High-Tc superconductivity and the Kondo lattice

High-Tc superconductivity and the Kondo lattice

Physica C 153-155 (1988) 1263-1264 North-Holland, Amsterdam HIGH-T c SUPERCONDUCTIVITY AND THE KONDO LATTICE E.W. FENTON N a t i o n a l Research C o...

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Physica C 153-155 (1988) 1263-1264 North-Holland, Amsterdam

HIGH-T c SUPERCONDUCTIVITY AND THE KONDO LATTICE E.W. FENTON N a t i o n a l Research C o u n c i l of Canada, Ottawa, Canada KIA OR6 Two e l e c t r o n bands r a t h e r than one may be r e q u i r e d to d e s c r i b e c o p p e r - o x y g e n p l a n e s . Physical consequences of a r e s o n a t i n g - v a l e n c e - b o n d (RVB) s t a t e f o r a two-band system or e q u i v a l e n t l y a K o n d o - l a t t i c e s t a t e are much d i f f e r e n t than f o r a one-band RVB s t a t e .

i.

INTRODUCTION There are strong indications of spin-singlet magnetic ordering of the "normal" state of the oxide compounds which are actually superconductors. Magnetic and nonmagnetic impurities have the same effect on T c (1-4) while occurrences of superconductivity in very dirty oxide materials and the temperature dependence of the London penetration depth both indicate that an s-wave or similarly symmetric pair orbital occurs. This contrasts with very different effects of magnetic and nonmagnetic impurities on T c in usual s-wave superconductors, and would occur if the spin rotation degree of freedom of the magnetic impurities is restricted by intrinsic magnetic order (5). Secondly, the spectral weight for spin-scattering of neutrons with transfer frequency he ~ 300 k B corresponds to only 0.01 ~B spin per Cu atom, indicating magnetic ordering with transition temperature much higher than 300 K (6). Finally, nuclear quadrupole resonance on two isotopes of Cu at every Cu site shows that no magnetic induction occurs in the crystal, above o£ below T c for superconductivity, so that the magnetic ordering indicated can only be spin-singlet correlations (7,8). Although this case for intrinsic spin-singlet ordering of the normal state is a fairly strong one, it is not conclusive because, e.g., there is some possibility that magnetic impurities may not he substituting for atoms in the active superconductivity volume, despite considerable care taken on this point in the experiments, there is some possibility that the pair wave function is not s-wave, pairing does not occur in the superconductivity, etc. 2.

NORMAL STATE There are two states presently conceived which describe spin-singlet ordering of the normal state, which are the one-band resonating-valence-bond (RVB) state proposed by P.W. Anderson and co-workers, and the Kondo lattice state from theory of heavy-Fermion metals (9). If in the one-band RVB state we

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substitute for the spin-singIet correlation of two similar electron states with a spin-singlet correlation of a highly-localized electron state with a less-localized electron state, here denoted as f and c states, than this repeated on a lattice is a Kondo-lattice state. Strictly speaking, the two-band RVB state is equivalent to a Kondo-lattice state if the energy of the more localized state Ef is lower than ee, the on-site coulomb interaction Uf cannot be eliminated by inclusion in a simple one-electron hand structure while U c can be, and the wider c band centred at ~c > Ef has a Fermi surface. For oxide superconductors, the last requirement is satisfied only if there is "hole-doping" of the copper-oxygen plane, end this is also the situation when spin-singlet ordering of the normal state apparently occurs rather than antiferromagnetism. Finally, the characteristic temperature TK1 for spin-singlet Kondo ordering of the lattice-(conceivably including f-f as well as f-c spin-singlet pairing) need not be low as occurs for heavy-Fermion systems, but may even be much l a r g e r than the m e l t i n g t e m p e r a t u r e of the c r y s t a l , c o r r e s p o n d i n g t o the range f o r TK i n the s i n g l e - i o n Kondo s t a t e . The s p i n - s i n g l e t Kondo o r d e r i n g a t z e r o temperature is just I < f i + c i + > l : l & K l ( i ~ v )~8 ~ O, whereas < f : + c i + > = 0 i n phase a v e r a g i n ~ oP t h e p a i r wave # u n c t i o n , ~Ni= I

f de i e iNioi

where N i is the number of pairs at site i and the phase 8 i of the pair wave function is quantum-mechanically uncertain when N i = i. With hole-doping of the copper-oxygen plane, which occurs only for the wider-bend c states because eo > e~, .T negligible change of the f-state l o c a h z a t i o n should occur and the f-c spin-singlet Kondo pairing of electrons should remain "real-space" pairing with spatially incoherent phase, in contrast to coherent-phase Cooper pairing where the number of pairs is

