Recent scanning tunneling spectroscopy experiments have provided evidence that dopant impurities in high- Tc superconductors can strongly modify the electronic structure of the CuO2 planes nearby, and possibly influence the pairing. To investigate this connection, we calculate the local magnetic superexchange J between Cu ions in the presence of dopants within the framework of the three-band Hubbard model, up to fifth-order in perturbation theory. We demonstrate that the sign of the change in J depends on the relative dopant-induced spatial variation of the atomic levels in the CuO2 plane, contrary to results obtained within the one-band Hubbard model. We discuss some realistic cases and their relevance for theories of the pairing mechanism in the cuprates
A systematic inelastic neutron scattering study of the superexchange interaction in three different undoped monolayer cuprates (La_2CuO_4, Nd_2CuO_4 and Pr_2CuO_4) has been performed using conventional triple axis technique. We deduce the in-plane antiferromagnetic (AF) superexchange coupling $J$ which actually presents no simple relation versus crystallographic parameters. The absolute spectral weight of the spin susceptibility has been obtained and it is found to be smaller than expected even when quantum corrections of the AF ground state are taken into account.
We propose a novel electron-phonon interaction arising from the modulation of the superexchange interaction by phonons. It is enhanced by spin and superconducting fluctuations, which are developed mainly because of the superexchange interaction. It must be responsible for the softening of phonons and kinks in the dispersion relation of quasi-particles. However, the superexchange interaction must be mainly responsible for the formation of Cooper pairs.
An electron-phonon interaction arising from the modulation of the superexchange interaction by phonons is studied within the theoretical framework of Kondo lattices. It is relevant in strongly correlated electron liquids in cuprate oxide superconductors, which lie in the vicinity of the Mott-Hubbard metal-insulator transition. It is enhanced by antiferromagnetic and superconducting fluctuations, which are developed mainly because of the superexchange interaction. When the enhancement of the electron-phonon interaction is large enough, it can explain the softening of phonons and kinks in the qu…
Recent experiments on Bi-based cuprate superconductors have revealed an unexpected enhancement of the pairing correlations near the interstitial oxygen dopant ions. Here we propose a possible mechanism -- based on local screening effects -- by which the oxygen dopants do modify the electronic parameters within the CuO_2 planes and strongly increase the superexchange coupling J. This enhances the spin pairing effects locally and may explain the observed spatial variations of the density of states and the pairing gap.
We have studied the superexchange interaction $J_{ij}$ in doped $2D$ cuprates. The AFM interaction strongly depends on the state of the lattice of a CuO$_2$ layer surrounded by two LaO rock salt layers. In a static $U$ and $D$ stripe nanostructure, the homogeneous AFM interaction is impossible due to the $U/D/U...$ periodic stripe sequence and $T_N=0$. In a dynamic stripe nanostructure, the ideal CuO$_2$ layer with nonlocal effects and the homogeneous AFM interaction are restored. However the interaction $J_{ij}$ decreases by the exponential factor due to partial dynamic quenching. The meaning…
We present ab initio calculations of the superexchange antiferromagnetic spin coupling $J$ for two cuprates, Sr$_2$CuO$_3$ and La$_2$CuO$_4$. Good agreement with experimental estimates is obtained. We find that $J$ increases substantially as the distance between Cu and apical O is increased. There is an important synergetic effect of the Coulomb interaction, expanding the Cu $3d$ orbital when an electron hops into this orbital, and the O-Cu hopping, being increased by this orbital expansion (breathing). This is a new ingredient in superexchange models. In a model with a fixed basis, breathing …
We study a multi-orbital Hubbard--Su-Schrieffer-Heeger model for the one-dimensional (1D) corner-shared cuprates in the adiabatic and nonadiabatic limits using the exact diagonalization and determinant quantum Monte Carlo methods. Our results demonstrate that lattice dimerization can be achieved only over a narrow range of couplings slightly below a critical coupling $g_c$ at half-filling. Beyond this critical coupling, the sign of the effective hopping changes, and the lattice becomes unstable. We also examine the model's temperature-dependent uniform magnetic susceptibility and the dynamical…
Scanning tunneling spectroscopy has recently discovered a positive correlation between the magnitude of the superconducting gap and positions of dopant oxygen atoms in Bi-based cuprates. We propose a microscopic mechanism that could be responsible for this effect. In particular, we demonstrate that the dopant-induced spatial variation of the atomic levels always enhances the superexchange interaction.
