Dispersion of quasi-particles in high Tc cuprates

The interplay between superconductivity (SC) and antiferromagnetism (AFM) is studied in strongly correlated systems of high T _c Cuprate superconductors. It is assumed that superconductivity arises due to BCS pairing mechanism in presence of AFM in Cu lattices of Cu-O planes. The total Hamiltonian of the system is mean field one and has been solved exactly by writing the equations of motion for the single particle Green’s functions. Equations for the appropriate single particle co-relation functions are derived and the order parameters corresponding to SC and AFM are determined. It is assumed that the Fermi energy ∈ _F = 0 and the renormalized localized f energy level coincide with the Fermi level. All the quantities in the final equation for h and Δ are made dimensionless by dividing by 2t, where t is the hopping integral. The temperature dependent values of staggered magnetic field (h) and SC gap (Δ) were determined by solving self-consistent equations for h and Δ. The quasiparticle energy bands are function of AFM gap (h), SC gap (Δ) and hybridization (V). Then the dispersion of quasi-particles are studied at different temperatures by considering temperature dependent values of h and Δ and varying other different model parameters.      

Triplet <Emphasis Type="Italic">p</Emphasis>-wave superconductivity in the low-density extended hubbard model with Coulomb repulsion

We analyze superconducting instabilities in 3D and 2D extended Hubbard model with Coulomb repulsion between electrons on neighboring sites in the limit of low electron density (n _el → 0) on simple cubic (square) lattice. We show that in a realistic strong-coupling case U ≫ V ≫ W (U and V are the onsite and the intersite Coulomb repulsions, respectively, and W the bandwidth) the main SC instability corresponds to the p-wave pairing and in the leading order is correctly described by the equations obtained earlier in the absence of the intersite Coulomb interaction V = 0.     

Effect of hybridization and dispersion of quasiparticles on the coexistent state of superconductivity and antiferromagnetism in <Emphasis Type="Italic">R</Emphasis>Ni<Subscript>2</Subscript>B<Subscript>2</Subscript>C

The effect of hybridization of conduction electrons and f-level on superconductivity (SC) and antiferromagnetism (AFM) in the coexistent phase of rare-earth nickel borocarbide superconductors (RNi₂B₂C) is reported. The Hamiltonian of the system is a mean field one and has been solved by writing equations of motion for the single-particle Green functions. It is assumed that superconductivity arises due to BCS pairing mechanism in the presence of antiferromagnetism in nickel lattices of Ni₂B₂ plane. The expressions for superconducting and antiferromagnetic order parameters are derived using double time electron Green functions. The quasiparticle energy bands are plotted and the nature of band dispersion of the quasiparticles is studied.     

Phase diagram of superconductivity and antiferromagnetism in high-Tc hole-doped cuprates

A phase diagram of superconductivity (SC) and antiferromagnetism (AFM) for hole-doped cuprate superconductors in presence of chemical potential (μ) by using a model Hamiltonian is reported here. The Hamiltonian of the system is a mean field one and has been solved by writing equations of motion for the single particle Green functions. The expressions for appropriate single particle correlation function are derived. It is assumed that SC arises due to BCS pairing mechanism and AFM order is simulated by staggered magnetic field in lattices of Cu–O planes. The expressions for SC order parameter, AFM order parameter and dopant concentration are calculated analytically by using Green function technique of D.N. Zubarev. The value of SC gap (z), AFM gap (h) and chemical potential (μ) are solved self consistently for different dopant concentrations (x) by changing model parameters. It is found that a disordered phase appears after antiferromagnetism is destroyed in the range of very small doping. On further increase of the doping, the SC critical temperature first increases, attains a maximum value (?39 K) and then decreases which agrees well with experimental observations for hole-doped cuprates. Our theoretical findings suggest that the AFM coupling plays the vital role of the glue for the Cooper pairs.     

Theory of high temperature superconductivity in YBa2Cu3O7_δ

A theory of high temperature superconductivity in YBa₂Cu₃O₇__δ compound has been developed on the basis of the momentum pairing of electrons through the relativistic Darwin interaction. The transport behaviour of electrons is explained in terms of a mechanism of correlated electron transfer arising from the electron-phonon coupling. A model Hamiltonian has been developed to describe the superconducting properties of the system. This gives an energy gap which is higher than the BCS value. Attempts have been made to explain the absence of isotope effect, the linear dependence of specific heat, the presence of larger temperature-independent paramagnetism in the normal phase and the softening of some of the optic phonon modes observed in this system.     

