Intralayer Pairing Research Articles

Frustrated superconductivity and intrinsic reduction of <i>T</i><sub><i>c</i></sub> in trilayer nickelate

<p>Identifying the key factors controlling the magnitude of <i>T</i><sub><i>c</i></sub> is of critical importance in the pursuit of high-temperature superconductivity. In cuprates, <i>T</i><sub><i>c</i></sub> reaches its maximal value in trilayer structure, leading to the belief that interlayer coupling may help promote the pairing. In contrast, for the recently discovered nickelate superconductors under high pressure, the maximum <i>T</i><sub><i>c</i></sub> is reduced from about 80 K in the bilayer La<sub>3</sub>Ni<sub>2</sub>O<sub>7</sub> to 30 K in the trilayer La<sub>4</sub>Ni<sub>3</sub>O<sub>10</sub>. Motivated by this opposite trend, we propose an interlayer pairing scenario for the superconductivity of La<sub>4</sub>Ni<sub>3</sub>O<sub>10</sub>. Our theory reveals intrinsic frustration in the spin-singlet pairing that the inner layer tends to form with both of the two outer layers respectively, leading to strong superconducting fluctuations between layers. This explains the reduction of its maximum <i>T</i><sub><i>c</i></sub> compared to that of the bilayer La<sub>3</sub>Ni<sub>2</sub>O<sub>7</sub>. Our findings support a fundamental distinction between multilayer nickelate and cuprate superconductors, and ascribe it to their different (interlayer versus intralayer) pairing mechanisms. Furthermore, our theory predicts extended <i>s</i><sup><i>±</i></sup>-wave gap structures in La<sub>4</sub>Ni<sub>3</sub>O<sub>10</sub>, with varying signs and possible nodes on different Fermi pockets. We also find an intrinsic Josephson coupling with potentially interesting consequences that may be examined in future experiments. Our work reveals the possibility of rich novel physics in multilayer superconductors with interlayer pairing.</p>

Josephson effect in graphene bilayers with adjustable relative displacement

The Josephson current is investigated in a superconducting graphene bilayer where pristine graphene sheets can make in-plane or out-of-plane displacements with respect to each other. The superconductivity can be of an intrinsic nature, or due to a proximity effect. The results demonstrate that the supercurrent responds qualitatively differently to relative displacement if the superconductivity is due to either intralayer or interlayer spin-singlet electron-electron pairing, thus providing a tool to distinguish between the two mechanisms. Specifically, both the AA and AB stacking orders are studied with antiferromagnetic spin alignment. For the AA stacking order with intralayer and on-site pairing no current reversal is found. In contrast, the supercurrent may switch its direction as a function of the in-plane displacement and out-of-plane interlayer coupling for the cases of AA ordering with interlayer pairing and AB ordering with either intralayer or interlayer pairing. In addition to sign reversal, the Josephson signal displays many characteristic fingerprints which derive directly from the pairing mechanism. Thus, measurements of the Josephson current as a function of the graphene bilayer displacement open up the means achieve deeper insights into the superconducting pairing mechanism.

Time-reversal-invariant topological superfluids in Bose-Fermi mixtures

A mixed dimensional system of fermions in two layers immersed in a Bose-Einstein condensate (BEC) is shown to be a promising setup to realise topological superfluids with time-reversal symmetry (TRS). The induced interaction between the fermions mediated by the BEC gives rise to a competition between p-wave pairing within each layer and s-wave pairing between the layers. When the layers are far apart, intra-layer pairing dominates and the system forms a topological superfluid either with or without TRS. With decreasing layer separation or increasing BEC coherence length, inter-layer pairing sets in. We show that this leads either to a second order transition breaking TRS where the edge modes gradually become gapped, or to a first order transition to a topologically trivial s-wave superfluid. Our results provide a realistic roadmap for experimentally realising a topological superfluid with TRS in a cold atomic system.