Extensive Cu-NMR studies on multilayered high-Tc cuprates have deduced the following results;(1) Antiferromagnetic (AFM) moment M_{AFM} is decreased with doping, regardless of the number of CuO_2 layers n, and collapses around a carrier density N_h = 0.17. (2) The AFM ordering temperature is enhanced as the out-of-plane coupling J_{out} increases with increasing n. (3) The in-plane superexchange J_{in} is invariant with doping, but is even increased. (4) The dome shape of T_c from the underdoped to the overdoped regime with a maximum T_c at N_h = 0.22 does not depend on n, but its maximum valu…
Resonating valence bond states in a doped Mott insulator was proposed to explain superconductivity in cuprates in January 1987 by Anderson. A challenging task then was proving existence of this unconventional mechanism and a wealth of possibilities, with a rigor acceptable in standard condensed matter physics, in a microscopic theory and develop suitable many body techniques. Shortly, a paper by Anderson, Zou and us (BZA) undertook this task and initiated a program. Three key papers that followed, shortly, essentially completed the program, as far as superconductivity is concerned: i) a gauge …
In view of the continuous theoretical efforts aimed at an accurate microscopic description of the strongly correlated transition metal oxides and related materials, we show that with continuum quantum Monte Carlo (QMC) calculations it is possible to obtain the value of the spin superexchange coupling constant of a copper oxide in a quantitatively excellent agreement with experiment. The variational nature of the QMC total energy allows us to identify the best trial wave function out of the available pool of wave functions, which makes the approach essentially free from adjustable parameters an…
We use scanning tunneling microscopy to visualize the atomic-scale electronic states induced by a pair of hole dopants in Ca2CuO2Cl2 parent Mott insulator of cuprates. We find that when the two dopants approach each other, the transfer of spectral weight from high energy Hubbard band to low energy in-gap state creates a broad peak and nearly V-shaped gap around the Fermi level. The peak position shows a sudden drop at distance around 4 a0 and then remains almost constant. The in-gap states exhibit peculiar spatial distributions depending on the configuration of the two dopants relative to the …
The discovery of superconductivity in a $d^{9-δ}$ nickelate has inspired disparate theoretical perspectives regarding the essential physics of this class of materials. A key issue is the magnitude of the magnetic superexchange, which relates to whether cuprate-like high-temperature nickelate superconductivity could be realized. We address this question using Ni L-edge and O K-edge spectroscopy of the reduced trilayer nickelate $d^{9-1/3}$ La4Ni3O8 and associated theoretical modeling. A magnon energy scale of ~80 meV resulting from a nearest-neighbor magnetic exchange of $J = 69(4)4$ meV is obs…
A compact expression has been obtained for the superexchange coupling of magnetic ions via intermediate anions with regard to polaron effects at both magnetic ions and intermediate anions. This expression is used to analyze the main features of the behavior of isotope shifts for temperatures of three types in layered cuprates: the Neel temperatures ($T_N$), critical temperatures of transitions to a superconducting state ($T_C$), and characteristic temperatures of the pseudogap in the normal state ($T^*$).
The nanometer scale lattice deformation brought about by the dopants in high temperature superconducting cuprate La$_{2-x}$Sr$_x$CuO$_4$(x=0.08) was investigated by measuring the associated X-ray diffuse scattering around multiple Bragg peaks. A characteristic diffuse scattering pattern was observed, which can be well described by continuum elastic theory. With the fitted dipole force parameters, the acoustic type lattice deformation pattern was re-constructed and found to be of similar size to lattice thermal vibration at 7 K. Our results address the long-term concern of dopant introduced loc…
Superconducting transition temperature is calculated for differently doped bilayer cuprates. Superexchange is assumed to be the dominating mechanism of high-temperature superconductivity, but the contribution from the phonon potential is not negligible, which qualitatively explains the observed weak isotopic effect. The calculated value 2$Δ_{max}/k_B T_C \simeq 4.5$ is close to the experiment in the case of optimum doping.
