Interlayer Pairing Research Articles

Intralayer versus interlayer pairing in the copper oxide superconductors: The three- and four-layer problems.

We have analyzed the possible superconducting states of a model layered superconductor with N conducting layers in a unit cell, for N=3 and 4, in the presence of both intralayer and interlayer pairing interactions. In case all layers are identical, the system has the same behavior as one-layer and two-layer systems, namely that pure intralayer pairing interaction stabilizes an s-wave state with equal and isotropic gaps in all N quasiparticle bands, while interlayer pairing produces both singlet and triplet paired states with anisotropic gap functions. The singlet state is always energetically more stable than the triplet state. The analysis can be easily extended to nonidentical layers. As one example, a model for ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ consisting of two ${\mathrm{CuO}}_{2}$ layers in a unit cell separated by a layer of CuO chains is discussed. It is shown that the system reduces to an effective two-layer model, due to the large difference in electronic energy states between the planes and the chains. The chains are most likely nonsuperconducting. In another example, we show that ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$ can be reduced to an effective three-layer system. Recent tunneling data can be understood on the basis of this model.

Interlayer pairing and c-axis versus ab-plane gap anisotropy in high- Tc superconductors

Interlayer BCS-like pairing in nearly two-dimensional superconductors with N=1, 2 conducting layers per unit cell is investigated. For N=1, the singlet Δ s and triplet Δ t, order parameters have identical T c's ( Tcs = T ct) and magnitudes, and the gap is isotropic. For N= 2, T cs ⩾ T ct and | Δ s|⩾ Δ t. In region I of the parameters, the gap is anisotropic and nodeless for T < T cs. In region II, the gap has nodes near T cs but is nodeless at low T. In a magnetic field, non-unitary states are possible. For N = 1 (2), intra-and interlayer pairing are completely (essentially) incompatible.

Elastic and coulombic contributions to real-space hole pairing in doped La2CuO4

The energetics of three types of possible polaron pair in doped La2CuO4 have been investigated by computer-simulation techniques based on lattice-energy minimisation. The most energetically favourable pairing configurations have been obtained. O–—O– pairing is calculated to be bound by 0.119 eV. For Cu3+—Cu3+ and Cu3+—O– pairing, interlayer configurations are found to be more favourable than intralayer pairing and the nearest-neighbour pairing is unfavourable. The binding energy of the pairs is found to be related to the pair distance and geometry of the pair. The Coulomb repulsive energy between hole pairs is estimated and the interlayer pairing is found to be more effective at screening Coulomb interactions between holes. The lattice distortion energy caused by polaron pairing is estimated and is taken into account in the calculation.

Significance of interlayer interactions to the superconducting mechanism of high- Tc copper oxides

A systematic analysis of various experimental data on T c and α (isotope effects) within the Eliashberg formalism including both the intralayer and the interlayer pairing leads us to conclude that i) the trends of T c for known high- T c copper oxides are well described in terms of a non-phonon, BCS type (λ<1 and the Cooper-pair like) pairing mechanism whose identity is yet to be understood, and ii) the effective interlayer pair scattering in multilayer compounds, though weaker than the intralayer counterpart, is estimated to be rather substantial (λ interlayer≈ 0.1). The presence of the appreciable interlayer scattering in the system casts doubt on the possibility of anyon superconductivity which requires two-dimensional topology.

Zn and Ga play the role of effective magnetic scatterers in high Tc superconductors

The drastic decrease and ultimate vanishing of T c in Zn- and Ga-doped YBa 2Cu 3O 7 and La 1.85Sr 0.15CuO 4 is studied theoretically with a model in which Zn and Ga ions play the role of effective magnetic scatterers. The experimental curve for T c( x) in doped YBa 2Cu 3O 7 can be fitted by the model with both intra-and inter-layer pairing, while T c( x) in doped La 1.85Sr 0.15CuO 4 is better described by intra-layer pairing only.