Superfluidity and density order in a bilayer extended Hubbard model

We use cluster dynamical mean field theory to study the phase diagram of the square lattice bilayer Hubbard model with an interlayer interaction. The layers are populated by two-component fermions, and the densities in both layers and the strength of the interactions are varied. We find that an attractive interlayer interaction can induce a checkerboard density ordered phase and superfluid phases, with either interlayer or intralayer pairing. Remarkably, the latter phase does not require an intralayer interaction to be present: it can be attributed to an induced attractive interaction caused by density fluctuations in the other layer.

Phases of a bilayer Fermi gas

We investigate a two-species Fermi gas in which one species is confined in two parallel layers and interacts with the other species in the three-dimensional space by a tunable short-range interaction. Based on the controlled weak coupling analysis and the exact three-body calculation, we show that the system has a rich phase diagram in the plane of the effective scattering length and the layer separation. Resulting phases include an interlayer s-wave pairing, an intralayer p-wave pairing, a dimer Bose-Einstein condensation, and a Fermi gas of stable Efimov-like trimers. Our system provides a widely applicable scheme to induce long-range interlayer correlations in ultracold atoms.

Structure and thermodynamics of a ferrofluid bilayer

We present extensive Monte Carlo simulations for the thermodynamic and structural properties of a planar bilayer of dipolar hard spheres for a wide range of densities, dipole moments, and layer separations. Expressions for the stress and pressure tensors of the bilayer system are derived. For all thermodynamic states considered, the interlayer energy is shown to be attractive and much smaller than the intralayer contribution to the energy. It vanishes at layer separations of the order of two hard sphere diameters. The normal pressure is negative and decays as a function of layer separation h as -1/h;{5} . Intralayer and interlayer pair distribution functions and angular correlation functions are presented. Despite the weak interlayer energy, strong positional and orientational correlations exist between particles in the two layers.

Analytic theory of pair distribution functions in symmetric electron–electron and electron–hole bilayers

We present a self-consistent analytic theory of the intra-layer and inter-layer pair correlation functions in electron–electron and electron–hole fluid bilayer systems. Our approach involves the solution of a zero-energy scattering Schrödinger equation with an effective potential which includes a Bose-like term from Jastrow–Feenberg correlations and a Fermi term from kinetic energy and exchange, tailored to yield the Hartree–Fock limit at high carrier density. The theory is also shown to satisfy the plasmon sum rule and the charge neutrality condition. We obtain good agreement with the available Quantum Diffusion Monte Carlo (DMC) data in symmetric bilayers over a wide range of carrier density and layer spacing. Signals of impending transitions to density-modulated states at strong coupling and low layer spacing appear in the calculated pair correlations through inter-layer in-phase oscillations for electron–hole bilayers and out-of-phase oscillations for electron–electron bilayers, in agreement with the DMC findings.

Longitudinal collective modes in asymmetric charged-particle bilayers

We have analysed the dispersion of longitudinal collective modes in classical asymmetric charged-particle bilayer liquids in the strong coupling regime. The theoretical analysis is based on a dielectric matrix calculated in the quasi-localized charge approximation (QLCA). The matrix elements are expressed as integrals over inter-layer and intra-layer pair correlation function data that we have generated by molecular dynamics (MD) simulations. At the same time, MD simulations of density and current fluctuation spectra were analysed to infer the collective mode dispersion. The long-wavelength finite frequency (energy) gap, brought about by strong inter-layer correlations, is a monotonically increasing function of the density ratio, n2/n1, and, for the smallest value of the inter-layer spacing considered, the gap reaches its maximum value when the two layer densities are equal. It appears that it stays at that value for n2/n1 > 1.

Phase diagram of classical electronic bilayers

Extensive molecular dynamics calculations have been performed on classical, symmetric electronic bilayers at various values of the coupling strength Γ and interlayer separation d to delineate its phase diagram in the Γ–d plane. We studied the diffusion, the amplitude of the main peak of the intralayer static structure factor and the peak positions of the intralayer pair correlation function with the aim of defining equivalent signatures of freezing and constructing the resulting phase diagram. It is found that for Γ greater than 75, crystalline structures exist for a certain range of interlayer separations, while liquid phases are favoured at smaller and larger d. It is seen that there is good agreement between our phase diagram and previously published ones.