We address the question of whether the superconducting transition temperature (Tc) of high-Tc cuprates is enhanced when randomly distributed dopant atoms form an ordered array in the charge reservoir layers. This study is possible for the Sr2CuO3+d superconductor with K2NiF4-type structure in which oxygen atoms only partially occupy the apical sites next to the CuO2 planes and act as hole-dopants. We show that remarkable Tc enhancement up to 95K in this mono CuO2 layered HTS is associated with the apical oxygen ordering, not to the hole concentration change. The result points a route toward fu…
A simple model is proposed as a possible explanation for the checkerboard pattern of modulations in the hole density observed in recent tunneling experiments on underdoped cuprates. Two assumptions are made; first, an enhanced hole density near the acceptor dopants and secondly short range correlations in the positions of these dopants caused by their electrostatic and anisotropic elastic interactions. Together these can lead to a structure factor in qualitative agreement with experiment.
We present an investigation of charge-compensated antiferromagnetic (Ca$_{x}$La$_{1-x}$)(Ba$_{1.75-x}$La$_{0.25+x}$)Cu$_{3}$O$_{y}$ single crystals using Raman scattering as well as muon spin rotation. In this system the parameter $x$ controls the Cu-O-Cu superexchange interaction via bond distances and buckling angles. The oxygen content $y$ controls the charge doping. In the absence of doping the two-magnon peak position is directly proportional to the superexchange strength $J$. We find that both $x$ and $y$ affect the peak position considerably. The Néel temperature determined from muon sp…
We analyze the hole doping mechanism in Bi_2Sr_{2-x}La_xCuO_{6+δ} (BSLCO). The singular optimum around x=0.35 is found to be connected with a feedback between the doped CuO_2 layers and its dopant reactant [La^{3+}/Bi^{3+}-O_δ] locking the number of doped holes preferentially on to the universal optimum n_opt=0.16.
The strong electron correlation in the cuprates can lead to an enhanced effective mass for both bosonic and fermionic quasiparticles. Where this correlation is characterized by a length that is inversely proportional to the effective temperature, the thermal wavelength for the bosonic quasiparticles becomes essentially independent of temperature. Applying this concept to a preformed pair model, such as the (Cu)13 cluster model, gives Tc vs dopant curves and superconducting gaps in good agreement with experiment. In addition, a correlation-enhanced effective mass provides a natural explanation …
On the basis of the Hubbard model, we extend the fluctuation-exchange (FLEX) approach to investigating the properties of antiferromagnetic (AF) phase in electron-doped cuprate superconductors. Furthermore, by incorporating the effect of scatterings due to the disordered dopant-atoms into the FLEX formalism, our numerical results show that the antiferromagnetic transition temperature, the onset temperature of pseudogap due to spin fluctuations, the spectral density of the single particle near the Fermi surface, and the staggered magnetization in the AF phase as a function of electron doping can…
We present a microscopic model for `electron doped' $Nd_{2-x}Ce_xCuO_4$ family and offer a resolution to a long standing doping asymmetry puzzle. Here, i) Ce atoms do not dope free electrons, instead a Ce atom effectively quenches a $Cu^{2+}$ spin moment at an adjacent site, at an energy scale > superexchange J of $CuO_2$ plane and `site dilutes' the Mott insulator. ii) Effective chemical pressure, caused by increased Ce substitution, induces a {\em first order Mott insulator to superconductor transition} in the $CuO_2$ plane. We predict, i) {\em equal number of +e and -e carriers} in metallic…
Many theoretical models of high temperature superconductivity focus only on the doping dependence of the CuO2 plane electronic structure. But such models are manifestly insufficient to explain the strong variations in superconducting critical temperature Tc among cuprates which have identical hole-density but are crystallographically different outside the CuO2 plane. A key challenge, therefore, has been to identify a predominant out-of-plane influence controlling the superconductivity - with much attention focusing on the distance $d_A$ between the apical oxygen and the planar copper atom. Her…
We propose a model for high-Tc superconductors that includes both the spin fluctuations of the Cu++ magnetic ions and of the spins of O-- doped holes (spinons). The charge of the dopants (holons) is associated to quantum skyrmion excitations of the Cu++ spin background. The quantum skyrmion effective interaction potential is evaluated as a function of doping and temperature, indicating that Cooper pair formation is determined by the competition between these two types of spin fluctuations. The superconducting transition occurs when the effective potential allows for skyrmion bound states. Our …
