe the magnetic-field and current-density distributions generated by two-dimensional (2D) pancake vortices in infinite, semi-infinite, and finite-thickness stacks of Josephson-decoupled superconducting layers. Arrays of such vortices have been used to model the magnetic structure in highly anisotropic layered cuprate high-temperature superconductors. I show how the electromagnetic forces between pancake vortices can be calculatated, and I briefly discuss the effects of interlayer Josephson coupling.

Depression of the interlayer Josephson coupling in Bi 2Sr 2CaCu 2O 8+ x single crystals by spin-polarized current injection along the c-axis

We studied the effect of spin-injection on tunneling conduction properties of intrinsic Josephson junctions (IJJs) formed in Bi 2Sr 2CaCu 2O 8+ x single crystals. Properties of an identical stack (10 × 5 × 0.030 μm 3) of IJJs were compared for the bias current injection through Au and Co electrodes. Clear quasiparticle branches in tunneling current–voltage ( I– V) curves from the IJJs in the stack were observed for an unpolarized bias current through the Au electrode. Spin-injection through the Co electrode caused pair breaking in the CuO 2 double layers, which led to reduction of the Josephson critical current and the superconducting gap revealed in the tunneling I– V curves.

Far infrared c-axis optical conductivity in an oriented Bi 2Sr 2Ca 2Cu 3O 10 polycrystal

Polarized reflectivity measurements were performed on an oriented Bi 2Sr 2Ca 2Cu 3O 10 polycrystal. We found that FIR c-axis optical response exhibits similarities with other multilayer compounds such as YBa 2Cu 3O x or Bi 2Sr 2Ca 1Cu 2O 8. As temperature is decreased, a broad band developing around 450 cm −1 and nearby phonon anomalies are observed. Moreover, two oxygen bond-bending modes are evidenced at 362 and 392 cm −1. This latter grows in intensity as temperature decreases, contrary to bilayer superconductors. The appearance of the 450 cm −1 broad band is well described by the model of Munzar in which the superconductor is considered as stacked superconducting layers with non equivalent intra-trilayer and interlayer Josephson coupling constants. Our results show that oriented polycrystals are useful to investigate c-axis optical properties of high T c superconductors.

Dimensional crossover of vortex dynamics induced by Gd substitution on Bi2212 single crystals

The vortex dynamics of Bi 2Sr 2Ca 1− x Gd x Cu 2O 8+ δ single crystals is investigated by magnetic relaxation and hysteresis measurements. By substituting Ca with Gd, it is found that the interlayer Josephson coupling is weakened and the anisotropy is increased, which leads to the change of vortex dynamics from 3D elastic to 2D plastic vortex creep. Moreover, the second magnetization peak, which can be observed in samples near the optimal doping, is absent in the strongly underdoped (with 2D vortex) region.

Interlayer Josephson coupling in layered superconductors

The dependence of the Josephson interlayer coupling in layered superconductors on the magnetic field H is studied numerically in the limit of complete disorder of the positions of pancake vortices (pancake gas). We find that the spatial average 〈cosϕ(r)〉 is proportional to 1/H1/2, where ϕ is the gauge-invariant phase difference between two layers. This result is compared with the magnetoabsorption resonances observed in layered superconductors.

Interlayer Josephson coupling for a gas of pancake vortices

The dependence of the Josephson interlayer coupling in layered superconductors on the magnetic field H is studied numerically in the limit of complete disorder of the positions of pancake vortices (pancake gas). We find that the spatial average (cos φ(r)> is proportional to 1/H 1 / 2 , where φ is the gauge-invariant phase difference between two layers. The implication of this result for the interpretation of the magnetoabsorption resonances observed in layered superconductors is discussed.

Mo/Si superlattices: phase transitions between the commensurate states in the vortex ensemble

The avalanche-type jumps of the resistivity in the mixed state have been observed on the artificial superconducting multilayers Mo/Si with weak Josephson interlayer coupling when an applied magnetic field was oriented along the layer planes. These jumps are periodic with an inverse magnetic field. The simple model is proposed which explains the jump patterns on different samples as the manifestation of the phase transitions between various commensurate states of the vortex lattice. The values of the jump fields and the distances between these fields are quantitatively consistent with the model considered. It is assumed that the set of the jumps corresponds to the sequence of the upper critical fields for different commensurate lattices in the strongly layered superconductor. These phase transitions belong to the class of the first order transitions in distinction to the corresponding transition in homogeneous type-II superconductors. The resistive curves are hysteretic and reveal considerable supercooling.

Quantum regime of Cooper pair tunneling in small-area Bi 2Sr 2CaCu 2O 8+ δ mesas in magnetic fields

We show that application of an c-axis magnetic field decreases the effective interlayer Josephson coupling in small-area Bi 2Sr 2CaCu 2O 8+ δ (Bi-2212) mesas at low temperatures. As magnetic field increases, the crossover from the classical regime of Cooper pair tunneling to the quantum regime leads to an additional drastic suppression of the Josephson coupling due to the Coulomb blockade. As result, the stack of many intrinsic junctions is nonsuperconducting at high fields. The quantum regime of superconducting tunneling may be reached in mesas with N junctions and area 0.3 μm 2 made of intercalated Bi-2212 crystals by applying c-axis magnetic fields B>4/ N 2 T at N≫1.