Interlayer Pair Tunneling Research Articles

Theoretical Investigation of the Four-Layered Self-Doped High-TcSuperconductors: Evidence of the Pair Tunneling Effect

Based on a four-layered self-doped t-J type model and the slave-boson mean-field approach, we study theoretically the superconductivity in the electron-doped and hole-doped layers. The neighbor layers are coupled through both the single electron interlayer hopping and pair tunneling effect. The superconducting gap magnitude for the electron-doped band is nearly twice that of the hole-doped one, which contrasts with our previous understanding of the electron-hole asymmetry in high-T(c) superconductors but is consistent with recent angle-resolved photoemission spectroscopy experiments in four-layered materials Ba2Ca3Cu4O8F2. Our results propose that the pair tunneling effect is important to examine the multilayered superconducting materials.

Importance of interlayer pair tunneling: A variational perspective

We study the effect of interlayer pair tunneling in a bilayer superconductor where each layer is described by a two dimensional t– J model and the two layers are connected by the Josephson pair tunneling term. We study this model using a grand canonical variational Monte Carlo (GVMC) method, for which we develop a new algorithm to perform Monte Carlo simulation of a system with fluctuating particle number. The variational wavefunction is taken to be the product of two Gutzwiller projected d-wave BCS wavefunctions with variable particle densities, one for each layer. We calculate the energy of the above state as a function of the d-wave superconducting gap parameter, Δ . We find that the interlayer pair tunneling energy, E ⊥ shows interesting variation with Δ . E ⊥ tends to enhance the optimal value of Δ , thereby the superconducting pairing. However the magnitude of the tunneling energy is found to be too small to have any appreciable effect on the physical properties. While the result is supported by early experiments and hence may appear known to the community, the current work presents a new approach to the problem and confirms the diminished role of interlayer pair tunneling by directly calculating its contribution to superconducting condensation energy.

Scaling of transition temperature and CuO 2 plane buckling in the cuprate superconductors

A universal feature of all high temperature superconductors is the existence of a chemical composition that gives maximum T c, separating so-called under- and over-doped region. Recently, it is seen by Chmaissem et al. [Nature 397 (1999) 45] that both T c and the buckling angle of the CuO 2 planes goes through a maximum at the same doping level. We show that only for optimal doping concentration the Fermi surface touches the M(0,π) point in the BZ, where the matrix element for interlayer pair tunneling amplitude is largest, so that the gain in delocalization energy by tunneling (in pairs) along the c-axis is largest. Buckling of the planes on the other hand modulates the separation between the planes and thereby modulates the interlayer pair tunneling amplitude. That is why both T c and buckling angle (oxygen atom displacement out of the plane) scales the same way with doping concentration. We have calculated T c and buckling angle for various doping concentration. The agreement with experiment is remarkably good. We also point out the possible reason for large (about 1%) change of the buckling mode phonon frequency, across the transition temperature for optimal doping concentration, observed in neutron scattering experiments by Pyka et al. [Phys. Rev. Lett. 70 (1993) 1457].

Spin polarized carrier injection into high-Tcsuperconductors: A test for the superconductivity mechanism

We point out in this short paper, that be it an s-wave or d-wave superconductor, in a nonequilibrium situation (i.e., in the presence of excess unpolarized and polarized quasiparticles maintained by an injection current) the superconducting gap suppression by the presence of the same amount of excess quasiparticles, can at best differ by a factor of 2, for a conventional BCS superconductor. For the high-${T}_{c}$ superconductors on the other hand, there is a huge difference in gap suppression between unpolarized and polarized quasiparticle injection, as observed in the experiments [V. A. Vasko et al., Phys. Rev. Lett. 78, 1134 (1997); T. A. Venkatesan et al., Appl. Phys. Lett. 71, 1718 (1997)]. We argue that this large anomaly has a natural explanation within the interlayer tunneling mechanism of Wheatley, Hsu, and Anderson [J. M. Wheatley, T. C. Hsu, and P. W. Anderson, Phys. Rev. B 37, 5897 (1988)], and is due to the excess polarized quasiparticles blocking the interlayer pair tunneling process. We also point out that spin polarized quasiparticle injection in a superconductor is a very easy way to distinguish between an s-wave or an anisotropic gap superconductor.

