Behaviour of superconductivity energetic characteristics in electron-doped cuprates. A simple model

A simple model to describe the energetic phase diagram of electron-doped cuprate superconductor is developed. Interband pairing operates between the UHB and the defect states created by doping and supplied by both extincting HB-s. Two defect subbands correspond to the (π,0) and (π/2,π/2) momentum regions. Extended doping quenches the bare normal state gaps (pseudogaps). Maximal transition temperature corresponds to overlapping bands ensemble intersected by the chemical potential. Illustrative results for Tc, pseudo- and superconducting gaps are calculated on the whole doping scale. Major characteristic features on the phase diagram are reproduced. Anticipated manifestation of gaps doping dynamics is discussed.     

Effects of competing orders and quantum phase fluctuations on the low-energy excitations and pseudogap phenomena of cuprate superconductors

We investigate the low-energy quasiparticle excitation spectra of cuprate superconductors by incorporating both superconductivity (SC) and competing orders (CO) in the bare Green’s function and quantum phase fluctuations in the proper self-energy. Our approach provides consistent explanations for various empirical observations, including the excess subgap quasiparticle density of states, “dichotomy” in the momentum-dependent quasiparticle coherence and the temperature-dependent gap evolution, and the presence (absence) of the low-energy pseudogap in hole- (electron-) type cuprates depending on the relative scale of the CO and SC energy gaps.     

Electron-phonon coupling constant of cuprate based high temperature superconductors

The electron-phonon coupling constant in two-dimensional cuprate high temperature superconductors has been determined by the ultrasonic method. The electron-phonon coupling constant in the Van Hove scenario was found to increase with transition temperature T_c. is in the range of 0.025-0.060 which is 10-100 times smaller than the conventional three-dimensional Bardeen-Cooper-Schrieffer coupling constant. The characteristic Debye temperature θ_D does not correlate with T_c. These findings show that the interplay between the Debye frequency and electron-phonon coupling in the two-dimensional system and their variations have a combined effect in governing the transition temperature.     

Momentum dependence of quasiparticle spectrum and Bogoliubov angle in cuprate superconductors

The momentum dependence of the low energy quasiparticle spectrum and the related Bogoliubov angle in cuprate superconductors are studied within the kinetic energy driven superconducting mechanism. By calculation of the ratio of the low energy quasiparticle spectra at positive and negative energies, it is shown that the Bogoliubov angle increases monotonically across the Fermi crossing point. The results also show that the superconducting coherence of the low energy quasiparticle peak is well described by a simple d-wave Bardeen-Cooper-Schrieffer formalism, although the pairing mechanism is driven by the kinetic energy by exchanging spin excitations.     

The mysterious pseudogap in high temperature superconductors: an infrared view

We review the contribution of infrared spectroscopy to the study of the pseudogap in high temperature superconductors. The pseudogap appears as a depression of the frequency dependent conductivity in the c-axis direction and seems to be related to a real gap in the density of states. It can also be seen in the Knight shift, photoemission and tunneling experiments. In underdoped samples it appears near room temperature and does not close with temperature. Another related phenomenon that has been studied by infrared is the depression in the ab-plane scattering rate. Two separate effects can be discerned. At high temperatures there is broad depression of scattering below 1000 cm⁻¹ which may be related to the gap in the density of states. At a lower temperature a sharper structure is seen, which appears to be associated with scattering from a mode at 300 cm⁻¹, and which governs the carrier life time at low temperatures. This mode shows up in a number of other experiments, as a kink in angle resolved photoemission dispersion, and a resonance at 41 meV in magnetic neutron scattering. Since the infrared technique can be used on a wide range of samples it has provided evidence that the scattering mode is present in all high temperature cuprates and that its frequency in optimally doped materials scales with the superconducting transition temperature. The lanthanum and neodymium based cuprates do not follow this scaling and appear to have depressed transition temperatures.     

Possible propagation of the Zhang-Rice singlet as a probable Cooper channel in the CuO2 planes

The issue of how superconductivity originate in the CuO₂ planes believed to be crucial to understanding the high Tc superconducting cuprates is still an going debate. In the wake of recent experimental observations of the Zhang-Rice singlet (ZRS), its formation and propagation need to be revisited especially by using a simple approach almost at a phenomenological level. Within a highly simplified correlated variational approach (HSCVA) in this Letter, a new formation of the ZRS as constituting the ground state of a single-band t-J model of the CuO₂ planes is developed. This formation is then used to demonstrate how the ZRS can be propagated as a probable Cooper channel in the CuO₂ planes.     