Impact of eigenvalues on the pseudopotential calculation of superconducting parameters of metals Ga, Cd and In

In the present paper some superconducting (SC) state parameters of metals Ga, Cd and In have been studied through Harrison’s First Principle [HFP] pseudopotential technique using McMillan’s formalism. The impact of choosing two different sets of core energy eigenvalues viz. Herman-Skillman and Clementi (or Experimental) has been studied. It has been observed that the choice of eigenvalues has appreciable impact on the form factor and consequently on the SC state transition parameter viz. electron-phonon coupling strength (λ) and superconducting transition temperature T _c . Hence the choice of suitable eigenvalues is essential for these computations. Reasonable agreement with experimental and theoretical data have been obtained.     

Self-Organized Forest-Fires Near the Critical Time

We consider a forest-fire model which, somewhat informally, is described as follows: Each site (vertex) of the square lattice is either vacant or occupied by a tree. Vacant sites become occupied at rate 1. Further, each site is hit by lightning at rate λ. This lightning instantaneously destroys (makes vacant) the occupied cluster of the site.This model is closely related to the Drossel-Schwabl forest-fire model, which has received much attention in the physics literature. The most interesting behaviour seems to occur when the lightning rate goes to zero. In the physics literature it is believed that then the system has so-called self-organized critical behaviour.We let the system start with all sites vacant and study, for positive but small λ, the behaviour near the ‘critical time’ t _c , defined by the relation 1 − exp(− t _c ) = p _c , the critical probability for site percolation.Intuitively one might expect that if, for fixed t > t _c , we let simultaneously λ tend to 0 and m to ∞, the probability that some tree at distance smaller than m from O is burnt before time t goes to 1. However, we show that under a percolation-like assumption (which we can not prove but believe to be true) this intuition is false. We compare with the case where the square lattice is replaced by the directed binary tree, and pose some natural open problems.Part of vdB’s research is supported by BRICKS project AFM 2.2.     

The role of CDW gap on the magnetic phase transition in CMR materials

We propose a model to study the magnetic phase transition in the Colossal-Magneto-Resistance (CMR) material of general type R_1−x A _x MnO₃ (R = La, Sm, Nd; A = Ca, Sr, Ba). The model Hamiltonian consists of a Charge Density Wave (CDW) gap in the e _g -band and the strong magnetic field due to the spin ordering in the localized t _g core electrons. The Hamiltonian is solved by using Zubarev’s Green’s function technique to calculate CDW gap (Δ) and magnetization (M ^d ) in t _2g band. Both of them are solved self-consistently. Their combined effect on the temperature dependent magnetization (M ^c ) due to the e _g band electrons is investigated. Both the magnitude and the transition temperature of (M ^c ) are strongly influenced by both Δ and M ^d . Hence the hopping of the band electrons are strongly controlled by these two long range interactions. The results are discussed by varying the model parameters of the manganite system.      

Superconducting state parameters of CuCZr100-C metallic glasses

The theoretical investigation of the superconducting state parameters (SSP) viz. electron-phonon coupling strength λ, Coulomb pseudopotential μ*, transition temperature T _c, isotope effect exponent α and effective interaction strength N ₀ V of ten Cu _C Zr_100−C metallic glasses have been reported using Ashcroft’s empty core (EMC) model potential. Three local field correction functions proposed by Hartree (H), Taylor (T) and Ichimaru-Utsumi (IU) are used in the current investigation to study the screening influence on the aforesaid properties. It is observed that the electron-phonon coupling strength λ and the transition temperature T _C are quite sensitive to the selection of the local field correction functions, whereas the Coulomb pseudopotential μ*, isotope effect exponent α and effective interaction strength N ₀ V show weak dependences on local field correction functions. The T _c obtained from IU-local field correction function are found an excellent agreement with available theoretical or experimental data. Also, the present results are found in qualitative agreement with other such earlier reported data, which confirms the superconducting phase in metallic glasses.      

Dynamics of the superconducting mixed state in YBa2Cu3O7-δ/PrBa2Cu3O7-δ superlattices in radio frequency regime

Epitaxial multilayers of YBa₂Cu₃O_7-δ and P₁Ba₂Cu₃O_7-δ have been deposited on (100) cut SrTiO₃ substrates using the technique of pulsed laser deposition. Standard ϑ-2ϑ X-ray diffraction measurements on the films showed excellent superlattice reflections. The mixed state of these superlattices has been probed through measurements of radio frequency penetration depth (λ) as a function of temperature (T), magnetic field (H) and it’s orientation (ϑ) with respect to the planes of the superlattices. These data reflect the two-dimensional nature of the mixed state in these systems.     

