A.K. Rajagopal

Generalized pairing theory of superconductivity in layered crystals

Abstract A generalized pairing theory of superconductivity in layered crystals is formulated in terms of an arbitrary dynamical interaction, V(r1r2; t1−t2), among the electrons. This has been done within the framework of the Gorkov mean field theory, with the introduction of an appropriate set of states to represent the single particle motion in the layered crystals. The layer representation is band-like in the plane of the layers and localized in the perpendicular direction. This enables us to derive the equation for the superconducting state which includes intra-and inter-layer polarization interactions involving exchange of all possible electronic and ionic excitations in the system within the strong coupling formalism. An equation for the critical temperature Tc of the system has been obtained by solving the linearized gap equation in terms of a suitably averaged dynamical interaction. We specify from first principles the various approximations required to obtain the simpler forms of the Tc-equation used in the literature for investigating its dependence on the structure and number of conducting layers in the new high-Tc systems. In general, we find that the dynamical interactions can involve a maximum of any four different layers with intra- and inter-layer pairings. In the extreme layer approximation, where the excitations are highly localized to within individual layers, the interaction connects only a maximum of any two layers. These considerations still imply that the required attractive interaction for intra-layer Cooper pairing in a conducting layer may arise from both intra- and inter-layer couplings and possible exchange of excitations in the neighboring layers whether conducting or insulating.

Critical temperature in high-Tc layered superconductors: Dependence on the number of interacting conducting layers per unit cell

Abstract The generalized BCS pairing thoery for layered superconductors is used to investigate the dependence of the transition temperature T c on the number N of interacting conducting Cu-O layers in any unit cell. The coupling constants, which describe intralayer and interlayer interactions in these layers where the Cooper pairing is assumed to take place, are explicity related to the microscopic polarization functions of all layers in the unit cell, including the insulating layers. With reasonable interlayer couplings it is possible to understand the experimental values of T c in many of the high- T c compounds discovered recently. One can indeed increase T c as a function of N , but we find T c (∞) to be less than 150K in polytypes of the [-(CuO 2 ) N -] class, as well as in the 1:2:3 class polytypes [-(CuO 2 )-(CuO-CuO 2 ) n -], N =2+1. This is based on the approximation involving only up to the nearest neighbour conducting layer couplings and the use of experimental results for T c in various thallium, bismuth and 1:2:3 compounds. A much higher T c (∞) is possible only of the single-layer T c (1) is high (>90 K) and interlayer couplings are significant.

THEORY OF FERROMAGNETISM IN (A, Mn) B SEMICONDUCTORS

Abstract A brief review of theory of ferromagnetism of diluted magnetic semiconductors of the form (A, Mn) B based on the double-exchange model is first given. A systematic investigation of the phenomena extending the current theory is outlined. We begin with an investigation of regions of instability of the non-magnetic towards the ferromagnetic state of a system of Mn atoms doped in an AB-type semiconductor. A self-consistent many-body theory of the ferromagnetic state is then developed, going beyond the mean-field approaches by including fluctuations of the Mn spins and the itinerant hole gas. A functional theory suitable for computation of system properties such as the Curie temperature as a function of the hole and the Mn concentrations, the spin current, etc., is formulated.

Critical temperature in high Tc layered superconductors: Dependence on structure and number of interacting conducting layers per unit cell

A simple model of intra- and inter-layer coupling based on a generalized BCS pairing theory of layered superconductors is used to correlate the Tcs of a large number of systems with varied structures, in terms of the ration of inter- and intra-layer coupling strengths. The largest Tc attainable by asymptotically increasing the number of layers is found to be about 143K in a model describing Tl1- and Tl2-systems, and 136.5K in the Bi2-system.

Neutron scattering as a probe of superconducting correlations in the new high Tc superconductors

Abstract We suggest that a direct experimental estimation of the superconducting gap and the coherence length may be possible by neutron scattering experiments in the new high Tc superconductors. We show that both orbital and spin currents associated with the Cooper pairs make equally important contributions to the inelastic neutron scattering, the former dominating the latter in the region of small wave vector transfer.

Broken-symmetry-adapted Green function theory of condensed matter systems: Towards a vector spin-density-functional theory

The group theory framework developed by Fukutome for a systematic analysis of the various broken symmetry types of Hartree-Fock solutions exhibiting spin structures is here extended to the general many body context using spinor-Green function formalism for describing magnetic systems. Consequences of this theory are discussed for examining the magnetism of itinerant electrons in nanometric systems of current interest as well as bulk systems where a vector spin-density form is required, by specializing our work to spin-density-functional formalism. We also formulate the linear response theory for such a system and compare and contrast them with the recent results obtained for localized electron systems. The various phenomenological treatments of itinerant magnetic systems are here unified in this group-theoretical description.

Pairing in layered superconductors in the presence of a magnetic field

Abstract Within the framework of the recently developed formalism for describing superconductivity in layered crystals, the intralayer pairing in the presence of a homogeneous magnetic field is examined. With phenomenological interlayer and intralayer couplings introduced by us earlier for different classes of high z . sbnd ; T c materials, the effect of the magnetic field on T c and the variation of the upper critical field H c 2 as a function of temperature are discussed. Explicit results are presented for the case of the magnetic field perpendicular to the layers, in the clean limit.

Neutron scattering from charged spinless paired boson superconductor

Abstract The neutron scattering cross section for a model charged spinless paired boson superconductor is presented. This is contrasted with our previous communications on the same topic for the paired fermion superconductor. It is suggested that a measurement of the current-current correlation function by neutron scattering or any other method may be a diagnostic tool for distinguishing the quasiparticle statistics as well as determining the superconducting parameters of the new high- T c oxide superconductors.

Superconductivity of interacting chains and planes - a model of high Tc YBa2Cu3O6+δ systems

Abstract A model for the new high T c YBa 2 Cu 3 O 6+δ superconductors based on interacting chains and planes of Cuue5f8O systems is proposed. There are three residual interaction parameters in the model. These are obtained from the transition temperature of 95 K for the δ = 1 system and the two low temperature (4.2 K) gaps associated with the coppers in the planes and chains. Using these we predict the transition temperatures for two possible superlattice configurations of the system with δ = 0.75 and δ = 0.5. The calculations employ the detailed band structures. The observed high T c for δ = 0.75 and 0.5 are consistent with the weak δ-dependence of the pairing interaction and partial preservation of the Cuue5f8O chains.

Chanchal Kumar Majumdar

Chanchal Kumar Majumdar, a leading condensed matter theorist in India, died on 20 June 2000 in Calcutta following a heart attack