Coexistence of superconducting and spiral spin orders: Models of ruthenate

The effect of a spiral spin structure on superconducting (SC) pairing in a three-band Hubbard model related to Sr2RuO4 is analyzed in the mean-field approximation. Such a structure with incommensurate vector Q=2π (1/3, 1/3) is the simplest one that removes the nesting instability of α and β bands. It is assumed that there is an intralayer pairing interaction between two types of neighbor sites, those with attraction in a singlet channel and with attraction in both two-singlet and triplet channels. In both cases, a mixed singlet-triplet SC order is observed in the γ band: a d-wave singlet order is accompanied by the formation of p-wave triplet pairs (k,-k-Q)⇈ and (k,−k+Q)⇊ with large total momenta ∓Q and the spin projections ±1 onto an axis perpendicular to the spin rotation plane of the spiral spin structure. Both the SC and normal states are states with broken time-reversal symmetry. In contradiction to the experiment, the models give different scales of T c for the γ band and for α and β bands. This fact shows that the models with intralayer interactions or with the spin structure assumed are insufficient.

An intralayer pairing mechanism for the coexistence of charge- and spin-density waves induced superconductivity in LaSrCuO

Starting from an effective two-dimensional dynamic interaction that includes screening of holes as carriers by charge density fluctuations and by optical phonons, we investigate the nature of a d-wave pairing mechanism leading to superconductivity in layered La-based cuprates. We consider the La–Sr–CuO system as an ionic solid containing layers of holes as carriers with a single CuO2 layer in a unit cell, where the localized spins form an antiferromagnetic (AF) order. The electron–phonon interaction matrix element in the case of an ordinary unit cell without the local AF order yields s-wave superconductivity. While for the unit cell with AF order, the wave-vector dependence of the intralayer effective interaction potential shows the sign reversal to create d-wave pairing due to localized antiferromagnetic spin order for the screened phonons. Following the strong coupling theory, the superconducting transition temperature, the isotope exponent, coherence length and magnetic penetration depth are also estimated. The implications of the intralayer pairing model and its analysis are discussed.

Molecular dynamics study of diffusion in a bilayer electron gas.

Molecular dynamics simulations of strongly coupled, classical electronic bilayers, interacting through the Coulomb potential, have been produced and studied. Values of the plasma coupling parameter Gamma between 10 and 80 and interlayer separations d from 0.1 to 3.0, (in units of Wigner-Seitz radius), were considered. The simulation results were used to calculate the intralayer and interlayer pair correlation functions and self-diffusion of charged particles in this system. The variation of self-diffusion with Gamma and d has been analyzed, and it is found that for the largest value of Gamma, the diffusion coefficient does not increase monotonically with layer separation, but has a distinct minimum for values of d slightly less than 1.

Theory of sinusoidal modulation of the resonant neutron scattering in high-temperature superconductors

A model with interlayer pairing is proposed to explain the sinusoidal modulation of the resonant neutron scattering in high-temperature superconductors. It is found that the interlayer pairing has s-wave symmetry in the ${\mathrm{CuO}}_{2}$ plane and has comparable magnitude with the d-wave intralayer pairing. It is also found that the interlayer pairing mainly affects momentum close to the hot spots on the Fermi surface while its effect on the gap nodes is negligible. It is pointed out that these characteristics of the interlayer pairing can be understood in a model in which the superconducting pairing originates from the exchange of the antiferromagnetic spin fluctuation.

Molecular dynamics studies of strongly coupled charged particle bilayers at finite temperatures.

The structure of strongly coupled charged particle bilayers was investigated using molecular dynamics simulation, in a wide range of the plasma coupling parameter Gamma=20-100. The simulations showed the existence of a series of structural transformations, controlled by the separation of the layers. At high values of Gamma a pronounced long-range order was found to develop at intermediate layer separations, with staggered square lattice configuration. The results show a fair agreement with those obtained by hypernetted chain calculations, in terms of intralayer and interlayer pair correlation functions and structure functions.