Effect of magnetic impurities on the BCS and Josephson interlayer pair transfer in high-T C superconductors

Our previous investigation of BCS and Josephson tunneling as interlayer transfer mechanisms is used to study the effect of magnetic impurities between the layers. With proper choice of parameters the Josephson mechanism can fit the strong decrease of Tc observed by Winzer in the Tl compound. We give arguments why the BCS coupling is relevant for the Y compound but not for the more distant planes in the Tl and Bi compounds.

Interlayer pairing in high temperature superconductors: effect of nonmagnetic impurities

The influence of impurity scattering is studied theoretically in a two-layer model for the high-Tc superconductor Y1Ba2Cu3O7−δ with intra- and inter-layer pairing. Two types of impurities are considered: (I) impurities which conserve the reflection symmetry of the two layers and (II) impurities which break it. Impurities of type (I) have no influence on the critical temperature. Type (II) impurities have strong influence onTc as well as onHc2 if there is a pairing interaction between carriers of different layers. The treatment of type (II) impurities is generalized to a periodic layer model appropriate for La2−xBaxCuO4. Available experiments on impurities in Y1Ba2Cu3O7−δ and La2−xBaxCuO4 are interpreted with our theory.

BCS versus Josephson pair hopping between the CuO2 layers in high-Tc superconductors.

We start with the two-dimensional (2D) scattering matrix for two electrons of opposite spin and momentum, accounting for the fluctuating pair correlations in a single ${\mathrm{CuO}}_{2}$ layer, and consider the interlayer pair hopping by (a) BCS scattering out of the layer and (b) Josephson tunneling between layers. The experimental 3D transition temperature ${T}_{c}$ is found as a function of the interlayer BCS coupling parameter and the Josephson-tunneling matrix element. We discuss the relative importance of both of these transfer mechanisms for the Y and Tl compounds.

The cuprate superconductors: Narrow correlated-electron bands and interlayer pairing via plane-chain charge transfer

The cuprate superconductors are modelled by two metallic CuO2planes, separated by insulating layers, in an extended Hubbard Hamiltonian. Hybridization of O(2p) and Cu(d) orbitals splits the wide bands of LDA theory, yielding a narrow conduction band of antibonding holes. Holes on the two CuO2 planes are correlated via interplane hopping, giving a non-magnetic normal Fermi liquid. Charge exchange between the planes and the intervening layers generates attraction and a BCS condensation.

On the theory of layered high-temperature superconductors

Assuming that charge carriers form a Fermi liquid state, we study a model for layered high-temperature superconductors with unretarded intralayer and interlayer pairing. Guided by band structure calculations and inverse photoemission experiments, we adopt a tight binding band with nearest and next-nearest neighbors hopping within the sheets and weak interlayer hopping. The gap equations are solved numerically, without imposing a cutoff energy, characteristic to phonon mediated superconductivity. On this basis we calculate the gap parameters,T c , the tunneling conductance, infrared absorption and the coherence length for various band fillings ρ=1/2−x by introducing excess holes of concentrationx. Assuming the interlayer coupling strength to be smaller than the intralayer one, our main results are as follows:T c is dominated by the intralayer properties, reaching a maximum atx≈0.3, where strong coupling features appear. In the presence of interlayer pairing, the gap becomes anisotropic perpendicular to the layers, and standard BCS-behavior is modified. In particular the BCS-square root singularity in the density of states and in the tunneling conductance is replaced by van Hove singularities characterizing the anisotropic gap. In particular, we investigate the anisotropy of the tunneling conductance for specular and diffuse tunneling for a junction parallel or perpendicular to the layers, infrared absorption, as well as the coherence length, parallel and perpendicular to the layers.

Plasmons and high-temperature superconductivity.

Long-wavelength charge fluctuation models are constructed for 1:2:3 superconductors. These include planar plasmons ($\ensuremath{\omega}\ensuremath{\sim}\sqrt{q}$) plus numerous acoustical plasmons ($\ensuremath{\omega}\ensuremath{\sim}q$). We show that these modes do not cause pairing of electrons into a superconductor state. Our results rule out interlayer and intralayer pairing by long-wavelength charge fluctuations.