Two-square-well model for layered superconductors: Effect of intralayer and interlayer Coulomb interactions on thed-wave gap

On the basis of Fermi liquid theory, we study the effect of intralayer and interlayer Coulomb interactions on the energy gap of layered superconductors assuming the BCS d-wave pairing model. The gap equation is derived for the two-square-well model, assuming a boson-mediated attraction and a long-range Coulomb repulsion that leads to intralayer and interlayer Coulomb scattering of Cooper pairs. The d-wave gap amplitude ${\ensuremath{\Delta}}_{1}$ at $T=0\mathrm{K}$ is evaluated as a function of the attractive pairing strength and of the screened Coulomb interactions. For optimally doped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ we find that intralyer Coulomb scattering reduces ${\ensuremath{\Delta}}_{1}$ by a factor between 1.5 and 2. The additional effect of interlayer Coulomb scattering depends in a crucial manner on the relative phases of the gap functions in adjacent layers. If Josephson and boson-assisted interlayer pair tunneling (ILT) are responsible, the three-dimensional phase coherence, that is, the phase difference between adjacent layers $\ensuremath{\Delta}\ensuremath{\varphi}=0,$ interlayer Coulomb scattering leads to a further reduction of the gap that can be comparable with or larger than the effect of intralyer scattering. If, however, the phase of the gap function alternates, that is $\ensuremath{\Delta}\ensuremath{\varphi}=\ensuremath{\pi},$ because the interlayer Coulomb scattering dominates the ILT effect, the interlayer Coulomb scattering of Cooper pairs enhances ${\ensuremath{\Delta}}_{1}.$ This effect is studied as a function of the strength of the Coulomb interaction and it is shown that, with increasing strength, the pseudo-Coulomb parameter ${\mathrm{\ensuremath{\mu}}}^{\mathrm{*}}$ decreases and may change sign when the Coulomb interaction is sufficiently strong. The possible role of the interlayer Coulomb effect is discussed in relation to scanning tunneling microscopy experiments.

Tunneling characteristics of I- and HgI 2-intercalated Bi 2Sr 2CaCu 2O 8+ x single crystals

We compared c-axis tunneling characteristics of small stacked intrinsic Josephson junctions prepared on the surface of pristine, I-, and HgI 2-intercalated Bi 2Sr 2CaCu 2O y (Bi2212) single crystals. Relation between the interlayer coupling and the in-plane gap, estimated from I– V characteristics, seems to contradict to the interlayer pair tunneling mechanism of high- T c superconductivity.

Non-k-Diagonality in the Interlayer Pair-Tunneling Model of High-Temperature Superconductivity

We investigate the effect of k-space broadening of the interlayer pairing kernel on the critical temperature Tc and the k-dependence of the gap function in a one-dimensional version of the interlayer pair-tunneling model of high-Tc superconductivity. We consider constant as well as k-dependent intralayer pairing kernels. We find that the sensitivity to k-space broadening is larger the smaller the width of the peak of the Fermi-level gap calculated for zero broadening. This width increases with the overall magnitude of the interlayer tunneling matrix element, and decreases with the bandwidth of the single-electron intralayer excitation spectrum. The width also increases as the Fermi level is moved towards regions where the excitation spectrum flattens out. We argue that our qualitative conclusions are valid also for a two-dimensional model. This indicates that at or close to half-filling in two dimensions, when the Fermi-surface gap for zero broadening attains its peaks at (±π/a, 0) and (0, ±π/a) where the excitation spectrum is flat, these peaks should be fairly robust to moderate momentum broadening.

