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Register a new userTheory of d-wave high temperature superconductivity in the cuprates involving non-linear lattice modes
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The transition mechanism in high temperature cuprate superconductors is an outstanding puzzle. A previous suggestion on the role of non-linear local lattice instability modes on the microscopic pairing mechanism in high temperature cuprate superconductors cite{Lee:JSNM09} is re-examined to provide a viable mechanism for superconductivity in these cuprates via an unusual lattice vibration in which an electron is predominantly interacting with a nonlinear $Q_2$ mode of the oxygen clusters in the CuO$_2$ planes. It is shown that the interaction has explicit d-wave symmetry and leads to an indirect coupling of d-wave symmetry between electrons. As a follow-up of cite{Lee:JSNM09}, in this paper, we report detailed derivation of the superconducting gap equation and numerical solutions for the transition temperature as inherently integrated into the so-called Extended Hubbard Model (EHM). A unique feature in the EHM is that the transition temperature has an inherent k-dependence. In addition, superconducting gap solutions are restrained to specific regions in the first Brillouin zone (1BZ). It is very feasible to expect that the EHM naturally inherits a huge parameter space in which experimentally measured results, such as the well-known superconducting dome and the phase diagram from electronic Raman scattering cite{Sacuto:RPP13} can be accommodated. The EHM model hence offers a viable venue to search for or confirm any signature in k-point-sensitive experimental measurements.
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The discovery of high temperature superconductivity in the cuprates in 1986 triggered a spectacular outpouring of creative and innovative scientific inquiry. Much has been learned over the ensuing 28 years about the novel forms of quantum matter that are exhibited in this strongly correlated electron system. This progress has been made possible by improvements in sample quality, coupled with the development and refinement of advanced experimental techniques. In part, avenues of inquiry have been motivated by theoretical developments, and in part new theoretical frameworks have been conceived to account for unanticipated experimental observations. An overall qualitative understanding of the nature of the superconducting state itself has been achieved, while profound unresolved issues have come into increasingly sharp focus concerning the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the normal state at elevated temperatures. New conceptual approaches, drawing from string theory, quantum information theory, and various numerically implemented approximate approaches to problems of strong correlations are being explored as ways to come to grips with this rich tableaux of interrelated phenomena.
We present a comparative study of magnetic excitations in the first two Ruddlesden-Popper members of the Hg-family of high-temperature superconducting cuprates, which are chemically nearly identical and have the highest critical temperature ($T_mathrm{c}$) among all cuprate families. Our inelastic photon scattering experiments reveal that the two compounds paramagnon spectra are nearly identical apart from an energy scale factor of $sim130%$ that matches the ratio of $T_mathrm{c}$s, as expected in magnetic Cooper pairing theories. By relating our observations to other cuprates, we infer that the strength of magnetic interactions determines how high $T_mathrm{c}$ can reach. Our finding can be viewed as a magnetic analogue of the isotope effect, thus firmly supporting models of magnetically mediated high-temperature superconductivity.
In the Eliashberg integral equations for d-wave superconductivity, two different functions $(alpha^2 F)_n(omega, theta)$ and $(alpha^2 F)_{p,d}(omega)$ determine, respectively, the normal and the pairing self-energies. We present a quantitative analysis of the high-resolution laser based ARPES data on the compound Bi-2212 to deduce the function$(alpha^2 F)_n(omega, theta)$. Besides its detailed $omega$ dependence, we find the remarkable result that this function is nearly independent of $theta$ between the ($pi,pi$)-direction and 25 degrees from it. Assuming that the same fluctuations determine both the normal and the pairing self-energy, we ask what theories give the function $(alpha^2 F)_{p,d}(omega)$ required for the d-wave pairing instability at high temperatures as well as the deduced $(alpha^2 F)_n(theta, omega)$. We show that the deduced $(alpha^2 F)_n(theta, omega)$ can only be obtained from Antiferromagnetic (AFM) fluctuations if their correlation length is smaller than a lattice constant. Using $(alpha^2 F)_{p,d}(omega)$ consistent with such a correlation length and the symmetry of matrix-elements scattering fermions off AFM fluctuations, we calculate $T_c$ an show that AFM fluctuations are excluded as the pairing mechanism for d-wave superconductivity in cuprates. We also consider the quantum-critical fluctuations derived microscopically as the fluctuations of the observed loop-current order discovered in the under-doped cuprates. We show that their frequency dependence and the momentum dependence of their matrix-elements to scatter fermions are consistent with the $theta$ and $omega$ dependence of the deduced $(alpha^2 F)_n(omega, theta)$. The pairing kernel $(alpha^2 F)_{p,d}(omega)$ calculated using the experimental values in the Eliashberg equation gives $d-wave$ instability at $T_c$ comparable to the experiments.
Recent experiments in the cuprates have seen evidence of a transient superconducting state upon optical excitation polarized along the c-axis [R. Mankowsky et al., Nature 516, 71 (2014)]. Motivated by these experiments we propose an extension of the single-layer $t-J-V$ model of cuprates to three dimensions in order to study the effects of inter-plane tunneling on the competition between superconductivity and bond density wave order. We find that an optical pump can suppress the charge order and simultaneously enhance superconductivity, due to the inherent competition between the two. We also provide an intuitive picture of the physical mechanism underlying this effect. Furthermore, based on a simple Floquet theory we estimate the magnitude of the enhancement.
Besides superconductivity, copper-oxide high temperature superconductors are susceptible to other types of ordering. We use scanning tunneling microscopy and resonant elastic x-ray scattering measurements to establish the formation of charge ordering in the high-temperature superconductor Bi2Sr2CaCu2O8+x. Depending on the hole concentration, the charge ordering in this system occurs with the same period as those found in Y-based or La-based cuprates, and displays the analogous competition with superconductivity. These results indicate the similarity of charge organization competing with superconductivity across different families of cuprates. We observe this charge ordering to leave a distinct electron-hole asymmetric signature (and a broad resonance centered at +20 meV) in spectroscopic measurements, thereby indicating that it is likely related to the organization of holes in a doped Mott insulator.
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