A Cud-d excitation model for the pairing in the high-T c cuprates

A new model for the pairing mechanism in the ceramic superconductors is presented. Like the magnetic models, we assume the limit of large correlation energies for the Cud electrons. We postulate that the pairing of the Op conduction holes occurs viad–d orbital excitations within thee _g manifold of thed hole of Cu⁺⁺, which is split because of tetragonal or lower symmetry at the Cu sites. This valence conserving charge degree of freedom has been ignored in the magnetic pairing models. Thed–d excitation model may provide a simple qualitative understanding of many experimental results.     

Theory of superconductivity in strongly correlated materials: Application to cuprate superconductors

A microscopic theory of superconductivity in systems with strong electron correlations is considered within the Hubbard model. The Dyson equation for the matrix Green function in terms of the Hubbard operators is derived and solved in the noncrossing approximation for the self-energy. Two channels of superconducting pairing are revealed: mediated by antiferromagnetic (AFM) exchange and spin-fluctuations. It is proved that AFM exchange interaction results in pairing of all electrons in the conduction band and high T _c proportional to the Fermi energy. T _c dependence on lattice constants (or pressure) and an oxygen isotope shift of T _c are explained. The text was submitted by the author in English.     

Effect of free electrons on growth of “cancers” in mixed electronic-ionic conductors

The reasons for the anomalously rapid (for solids) growth of “cancers” (filamentary crystals, hills, pores, and other formations) on the surface of samples of superionic conductors with mixed electronic-ionic conductivity (of the type Cu_2−x Se and Ag₂Te) are discussed. The effects are attributed to the acceleration of mobile ions and activated ions in the “core” of the superionic by free electrons in the joint “chemical” diffusion of ions and electrons in the samples. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 2, 97–100 (25 July 1996)     

Superconducting state parameters of binary metallic glasses

Ashcroft’s empty core (EMC) model potential is used to study the superconducting state parameters (SSPs) viz. electron-phonon coupling strength λ, Coulomb pseudopotential μ*, transition temperature T _C , isotope effect exponent αand effective interaction strength N _O V of some binary metallic glasses based on the superconducting (S), conditional superconducting (S’) and non-superconducting (NS) elements of the periodic table. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used for the first time with EMC potential in the present investigation to study the screening influence on the aforesaid properties. The T _C obtained from the H-local field correction function are in excellent agreement with available theoretical or experimental data. In the present computation, the use of the pseudo-alloy-atom model (PAA) was proposed and found successful. Present work results are in qualitative agreement with such earlier reported experimental values which confirm the superconducting phase in all metallic glasses. A strong dependency of the SSPs of the metallic glasses on the valence ‘Z’ is identified.      

Mass spectrum of elementary particles in a temperature-dependent model

We show that the temperature-generalization of a popular model of quark-confinement seems to provide a rather interesting insight into the origin of mass of elementary particles: as the universe cooled, there was an era when particles did not have an identity since their masses were variable; the temperature at which the conversion of these ‘nomadic’ particles into ‘elementary’ particles took place seems to have been governed by the value of a dimension-less coupling constantC _c. ForC _c=0.001(0.1) this temperature is of the order of 10⁹ K (10¹¹ K), below which the particle masses do not change.     