THEORY OF SINUSOIDAL MODULATION OF THE RESONANT NEUTRON SCATTERING IN HIGH TEMPERATURE SUPERCONDUCTORS

A model with interlayer pairing is proposed to explain the sinusoidal modulation of the resonant neutron scattering in high temperature superconductors. It is found that the interlayer pairing has s-wave symmetry in the CuO 2 plane and has comparable magnitude with the d-wave intralayer pairing. It is also found that the interlayer pairing mainly affects momentum close to the hot spots on the Fermi surface while its effect on the gap nodes is negligible. It is pointed out that these characteristics of the interlayer pairing can be understood in a model in which the superconducting pairing originates from the exchange of the antiferromagnetic spin fluctuation.

A POSSIBLE PAIRING MECHANISM FOR HTSC: TWO-DIMENSIONAL CONFINEMENT AND COULOMB OVER-SCREENING

Among all the common properties of HTCS cuprates, we build our model on two of them: their high anisotropy, and their extremely low density of charge carriers. The intra-layer pairing mechanism is provided by the two-dimensional over-screening of Coulomb repulsion.1,2 The c-axis zero point energy restricts this pairing to a low carrier density region. Below a critical density, the system behaves as a two-dimensional confined jellium where the energy gain due to charge pairing is larger than the c-axis localization energy. In the high density region, where the pairing energy cannot compensate the localization energy, the system delocalizes and crosses over to a three-dimensional regime. This competition between binding and confinement energies implies a monotonic decrease of mass anisotropy with doping. Pre-formed pairs which exist below a Mean Field (MF) temperature defined by the binding energy, account for pseudo-gap observations.3,4 The superconducting critical temperature T c is given by the Beresinskii–Kosterlitz–Thouless (BKT) transition of the two-dimensional layer, renormalized by quantum phase fluctuations (QPF).5 QPF account for the metal-insulator transition at very low doping.

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.

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.

Interlayer pairings in the Josephson-coupled layered superconductors

The general expression of the effective pairing Hamiltonian is proposed to obtain the multicomponent Ginzburg–Landau free energy functional for strongly anisotropic layered superconductors. The effective Hamiltonian contains an intralayer pairing interaction as well as all possible interlayer pairing potentials. It is shown that the problem with many order parameters can be reduced to the problem with two order parameters which characterize the effective intralayer and effective interlayer pairings. The interlayer interaction Ṽ 0, which corresponds to the coherently hopping of pairs from one layer to the nearest neighboring layers, renormalizes the Josephson tunneling strength for an intralayer effective order parameter. Mixing of two order parameters is characterized by the Lifschitz invariant in the free energy functional. The Lifschitz invariant is enhanced due to the interlayer pairing potential V 01 which represents an interaction of two particles on the layer with scattering one of them into the nearest neighboring layers. The interlayer interaction V 01 also stabilizes the mixing of two-order parameters. Since in the absence of V 01 the Lifschitz invariant vanishes for a half-filled band of two-dimensional electrons in a layer. The transition temperature T c to the superconducting state and upper critical magnetic field H c 2 are calculated. Effects of all possible interlayer pairing interactions on T c and H c 2 are studied.

Anisotropic order parameters with s- and d-wave-like symmetry and the transition temperature in high-Tc layered superconductors.

The wave-vector dependence of superconducting order parameters and the corresponding transition temperature in three-dimensional layered metals are investigated. It includes planar anisotropic s-wave-like as well as d-wave-like pairing contributions, but for simplicity only intralayer pairing of electrons has been considered for tetragonal and orthorhombic crystal structures, relevant to high-${\mathit{T}}_{\mathit{c}}$ materials. It is shown that for the orthorhombic case order parameters are likely to have mixed symmetry, whereas in tetragonal structures it is possible to have only planar d-wave-like symmetry with a possible correction term with an additional wave-vector dependence in the direction perpendicular to the reciprocal layer plane. \textcopyright{} 1996 The American Physical Society.