Band structure, electron correlations, and an interlayer pairing mechanism for high temperature superconductivity

We show that the conduction electrons in YBa 2Cu 3O 7−δ arise mainly from O2-O3 p-orbitals, and lie in a narrow band (of width ∼ 0.1 eV). The Cooper pairs in the superconducting state come from two distinct CuO 2 planes, and the “glue” which binds them is an electronic breathing mode of charge transfer within an interplanar O4-Cu1-O4 complex. Our picture is consistent with experiment.

Enhancement of the superconducting critical temperature in layered compounds.

It is shown that interlayer pairing interaction can enhance the superconducting critical temperature of layered compounds in comparison with the critical temperature of the intralayer processes. Possible implications for high-T/sub c/ oxidic superconductors are also discussed.

Correlated-electron bands and interlayer pairing in high-temperature superconductors

The conduction electrons in YBa2Cu3O7- δ are shown to derive mainly from 02-03 p-orbitals ; they lie in a narrow band (of width ∼ 0.1 eV). The Cooper pairs in the superconducting state come from two distinct CuO2 planes, and the glue which binds them is an electronic breathing mode of charge transfer within an interplanar O4-Cu1-O4 complex. Because the paired electrons are on different planes, the Coulomb repulsion between them is small, and is not inimical to superconductivity. Our picture is consistent with experiment.

Inter-layer pairing mechanism of high-Tc superconductors

In a layered material like YBa 2 Cu 3 O x , the effect of Coulomb repulsion is substantially reduced if Cooper pairs are formed out of electrons on neighboring layers. The strong coupling calculation shows that inter-layer pairing cannot coexist with intra-layer pairing. We give the condition for inter-layer pairing in the form of a phase diagram. Stability against impurities is also discussed. Small nuclear spin relaxation rate should distinguish inter-layer pairing from intra-layer pairing.

Inter-layer pairing of two-dimensional electrons

We point out the possibility that the high transition temperatures of the recently discovered oxide superconductors are dominantly caused by the inter-layer Cooper pairing of two-dimensional electrons that are coupled through the exchange of three-dimensional phonons.

Possible triplet superconductivity in thin films and layered compounds in a strong, parallel magnetic field

We consider a model of both singlet and triplet superconductivity in thin films and intercalated layered compounds in which the attractive electron-electron interaction has both $s$- and $p$-wave form in the layers and interlayer pairing is also possible for the layered materials. We include the effects of intralayer $s$- and $p$-wave impurity scattering. As expected, we find that the intralayer singlet state is not suppressed by scattering, but the interlayer state is suppressed by $s$-wave scattering and the intralayer $p$-wave state is suppressed by transport scattering. For thin films in a parallel magnetic field the $p$-wave state is dominant below the transition temperature ${T}_{i}$ at fields exceeding the $s$-wave Pauli limit ${H}_{p}$. For the layered compounds with interlayer tunneling matrix element $J$, there is a temperature ${T}^{*}&gt;0$ below which ${H}_{c2,\ensuremath{\parallel}}$ for one of the triplet states is divergent, provided that $J&lt;\frac{2\ensuremath{\pi}{T}_{I0}}{\ensuremath{\gamma}\sqrt{e}}$ or $J&lt;\frac{2\ensuremath{\pi}{T}_{i0}f(\frac{{\ensuremath{\tau}}_{s}}{{\ensuremath{\tau}}_{\mathrm{tr}}})}{\ensuremath{\gamma}}$, where $f(z)\ensuremath{\ge}1$ and ${T}_{i0}$ and ${T}_{I0}$ are the intra- and interlayer triplet transition temperatures in the absence of impurities, respectively. We also examine the behavior of the triplet states in small magnetic fields, and discuss the possibilities of observing the phenomenon in real materials.