A unified theory of weak interactions

A gauge model for the weak interactions of the leptons (v _e, e, μ, ν_μ) and the quarks (q _p, q_n,qλ,q _p′) is presented in which deviations from universality, such as the Cabibbo suppression, are explicitly and spontaneously generated. The gauge group is, to begin with SU(4). There are three quartets of Higgs scalars with suitable vacuum expectation values, sufficient and necessary to give masses to all gauge bosons. It turns out that this gauge group is too ‘large’ and fails to account for many observed symmetries of weak interactions, especially electron-muon symmetry. This symmetry corresponds to a discrete transformationR which is an element of SU(4). To accommodate it, the gauge group is restricted to the subgroup of SU(4) which commutes withR. There are now 7 gauge bosons, 4 charged and 3 neutral. One pair of charged bosons is necessarily heavier than the other pair (denotedW ^±) and two neutrals are necessarily heavier than the third (W ⁰). The electron and the muon become massive while the neutrinos and the quark fields remain massless. The dominant charged weak currents coupling toW ^± havee-μ universality and Cabibbo universality for both of whichR-symmetry is essential—the Cabibbo angle is a simple function of the vacuum expectation values. The same symmetry ensurese-μ symmetry and the absence of flavour-changing components in the neutral currents. The currents coupling to the heavier gauge bosons break all these symmetries but these bosons can be made arbitrarily heavy and so are relevant only in the domain of ‘ultraweak’ interactions. The Cabibbo angleϑ _c itself is determined by minimising a very general class of Higgs potentials, leading to a numerical valueϑ _c = ±π/8, | tanϑ _c | = √2 − 1 (an alternative solution | tanϑ _c | = (√2+1) is rejected), independent of the parameters and of the precise form of the potential. This is the ‘bare’ϑ _c; in low energy/momentum transfer processes, this value is renormalised by the structure of the hadrons. A model is given for this renormalisation which reduces the renormalised value of | tanϑ _c | to about 0.2–0.3 from the bare value 0.41. Recent data on highly inelastic neutrino interactions are shown to be not inconsistent with | tanϑ _c | = 0.4.     

GUT precursors and fixed points in higher-dimensional theories

Within the context of traditional logarithmic grand unification atM _GUT ≈ 10¹⁶ GeV, we show that it is nevertheless possible to observe certain GUT states such asX andY gauge bosons at lower scales, perhaps even in the TeV range. We refer to such states as ‘GUT precursors’. Such states offer an interesting alternative possibility for new physics at the TeV scale, even when the scale of gauge coupling unification remains high, and suggest that it may be possible to probe GUT physics directly even within the context of high-scale gauge coupling unification. More generally, our results also suggest that it is possible to construct self-consistent ‘hybrid’ models containing widely separated energy scales, and give rise to a Kaluza-Klein realization of non-trivial fixed points in higher-dimensional gauge theories.     

Superconducting state parameters of La<Subscript>100-<Emphasis Type="Italic">C</Emphasis></Subscript>Ga<Subscript><Emphasis Type="Italic">C</Emphasis></Subscript> binary metallic glasses

The theoretical investigations of the superconducting state parameters (SSP) viz. electron-phonon coupling strength λ, Coulomb pseudopotential μ*, transition temperature T _C , isotope effect exponent α and effective interaction strength N _O V of six binary La_100-C Ga _C (C = 16, 20, 22, 24, 26 and 28 at. %) metallic glasses have been reported using Ashcroft’s empty core (EMC) model potential for the first time. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used in the present investigation to study the screening influence on the aforesaid properties. It is observed that the electron-phonon coupling strength λ and the transition temperature T _C are quite sensitive to the selection of the local field correction functions, whereas the Coulomb pseudopotential μ*, isotope effect exponent α and effective interaction strength N _O V show weak dependences on the local field correction functions. The T _C obtained from H-local field correction function are found in qualitative agreement with available experimental data and show almost linear nature with the concentration (C) of ‘Ga’ element. A linear T _C equation is proposed by fitting the present outcomes for H-local field correction function, which is in conformity with other results for the experimental data. Also, the present results are found to be in qualitative agreement with other such earlier reported data, which confirms the superconducting phase in the metallic glasses.      

Static Extra Dimension and Acceleration of the Universe

We study a five dimensional FLRW type Kaluza-Klein cosmological model with static extra dimension. Accelerated expansion is found by assuming a linear relationship p _b =mp _a between pressures ‘p _a ’ corresponding to the usual four dimension, and ‘p _b ’ corresponding to the extra dimension. The field equations are obtained and solved, for different values of m, to analyse the cosmological consequences of the present model. It is found that m has the value between 2 and 3 to match with the present observational findings for the accelerated expansion of the universe.     

A new optical method for measuring the electron-phonon interaction parameter λ〈Ω2〉 using the spectral dependence of the relaxation rate

The spectral dependence of the electron-phonon relaxation rate γ_e−ph(ℏω) in metals is studied in pump-supercontinuum-probe (PSCP) experiments with femtosecond time resolution. Investigation of this spectral dependence, which exhibits a substantial slowing of the relaxation rate γ_e−ph(ℏω) near the Fermi level E _F , using the parametrization γ_e−ph(ℏω)∝λ〈Ω²〉 (ℏω−E _F )² makes it possible to determine directly the electron-phonon interaction parameter λ〈Ω²〉. The parameter λ〈Ω²〉 for YBa₂Cu₃O_7−δ is analyzed using this method. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 5, 329–332 (10 September 1999)