Anisotropy of infrared optical absorption in layered superconductors

We analyze the problem of infrared optical absorption in a clean layered London superconductor in the vicinity of the gap =2. We conclude that absorption of light with wave vectorqc is enhanced over ordinary Drude absorption (qc) due to resonance absorption (Landau damping). Experimental absorption studies with qc might therefore improve chances to observe a superconducting gap in the high-T _c superconductors.     

Magnetic field induced incommensurate resonance in cuprate superconductors

The influence of a uniform external magnetic field on the dynamical spin response of cuprate superconductors in the superconducting state is studied based on the kinetic energy driven superconducting mechanism. It is shown that the magnetic scattering around low and intermediate energies is dramatically changed with a modest external magnetic field. With increasing the external magnetic field, although the incommensurate magnetic scattering from both low and high energies is rather robust, the commensurate magnetic resonance scattering peak is broadened. The part of the spin excitation dispersion seems to be an hourglass-like dispersion, which breaks down at the heavily low energy regime. The theory also predicts that the commensurate resonance scattering at zero external magnetic field is induced into the incommensurate resonance scattering by applying an external magnetic field large enough.     

On the thermodynamic stability of odd-frequency superconductors

The thermodynamic stability of odd-frequency pairing states is investigated within an Eliashberg-type framework. We find the rigorous result that in the weak coupling limit a continuous transition from the normal state to a spatially homogeneous odd-in-ω superconducting state is forbidden, irrespective of details of the pairing interaction and of the spin symmetry of the gap function. For isotropic systems, it is shown that the inclusion of strong coupling corrections does not invalidate this result. We discuss a few scenarios that might escape these thermodynamic constraints and permit stable odd-frequency pairing states.     

Evolution of spin dynamics in electron-doped cuprate superconductors

Within the kinetic energy driven superconducting mechanism, the evolution of the magnetic excitations of the electron-doped cuprates in the superconducting state is studied. It is shown that there is a broad commensurate low energy magnetic scattering peak, while the magnetic resonance energy is located among this broad commensurate low energy scattering range. This broad commensurate low energy magnetic scattering disperses outward into a continuous ring-like incommensurate magnetic scattering at high energy.     

Order and quantum phase transitions in the cuprate superconductors

This is a summary of a review article appearing in Reviews of Modern Physics, July 2003. The ground state of the cuprate superconductors is described using the paradigm of competing orders. This approach has led to numerous predictions, some of which have been tested in recent nanoscale experiments.     

Antiferromagnetism and superconductivity in a model with extended pairing interactions

The competition between antiferromagnetism and the d + id superconducting state is studied in a model with near and next near neighbour interactions in the absence of any on-site repulsion. A mean field study shows that it is possible to have simultaneous occurrence of an antiferromagnetic and a singlet d + id superconducting state in this model. In addition, such a coexistence generates a triplet d + id superconducting order parameter with centre of mass momentum Q = (π,π) dynamically having the same orbital symmetry as the singlet superconductor. Inclusion of next nearest neighbour hopping in the band stabilises the d_xy superconducting state away from half filling, the topology of the phase diagram, though, remains similar to the near neighbour model. In view of the very recent observation of a broad region of coexistence of antiferromagnetic and unconventional superconducting states in organic superconductors, the possibility of observation of the triplet state has been outlined. Received 30 November 2000 and Received in final form 27 March 2001     

Origin and doping dependence of the photoemission pseudogap in Cu oxides

A recent report on ARPES on insulating , compared to previous data from and Dy-doped , sheds new light on the origin of the anisotropic pseudogap observed in the normal state of underdoped cuprate oxides. The energy dispersion of the insulator is attributed to strong AF correlations enhanced by the diagonal hopping between magnetic sites, which is progressively deformed by the possibility of nearest neighbour hopping, that increases with hole doping. Received 9 April 1999     

Mechanism of Pseudogap Detected by Electronic Raman Scattering： Phase Fluctuation or Hidden Order？

