IC/8T/125 IHTERHAL REPORT (Limited distribution) ABSTRACT

Oxide superconductors are described in terms of macroscopic vave -•-•^international Atomic Energy Agency functions 1(1 and 4> corresponding, respectively,, to electron pairs of the superconducting and insulating states. In terns of the total free energy United nations Educational Scientific and Cultural Organisation of the system, including the effect of interaction, ve discuss the electrodynamic responses of the oxide superconductors in relation with the IHTERHATIONAL CENTRE FOR THEORETICAL PHYSICS experiments to date.

A PHENOMKHOLOGICAL APPROACH TO HIGH T OXIDE SUPERCONDUCTORS

J. Chela-Flores * International Centre for Theoretical Physics, , , and Instituto International de Estudios Avanzados, IDEA, Caracas, Venezuela,

M.P. Das ** International Centre for Theoretical Physics, Trieste, Italy, and International School of Advanced Studies, Trieste, Italy,

and

A.G. Saif •*• International Centre for Theoretical Physics, Trieste, Italy.

MIRAMARE - TRIESTE June 1987

t Submitted for publication. * Also at the Department of Physics, Uniirersidad Simon Bolivar, Apartado 80659, Caracas, Venezuela. ** On leave of absence from: Department of Physios, Bambalpur University, Jyoti Vlhar, Sambalpur 76819, India. *** Permanent address: Department of Mathematics and Theoretical Physics, Atomic Energy Establishment, Cairo, Egypt. -1- t &J&1JL

The discovery of high T oxide superconductors, *'2 has not only conventional phonon-mediated strongly-coupled BCS superconductors; buC,

signalled a new era for technology, but it has aiso posed great challenges apparently, the Debye phonon frequency has an upper bound which will

regarding I he question as to how the oxides have such high T supercon- fail to give Che observed T in these materials within the conventional C 5 ductivity. During the past few months many interesting aspects of the ma- BCS picture. Another related mechanism which has been suggested for Che le-rials have been reported based on thermodynamics and spectroscopic mea - oxides,is due to bipolarons -bound pairs of electrons with a cloud of pho- suremenfs raising several controversies. As it stands today, these oxides nons. This picture, though attractive, fails to produce high T for belong to a new class of superconductors. C strong enough coupling, because the scale of energy is still due to pho - In general, most oxides are insulators or semiconductors at low nons. More recently Anderson has generalized the Pauling's theory of 6 resonant valence bond ( RVB ) relevant to the oxide materials ,In this temperature. Only a handful of them are poor metaLs. Particularly for picture the valence electrons are Heitler-London bonded singlet antiferro- materials like Ba-La-Cu-O, and related compounds, it has been known that magnetic pairs. It satisfies Hubbard's half-full band condition, so that 1 he basi:: material lanthanum cuprate is an ant if erromagtiet ic insulator. the virgin lanthanum cuprate is an insulator having all localized valence On doping with an alkali earth, the system undergoes an insulator-metal bond pairs as in a Neel state. Doping with the alkali earths the pairs Transition, and soon after the appears. There have been become mobile as in a liquid. Correlations amongst the pairs establish some more recent studies on the same materials having stoichiomecric compo- an order that is considered as the origin of superconductivity. Anderson's sition exhibiting superconductivity of high T . From structural consicl- proposal is based on the experimental facts on the oxides and It "Tvitionr. i| has been known that these materials are made up of perovkite

layers of corner-sharing CuO octaiiedra, interlinked with corner-sharing is considered to have the potential of giving very high T , since the square planar CuO^. Whether it is a doped, or a stoichiometric material, energy scale is no longer due to phonons, but rather it is due to inter-

CuO^ units Form a square lattice. At present the most considered opinion electronic exchange. A complete test of the RVB theory is yet to be is thai when i divalent r.lkali earth cation is substituted for the tri- carried out for all the superconducting properties of the oxides.