Effect of nonuniform hole-content distribution within the interlayer pair-tunneling mechanism of layered HTSC

The interlayer pair-tunneling (ILPT) mechanism for high- T c superconductivity predicts the dependence of the (optimal) critical temperature T c on the number of layers n within a homologous series of layered cuprate oxides. We generalize the mean-field procedure employed to evaluate T c within an extended in-plane Hubbard model in the presence of ILPT, developed for a bilayer complex ( n=2), to the case of n=3,4 inequivalent superconducting layers. As a function of doping, we show how a nonuniform hole-content distribution among different layers affects T c. In particular, depending on doping, the onset of superconductivity may be ruled by inner or outer layers. The latter result may be related to recent experimental data of T c as a function of pressure in Tl- and Bi-based layered superconductors.

K-space broadening in a non-Fermi liquid based model of high- Tc superconductivity

We investigate the effect of k-space broadening of the interlayer pairing kernel on the critical temperature T c and the k-space dependence of the gap in a one-dimensional version of the interlayer pair-tunneling model of high- T c superconductors. We identify the amount of broadening that will destroy the sharp k-space variation of the gap obtained with a k-diagonal interlayer pair tunneling, explaining our results in terms of Fermi surface features of the gap. The parameter controlling this amount of k-space broadening is T J / t, where T J is related to the interlayer pair-tunneling matrix element and t is the single-electron intralayer tunneling matrix element.

Sharpk-space features in the order parameter within the interlayer pair-tunneling mechanism of high-Tcsuperconductivity

We study the k-dependence of the gap function of a bilayer superconductor, using standard mean-field techniques applied to a 2D extended Hubbard model, in the presence of coherent interlayer pair-tunneling and quenched coherent single-particle tunneling. The intralayer pairing potential thus defined is expandable in a finite number of basis functions for the irreducible representations of the point-group of the perfectly square lattice, C_{4v}. This gives rise to a competition between s- and d-wave symmetry, as the chemical potential is increased from the bottom to the top of a realistic band for most cuprates. It allows for mixed-symmetry paired state at temperatures below T_c, but never at T_c on a square lattice. Inclusion of the interlayer pair-tunneling into the effective pairing potential leads to highly non-trivial k-space structures, such as pronounced maxima along the Fermi line not seen in the absence of interlayer pair-tunneling. We show how such a gap structure evolves with temperature and with band filling, and how it affects various observables. In particular, a nonuniversal value of the normalized jump in the specific heat at T_c will be evidenced, at variance with the conventional universal BCS result.

C-axis electrodynamics as evidence for the interlayer theory of high-temperature superconductivity

In the interlayer theory of high-temperature superconductivity, the interlayer pair tunneling energy (similar to the Josephson or Lawrence-Doniach energy) is the motivation for superconductivity. This connection requires two experimentally verifiable identities: the coherent normal-state conductance must be smaller than the "Josephson" coupling energy, and the Josephson coupling energy must be equal to the condensation energy of the superconductor. The first condition is well satisfied in the only case that is relevant, (La, Sr)2CuO4, but the second condition has been questioned. It is satisfied for all dopings in (La,Sr)2CuO4 and also in optimally doped Hg(Ba)2CuO5, which was measured recently, but seems to be strongly violated in measurements on single crystals of Tl2Ba2CuO6.