We study the electronic Raman scattering in the cuprates to distinguish the two possible scenarios of the pseudogap normal state. In one scenario, the pseudogap is assumed to be caused by phase fluctuations of the preformed Cooper pairs. We find that pair-breaking peaks appear in both the B1g and B2g Raman channels, and they axe smeared and tend to shift to the same energy with the increasing strength of phase fluctuations. Thus both channels reflect the same pairing energy scale, irrespectively of the doping level. In another scenario, the pseudogap is assumed to be caused by a hidden order that competes with the superconducting order. As an example, we assume that the hidden order is the d-density-wave （DDW） order. We find analytically and numerically that in the DDW normal state there is no Raman peak in the B2g channel in a tight-binding model up to the second nearest-neighbor hopping, while the Raman peak in the Big channel reflects the energy gap caused by the DDW order. This behavior is in agreement with experiments in the pseudogap normal state. To gain further insights, we also calculate the Raman spectra in the DDW＋SC state. We study the doping and temperature dependence of the peak energy in both channels and find a two-gap behavior, which is in agreement with recent Raman experiments. Therefore, our results shed light on the hidden order scenario for the pseudogap.     

On the phase diagrams of the ferromagnetic superconductors UGe2 and ZrZn2

A general phenomenological theory is presented for the phase behavior of ferromagnetic superconductors with spin-triplet electron Cooper pairing. The theory accounts in detail for the temperature-pressure phase diagram of ZrZn₂, while the main features of the diagram for UGe₂ are also described. Quantitative criteria are deduced for the U-type (type I) and Zr-type (type II) unconventional ferromagnetic superconductors with spin-triplet Cooper electron pairing. Some basic properties of quantum phase transitions are also elucidated.     

Checkerboard patterns and magnetic resonance peak in cuprate superconductors

We investigate a kind of spin-Peierls transition (SP) in high T_c superconductivity. It is found the antiferromagnetic exchange integral of SP corresponds to the magnetic resonance peak. The kind of spin-Peierls transition applied to cuprate superconductors is that without dimerization of lattice ions and with dimerization of localized hole h_Cu attached to the ion. Absence of the magnetic resonance peak in La-Sr-Cu-O results from the dimerized state of localized hole, h_Cu below T_c into tetramerized phase above T_c in SP transition without dimerization of copper-ion. The checkerboard patterns with four unit cell period originate from the SP of electronic part without ion-dimerization and from charge occupation probability of oxygen-atom around Cu.     

Effect of Mn substitution on the delicate balance between structure and properties of Gd1.4Ce0.6Sr2RuCu2O10

Some new members of a ruthenocuprate(2212) series have been synthesized by Mn substitution for Ru in Gd_1.4Ce_0.6Sr₂RuCu₂O₁₀. Characterization by x-ray diffraction (XRD) phase analysis has been carried out. Changes in structural features on substitution, including a significant change in lattice parameter for a very low substitution level, have been observed. Four-probe resistivity studies indicate the coexistence of superconductivity and magnetism for the pristine compound and a semiconductor-like upturn in resistivity and the absence of superconductivity even for very low levels of Mn substitution. AC susceptibility measurements show a progressive suppression of the magnetic transition temperature as well as a smearing of the magnetic transition as a function of Mn substitution. Possible reasons for the absence of superconductivity have been discussed.     

Interplay between superconductivity and pseudogap state in bilayer cuprate superconductors

The interplay between the superconducting gap and normal-state pseudogap in the bilayer cuprate superconductors is studied based on the kinetic energy driven superconducting mechanism. It is shown that the charge carrier interaction directly from the interlayer coherent hopping in the kinetic energy by exchanging spin excitations does not provide the contribution to the normal-state pseudogap in the particle–hole channel and superconducting gap in the particle–particle channel, while only the charge carrier interaction directly from the intralayer hopping in the kinetic energy by exchanging spin excitations induces the normal-state pseudogap in the particle–hole channel and superconducting gap in the particle–particle channel, and then the two-gap behavior is a universal feature for the single layer and bilayer cuprate superconductors.     

Universal scaling in BCS superconductivity in three dimensions in non-s waves

The solutions of a renormalized BCS equation are studied in three space dimensions in s, p and d waves for finite-range separable potentials in the weak to medium coupling region. In the weak-coupling limit, the present BCS model yields a small coherence length and a large critical temperature, , appropriate for some high- materials. The BCS gap, , and specific heat as a function of zero-temperature condensation energy are found to exhibit potential-independent universal scalings. The entropy, specific heat, spin susceptibility and penetration depth as a function of temperature exhibit universal scaling below in p and d waves. Received: 18 July 1997 / Revised: 8 September 1997 / Accepted: 29 September 1997