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E.W. Fenton / High-T~ superconductivity and the Kondo lattice

f i x e d , i f at a l l , o n l y in the e n t i r e volume of the c r y s t a l r a t h e r than a t each l a t t i c e s i t e . The s i n g i e - b a n d RVB s t a t e of Anderson et a l i s much d i f f e r e n t i n t h a t s u f f i c i e n t h o l e doping ensures e l e c t r o n t r a n s f e r from s i t e t o s i t e f o r both members of the s p i n - s i n g l e t e l e c t r o n p a i r , so t h a t a t r a n s i t i o n w i t h h o l e doping can occur from a normal s t a t e w i t h i n c o h e r e n t r e a l - s p a c e p a i r i n g t o a p h a s e - c o h e r e n t p a i r i n g s t a t e which is superconductivity with itinerant pairs (10,11). 3.

SUPERCONDUCTING STATE Because the f - o p a i r i n g of the Kondo l a t t i c e s h o u l d remain i n c o h e r e n t w i t h h o l e d o p i n g , s u p e r c o n d u c t i v i t y can occur o n l y w i t h p a i r i n g of q u a s i - p a r t i c l e s t a t e s which occur i n the presence of the f - c p a i r i n g , which would be second-order pairing. I f the p a i r i n g i n t e r a c t i o n i s mediated by c o l l e c t i v e modes of the Kondo I s t t i o e , t~9 ~ TO f o r s u ~ c o n d u c t i v i t y i s r o u g h l y T K I e - ± / ~ or TRVBe-~/~ where X i s the c o u p l i n g c o n s t a n t , which i n c l u d e s s f a c t o r Q ( t ) which i s an e f f e c t i v e - a v e r a g e d e n s i t y of s t a t e s for quasi-particles. M ( t ) and k f o r s e c o n d - o r d e r p a i r i n g cannot be s i g n i f i c a n t l y l a r g e u n t i l s u f f i c i e n t h o l e doping of the copper-oxygen plane occurs, f o r the f o l l o w i n g reasons. With maxima of the i n c o h e r e n t d e n s i t y of first-order f-c pairing regularly placed on lattice sites, the wave-function modulus squared is characterized by reciprocsl lattice vectors G of the host lattice. The wave-funCtion modulus not squared is characterized by ½G, and in this two-electron correlation the one-electron part is characterized by ¼G. In the copper-oxygen plane, the Fermi-surface line for the half-filled band is near four straight lines which are perpendicular to four vectors which are each ¼G. A qusi-gap due to the incoherent f-c pairing will occur at these four straight lines in k-space, and this Fermi surface for the half-~illed band is gapped or nearly gapped. Because the amplitude of the real-space f-c spin-singlet pairing varies commensurately with the host lattice, a quasi-gap due to the pairing is locked in k-space rather than to the Fermi surface and should remain centred near the Fermi surface for the half-filled band even when substantial hole doping occurs. In this case N(~Fermi) for quasi-particles will not be significantly large, nor will T c for superconductivity due to second-order pairing, until sufficient hole doping of the copper-oxygen plane occurs. 4.

SUMMARY I n c o h e r e n t Kondo s p i n - s i n g l e t p a i r i n g c h a r a c t e r i z e d by t e m p e r a t u r e TKL s h o u l d occur r a t h e r than the u s u a l RVB s t a t e i n a " n o r m a l "

s t a t e i f two e l e c t r o n bands are r e q u i r e d f o r the c o p p e r - o x y g e n p l a n e . In t h i s case s u p e r c o n d u c t i v i t y would be due t o co~9[ent s e c o n d - o r d e r p a i r i n g w i t h T O = TKLe-±/~ , which may occur o n l y when s u f f i c i e n t holes a r e added to the plane. In the s e c o n d - o r d e r p a i r i n g , e* = 2e f o r the c o h e r e n t p a r t . This d i s c u s s i o n is in part a precis of ref. 9.

REFERENCES (i) Y. Meeno, M. Kato, Y. Aoki, T. Nojima, and T. Fujita, Proc. Yamada Conf. XVIII, Sendal, Japan, Aug., 1987. (2) G. Xiao, F.H. Streitz, A. Gavrin, Y.W. Du, end C.L. Chien, Phys. Rev. B 355, 8782 (1987). (3) S.B. Oseroff et al, in print. (4) J.M. Terascon, L.H. Greene, B.G. Bagley, W.R. McKinnon, P. Barboux, and G.W. Hull, in "Novel Superconductivity", ed. S.A. Wolf and V.Z. Kresin (Plenum 1987), p. 705. (5) E.W. Fenton, S o l i d S t a t e Comm. 65, 1011 (1988), i n c l u d i n g r e f s . t o e x p e r i m e n t a l papers. (6) T. BrOoke1, H. Cspellmann, W. J u s t , O. Sch~rpf, S. Kemmler-Sack, R. l