We show that the low-energy fluctuations of the valence bond in underdoped high-T_c cuprates, originating from quantum fluctuations of the superexchange interaction, are pinned by the electronic disorder due to off-stoichiometric dopants, leading to a valence bond glass (VBG) pseudogap phase. The antinodal Fermi surface sections are gapped out, giving rise to a normal state Fermi arc whose length shrinks with underdoping. Below T_c, the superexchange interaction induces a d-wave superconducting gap that coexists with the VBG pseudogap. The evolution of the local and momentum-space spectroscopy…
The magnetic anisotropy af a rectangular Cu-O-Cu bond is investigated in second order of the spin-orbit interaction. Such a bond is characteristic for cuprates having edge sharing CuO_2 chains, and exists also in the Cu_3O_4 plane or in ladder compounds. For a ferromagnetic coupling between the copper spins an easy axis is found perpendicular to the copper oxygen plaquettes in agreement with the experimental spin structure of Li_2CuO_2. In addition, a pseudo-dipolar interaction is derived. Its estimation in the case of the Cu_3O_4 plane (which is present for instance in Ba_2Cu_3O_4Cl_2 or Sr_2…
It is proved that the ground state under the supreme single-site approximation (S^3A), the dynamical mean-field theory (DMFT), or the dynamical coherent potential approximation (DCPA) is the normal Fermi liquid in the presence of an infinitesimally weak hybridization with an electron reservoir, except for the just half filling of electrons and the infinite on-site repulsion. In the strong-coupling regime, in particular, the Fermi liquid is stabilized under S^3A, DMFT, or DCPA by the Kondo effect, which stabilizes a local singlet on each unit cell, and is further stabilized beyond it by the Foc…
A strong electron-phonon interaction arises from the modulation of the superexchange interaction by phonons. As is studied in Phys. Rev. B 70, 184514 (2004), Cu-O bond stretching modes can be soft around (pm pi/a, 0) and (0, pm pi/a), with a the lattice constant of CuO_2 planes. In the critical region of SDW, where antiferromagnetic spin fluctuations are developed around nesting wave numbers Q of the Fermi surface, the stretching modes can also be soft around 2Q. Almost symmetric energy dependences of the 2Q component of the density of states, which are observed in the so called stripe and che…
We study the zero-point and thermal ionic motion in La$_2$CuO$_4$ by means of high-resolution neutron diffraction experiments. Our results demonstrate anisotropic motion of O and to a lesser extent of Cu ions, both consistent with the structure of coupled CuO$_6$ octahedra, and quantify the relative effects of zero-point and thermal contributions to ionic motion. By substitution of $^{18}$O, we find that the oxygen isotope effect on the lattice dimensions is small and negative ($-0.01\%$), while the isotope effect on the ionic displacement parameters is significant ($-6$ to $50\%$). We use our…
We present ab-initio calculations of effective magnetic exchange, $J$, as well as Hubbard parameters ($t$, $U$ and $δ\varepsilon$) as a function of the local distribution of doping atoms for the high-$T_c$ superconducting $\rm (Ca_xLa_{1-x})(Ba_{1.75-x}La_{0.25+x})Cu_3O_y$ family. We found that both the exchange and the energies of the magnetic orbitals are strongly dependant on the local dopant distribution, both through the induced modification of the apical oxygen location and of the induced local electrostatic potential. The $J$ real-space map, for a random distribution of dopants, positiv…
Using model calculations of a disordered d-wave superconductor with on-site Hubbard repulsion, we show how dopant disorder can stabilize novel states with antiferromagnetic order. We find that the critical strength of correlations or impurity potential necessary to create an ordered magnetic state in the presence of finite disorder is reduced compared to that required to create a single isolated magnetic droplet. This may explain why in cuprates like LSCO low-energy probes have identified a static magnetic component which persists well into the superconducting state, whereas in cleaner systems…
It has gone almost unquestioned that superexchange in the t-J (or Hubbard) model, and not phonons, is responsible for the unconventional ("d-wave") pairing symmetry of cuprate superconductors. However a number of advanced numerical studies have not found superconductivity in the Hubbard model. On the other hand compelling experimental evidence for a strong electron-phonon interaction (EPI) has currently arrived. Here I briefly review some phonon-mediated unconventional pairing mechanisms. In particular the anisotropy of sound velocity makes the phonon-mediated attraction of electrons non-local…