Impurity effects on thed-wave state of the pair tunneling mechanism for high-Tcsuperconductors

We consider the impurity effects on the d-wave state in Anderson{close_quote}s interlayer pair tunneling (IPT) mechanism for high-T{sub c} superconductors. We found that the change of density of states and the T{sub c} suppression with impurities are qualitatively the same as the conventional BCS-type d-wave theory despite different gap equations. In particular, for the T{sub c} suppression with the in-plane impurities we solve the T{sub c} equation of the IPT mechanism explicitly including strong inelastic scattering [{Sigma}{sup {double_prime}}{approximately}{alpha}({h_bar}w+{pi}k{sub B}T)]. As expected, the effect of impurities for the T{sub c} suppression is strongly reduced by inelastic scattering and the results can fit most of the experimental data by varying the impurity scattering strength. The insensitivity of T{sub c} with the out-of-plane rare-earth impurities is shown to be consistent with the IPT mechanism. {copyright} {ital 1998} {ital The American Physical Society}

C-axis phonons and the enhancement of pairing correlations in high-temperature superconductors

We consider the two-dimensional Hubbard model including electron-phonon interaction. Strong local correlations (U→∞ limit) are taken into account within the mean-field approximation for auxiliary boson fields. Phonon-assisted transitions between intraand interlayer states are introduced as the source of coupling between two-dimensional CuO2 layers. This type of processes effectively leads to the nonlinear (quadratic) interaction of intralayer electrons withc-axis phonons. We construct the Eliashberg equations for the resulting Hamiltonian and evaluate the superconducting transition temperatureT c. Our model calculation demonstrates that a pronounced enhancement ofT c in thed-wave channel is possible. The largest enhancement ofT c tends to take place for small hole concentrations. This means that the coupling toc-axis phonons could compete with two-dimensional correlations responsible for the onset of antiferromagnetic order. It is remarkable that the two-dimensional features in the normal state are hardly affected by this specific interlayer interaction. Therefore,c-axis two-phonon-mediated interlayer coupling can cooperate with interlayer pair tunneling and substantially contribute to an increased pairing.

Impurity effects on the anisotropic s-wave superconductor of the interlayer pair tunneling mechanism.

We study the effects of nonmagnetic impurities in the interlayer pair tunneling mechanism for an anisotropic s-wave (ASW) superconductor proposed by Anderson et al. using the self-consistent T-matrix approximation. We found that the impurity effects on this particular model are quite different from those of the conventional ASW model of the BCS-type pairing. It shows a much stronger suppression of ${\mathit{T}}_{\mathit{c}}$ upon doping with nonmagnetic impurities than in the conventional ASW pairing state. Moreover, the minimum-energy gap does not monotonically grow with increasing impurity concentration but instead it quickly shrinks. We also show that the temperature dependence of the gap anisotropy ratio, R(T)=${\mathrm{\ensuremath{\Delta}}}_{\mathrm{max}}$(T)/${\mathrm{\ensuremath{\Delta}}}_{\mathrm{min}}$(T) increases with increasing temperature which has a similar trend with a recent experiment by Ma et al.

EFFECT OF SINGLE PARTICLE HOPPING AND OUT OF PLANE MAGNETIC IMPURITY ON COUPLED PLANAR SUPERCONDUCTORS

It is shown that the single particle band motion along the c axis is harmful for superconductivity in anisotropic systems. Variation of T c with c axis hopping parameter is shown for both the conventional Josephson coupled, planar superconductors and for interlayer pair tunneling mechanism of Wheatley, Hsu, and Anderson (WHA). Effect of out-of-plane magnetic impurity substitution is shown to suppress T c more for conventional superconductors whereas there is a very sharp decrease of T c in the WHA mechanism at larger concentrations.

Phase and amplitude modes in a superconductor with interlayer pair tunneling.

Chakravarty, Sudb\o{}, Anderson, and Strong have introduced a simple model for high ${T}_{c}$ oxides based on the effect of Cooper pair tunneling in a bilayer (with strength ${T}_{J}$) with $s$-wave pairing ($g$) in the layers. We discuss the order parameter fluctuations of this model. Besides the usual Anderson-Bogoliubov phase and Littlewood-Varma amplitude modes, we find new out-of-phase phase and amplitude modes. Their energy and damping depend critically on whether ${T}_{J}>g$ or ${T}_{J}<g$. Such fluctuations in the relative phase and amplitude of two coupled condensates were first discussed in a different system by Leggett in 1966.