2+ 3+ vaJent lanthanum (or yttrium), the Cu ion tends to go to Cu . The In this paper, by following the spirit of Anderson's work, we attempt occurrence of Cu also depends on the vacancy. On the whole to develop a phenomenological macroscopic approach to understand some of copper remains in a mixed valent state, which is a requirement for the the electrodynamical aspects of the oxide superconductors. Based on the Cu-0 plane (o be metallic and this condition is essential for supercon- fact that the nature of the materials is inhomogeneous, with several duct iviiy, experimentally observed anomalies imfor instance, resistivity and phonon

spectrum, we start with a hypothesis that in the normal state ( Just Quite a few at Icmpls have been made to understand how these materials 4 above T ) there exists quasilocalized domains of valence-bond pairs, possess superconductivity. Some workers believe that the oxides are

-2- -3- Here, e* = 2e, and m* denotes the effective mase of the itinerant pair,

_i •* which are characterized by a complex order parameter © » These domains where A is the vector potential corresponding to the magnetic field H; 8 are weakly linked and, therefore, the resistivity of the sample is very

The strength of the coupling is further assumed to_depend on the paired

densities in both phases. I - - - I ' C ' (3)

where B is the coupling strength in appropriate units, incorporating

Assuming that, the order parameters are spatially inhomogeneous close the effective mass. The free energy jF is given by, to T , we can write the free energy F of the system,in the presence of a magnetic field H, as composed of functionals of the order parameters: 5= J d? T(?) . (4)

We minimize & with respect to ^ and obtain the equation!

where F[ V J and F[

Kit ion involving a quas ilocalized RVB and superconducting { itinerant ) A similar equation follows by varying .3? with respect to CD . state: Finally, we minimize jF with respect to A . By considering the

mass of the localized pairs to be heavier relative to those of the itinerant

(2)

g7r

-5- pairs, wo omitted the contribution from the F[ ^ ] to obtain j is the new coherence length, which Is temperature dependent through

(he current" density as OC and j . For a negative coupling strength ^J , we find from eqns.

(9) and (10) that,

and

For , ,w have J QL , A GL and C C 0L. denote the corresponding values of Che parameters in the GL theory.

In deriving Eqns, ( 5-7 ) we have used the corresponding boundary condi - He calculate the total flux density ^> as given by,

lions. By setting | \j/ \ = | ^ | , and by assuming^ as spatially weakly irthomogeneous, to first order in H ,eqn. (7) can be cast in = J A'Jl = J H. the form: VH =1 H

(8) (13) where, where,

L —-—: + = ch/2e ^ 2 X gauss cir

(9) is the flux quantum in the GL theory, and n , n , and £ are integers or

In oihcr words, A denotes the new penetration length. zero. This condition fixes the relationship of X and / (p |. Now, by using T \ and (6 as given above, we find that, For a very weak field, and by setting J \l/ , yti* f tf x« becomes ,

(14) •*«

CK (10) and where, H PI - L. (H. (15) (11)

-6- -7- ACKHOWLEDGIMEHTS

The authors would like to thank Professor Abdus Salsm, the In summary, we have developed a phenomenological approach to under- International Atomic Energy Agency and UNESCO for hospitality at the stand m-ninly Che electrodynamical properties of the high T oxide super- International Centre for Theoretical Physios, Trieste. One of the authors (J.C.F.) would like to acknowledge a grant from II Dipartiraento conductors. Due to the structural inhomogenetty it is likely chat anti- per la Cooperazione allo Sviluppo del Minister© degli Affari Eateri, ferromagnetic fluctuations help to develop superconducting grains ran- Italy,and one of the authors (M.P.D.) would like to acknowledge the domly in otherwise domains of Mott-Hubbard insulators having localized University Grants Commission, Hew Delhi^for support. The authors pairs. By assuming a coupling between these two domains through an would also like to thank Professors Dong Jin Ming, SuDOdh Shenoy, iniernal field we have obtained the following features! Su Zhao-Bin, Erio Tosatti and Yu Lu for many helpful discussions.

(i) Large penetration depth,

(ii) Small superconducting coherence length, implying narrow cores

in tho vortex structures,

(iiL) High H ,

(i v) Low H , and c

(v) A small pinning force.

9, 10 All of these features observed in the recent experiments are reconciled with the predictions of our theory. We further argue that the high T is a consequence of strong correlations in the order parameters, which can be realized from our calculated small coherence lengths ( the laitcr being inversely proportional to the T ). The Meissner stale is reduced since rhe H is lower. In this state all the pairs in ihe sample go to the extended states by forming a glassy superconduc- tor which we may call an insulator-metal transition of the second kind.

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