One of the major puzzles regarding unconventional superconductivity is how some of the most interesting superconductors are related to an insulating phase that lies in close proximity. Here we report scanning tunneling microscopy studies of the local electronic structure of Cu doped NaFeAs across the superconductor to insulator transition. We find that in the highly insulating regime the electronic spectrum develops an energy gap with diminishing density of state at the Fermi level. The overall lineshape and strong spatial variations of the spectra are strikingly similar to that of lightly dop…
A theory of Kondo lattices is applied to the crossover between local-moment magnetism and itinerant-electron magnetism in the t-J model on a quasi-two dimensional lattice. The Kondo temperature T_K is defined as a characteristic temperature or energy scale of local quantum spin fluctuations. Magnetism with T_N >> T_K, where T_N is the N\eel temperature, is characterized as local-moment one, while magnetism with T_N << T_K is characterized as itinerant-electron one. The Kondo temperature, which also gives a measure of the strength of the quenching of magnetic moments, is renormalized by the Foc…
I discuss here some well established experimental facts which have been shown to be generic of the pseudogap in underdoped cuprates. Some recent developments on Cellular Dynamic Mean Field Theories of the doped Hubbard model on a square lattice are nowadays allowing one to compute physical properties and k resolved single particle spectra. At high temperatures, recent results present qualitative features which perfectly fit the experimental observations done for more than two decades on the pseudogap in the cuprates. Most various broken symmetry states detected recently at lower temperatures t…
On the basis of the Hubbard model, we present the formulation of antiferromagnetism in electron-doped cuprates using the fluctuation-exchange approach. Taking into account the spin fluctuations in combination with the impurity scattering effect due to the randomly distributed dopant-atoms, we investigate the magnetic properties of the system. It is shown that the antiferromagnetic transition temperature, the onset temperature of the pseudogap formation, the single particle spectral density, and the staggered magnetization obtained by the present approach are in very good agreement with the exp…
We argue that recent measurements on both the superfluid density and the optical conductivity of high-quality LSCO films can be understood almost entirely within the theory of disordered BCS d-wave superconductors. The large scattering rates deduced from experiments are shown to arise predominantly from weak scatterers, probably the Sr dopants out of the CuO$_2$ plane, and correspond to significant suppression of $T_c$ relative to a pure reference state with the same doping. Our results confirm the "conventional" viewpoint that the overdoped side of the cuprate phase diagram can be viewed as a…
We study disorder-induced magnetism within the Gutzwiller approximation applied to the t-J model relevant for cuprate superconductors. In particular, we show how disorder generates magnetic phases by inducing local droplets of antiferromagnetic order which eventually merge, and form a quasi-long range ordered state in the underdoped regime. We identify two distinct disorder-induced magnetic phases of this type depending on the strength of the scatterers. For weak potential scatterers used to model dopant disorder, charge reorganization may push local regions in-between the impurities across th…
We model the underdoped cuprates using fermions moving in a background with local antiferromagnetic order. The antiferromagnetic order fluctuates in orientation, but not in magnitude, so that there is no long-range antiferromagnetism, but a 'topological' order survives. The normal state is described as a fractionalized Fermi liquid (FL*), with electron-like quasiparticles coupled to the fractionalized excitations of the fluctuating antiferromagnet. The electronic quasiparticles reside near pocket Fermi surfaces enclosing total area x (the dopant density), centered away from the magnetic Brillo…
Taking the spin-fermion model as the starting point for describing the cuprate superconductors, we obtain an effective nonlinear sigma-field hamiltonian, which takes into account the effect of doping in the system. We obtain an expression for the spin-wave velocity as a function of the chemical potential. For appropriate values of the parameters we determine the antiferromagnetic phase diagram for the YBa$_2$Cu$_3$O$_{6+x}$ compound as a function of the dopant concentration in good agreement with the experimental data. Furthermore, our approach provides a unified description for the phase diag…
We use a renormalized mean field theory to investigate the superconducting properties of underdoped cuprates embedded with overdoped or metallic regions that carry excess dopants. The overdoped regions are considered, within two different models, first as stripes of mesoscopic size larger than the coherence length and then as point impurities. In the former case we compute the temperature dependent superfluid stiffness by solving Bogoliubov de Gennes equations within the slave boson mean field theory. We average over stripes of different orientations to obtain an isotropic result. To compute t…
The strong coupling effect in the (2+1)-dimensional quantum electrodynamics (QED_3) description of the $S=1/2$ Heisenberg antiferromagnet is studied in terms of a canonical transformation which has been used in the small polaron theory in electron-phonon systems. In the N{\' e}el ordered phase, we show that the Dirac fermions are localized and the spectral function is of the Gaussian form due to the coupling to the longitudinal gauge field. The width of the broad line shape is \sim 4J with J the superexchange interaction energy and the localization length is sim 3a, with a the lattice constant…
Electron correlation effects are particularly strong in the high temperature superconducting materials. Devising an accurate description of these materials has long been a challenge, with these strong correlation effects historically being considered impossible or impractical to simulate computationally. Using quantum Monte Carlo techniques, we have explicitly simulated electron correlations in several cuprate materials from first principles. These simulations accurately reproduce many important physical quantities about these materials, including the interaction-induced gap and the superexcha…
Cuprate superconductors have many different atoms per unit cell. A large fraction of cells (5-25%) must be modified ("doped") before the material superconducts. Thus it is not surprising that there is little consensus on the superconducting mechanism, despite almost 200,000 papers. Most astonishing is that for the simplest electrical property, the resistance, "despite sustained theoretical efforts over the past two decades, its origin and its relation to the superconducting mechanism remain a profound, unsolved mystery." Currently, model parameters used to fit normal state properties are exper…
The antiferromagnetic insulating cuprate Ba$_3$Cu$_2$O$_4$Cl$_2$ contains folded CuO$_2$ chains with four magnetic copper ions ($S=1/2$) per unit cell. An underlying multiorbital Hubbard model is formulated and the superexchange theory is developed to derive an effective spin Hamiltonian for this cuprate. The resulting spin Hamiltonian involves a Dzyaloshinskii-Moriya term and a more weak symmetric anisotropic exchange term besides the isotropic exchange interaction. The corresponding Dzyaloshinskii-Moriya vectors of each magnetic Cu-Cu bond in the chain reveal a well defined spatial order. Bo…
Identifying the essence of doped Mott insulators is one of the major outstanding problems in condensed matter physics and the key to understanding the high-temperature superconductivity in cuprates. We report real space visualization of Mott transition in Sr1-xLaxCuO2+y cuprate films that cover the entire electron- and hole-doped regimes. Tunneling conductance measurements directly on the cooper-oxide (CuO2) planes reveal a systematic shift in the Fermi level, while the fundamental Mott-Hubbard band structure remains unchanged. This is further demonstrated by exploring atomic-scale electronic …
The role of Coulomb disorder, either of extrinsic origin or introduced by dopant ions in undoped and lightly-doped cuprates, is studied. We demonstrate that charged surface defects in an insulator lead to a Gaussian broadening of the Angle-Resolved Photoemisson Spectroscopy (ARPES) lines. The effect is due to the long-range nature of the Coulomb interaction. A tiny surface concentration of defects about a fraction of one per cent is sufficient to explain the line broadening observed in Sr$_2$CuO$_2$Cl$_2$, La$_2$CuO$_{4}$, and Ca$_{2}$CuO$_{2}$Cl$_{2}$. Due to the Coulomb screening, the ARPES …
The elementary CuO2 plane sustaining cuprate high-temperature superconductivity occurs typically at the base of a periodic array of edge-sharing CuO5 pyramids. Virtual transitions of electrons between adjacent planar Cu and O atoms, occurring at a rate $t/{\hbar}$ and across the charge-transfer energy gap E, generate 'superexchange' spin-spin interactions of energy $J\approx4t^4/E^3$ in an antiferromagnetic correlated-insulator state. However, Hole doping the CuO2 plane converts this into a very high temperature superconducting state whose electron-pairing is exceptional. A leading proposal fo…
