A prosaic explanation for linearly temperature-dependent penetration depths in YBa2Cu3O6.95

PHYSICA ELSEVIER

Physica C 228 (1994) 171-174

A prosaic explanation for linearly temperature-dependent penetration depths in YBa2Cu306.95 J.c. Phillips AT&T Bell Laboratories, Murray Hill, NJ 07974-0636, USA Received 6 May 1994

Abstract

One of the main props for the: exotic d wave pairing theory of high-temperature superconductivity in the layered cuprates has been the observation in microwave experiments of a temperature-dependent surface resistivity which has been interpreted to mean that A(T) ct Tfor T/To_<0.3. From this it has been argued that the Cooper pair energy-gap amplitude A(k) must have nodes in k space. We present a prosaic alternative explanation for the data based on nodal regions in r space, which is consistent with s wave pairing. Our model explains in a natural way why the linearity of A(T) disappears with a small amount of Zn doping.

The phenomenon of high-temperature (T~ ~> 100 K) superconductivity in the layered cuprates has attracted unprecedented interest ( ~ 35 000 publications so far) [1]. Broadly speaking, research on HTS is divided between two different approaches: conventional, based on extending the conventional BCS theory of superconductivity in metallic compounds into the new area of ceramic metallic oxides, and unconventional, in which conventional theory is ignored and exotic new mechanisms are proposed. When one considers that it required nearly 50 years after the discovery of superconductivity to produce the BCS theory, it seems extremely unlikely that a second theory should exist and be necessary to explain the high To' s of the cuprates. Nevertheless, exotic theories have proved extremely popular, not only with theorists but with experimentalists as well. Several of these exotic theories have already been laid to rest (for instance, RVB and anyons), but new ones are constantly appearing. One of the currently popular exotic theories is that the Cooper pairs are in d wave, rather than s wave, states. On the face of it, this proposal seems absurd, 0921-4534/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSD10921-4534 ( 9 4 ) 0 0 3 1 2 - 4

because in general d wave interactions are much weaker than s wave interactions, and should produce Tc's which are of order 10 -2 K, rather than 102 K. Several experiments [ 2] which have purported to demonstrate d wave pairing have already been explained prosaically in other ways [3,4]. However, the report [5] that the change AA(T) in the penetration depth A of a single crystal is linear in Tup to - 25 K has yet to be explained prosaically. It is claimed [5] that these measurements provide "strong evidence for nodes [ in k space] in the gap function". It is also noted that this linear dependence is absent in the presence of a high concentration of point defects, for instance, ~ 1% substitutional Zn impurities [6]. The prosaic explanation which we believe describes these data correctly is that even so-called "extremely high-quality" [5] crystals (ATe~0.25 K) contain intrinsic spatial inhomogeneities. These inhomogeneities include layer buckling, oxygen disordering and weak links which are normal metallic regions even at T = 0. Thus instead of nodes in the gap functions in k space, one has nodal regions in r space. Wherever such

172

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nodes are, they lead immediately to AA( Tt ct T at Imv temperatures, by the same argument in r space as m k space. Also the presence of normal metallic bridges m a superconductive network will automatically produce a linear dependence in A, because the latter will depend in part on the normal state skin depth ,8, which itself is linear in T. There are two questions which this prosaic explanation must answer. First, what is it about the layered cuprates that would produce such nodal regions even in a single crystal, when they are absent from elemental alloys such as Pbo,~sSnn o5 [5] ? Second, why does this mechanism lose its effectiveness with the addition of small amounts of Zn replacing Cu? The first question is easy to answer. Unlike fcc Pb, the bonding architecture of the layered cuprates is extremely complex, but its chief feature is easily understood. These crystals consist of alternating metallic layers (such as CuO2) and semiconductive layers (such as BaO). One can imagine these layers in isolation, with interlayer bonds along the c-axis replaced by terminating H bonds. Then each such layer c~ would be in equilibrium with certain planar lattice constants a,, and b,. (These are sometimes called prototypical lattice constants.) In general there is no reason to assutne that a,, is the same for all layers o~, c~'. .... and similarly fl~r b,. This means that in actual crystals there will be a substantial interlayer stress associated with the lattice constant misfit a , - a~, [ 7 ]. This point was discussed long ago [8], and it was shown that the energy associated with a-axis misfit increases nonlocally as the length L, of a given region as L:], or L] per unit length, simply because strain energies are harmonic. Thus as L, increases the strain energy diverges, and some anharmonte stress relief mechanism must come into play. At semiconductor heterointerfaces this relief mechanism is misfit dislocations [8], which have been studied extensively with electron microscopy. For the layered cuprates there are two relief mechanisms, layer buckling (which has been observed [9 ] in Bi2Sr2CuO6, ~, where it is very large because of easy cleavage of the Bi202 double layers, and the weak stabilizing effect of a single CuO2 plane/unit cell), and oxygen defect disordering (associated with Oa). We have consistently argued [10] that oxygen ordering (in the case of Y B a 2 C u 3 0 7 ~, of the O~ vacancies) is responsible for high-T~ superconductivity, so oxygen disordering can be responsible for nodal gap regions in r space.

22~'11994~ I 7 / /:.i

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.

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Z,

Fig i Interlayer n/lsllt produces kugc layer buckhng ,,,,hen , . relieve~ lhe lnterla}t:l stress, m a manner anah,gous to tha! of mislil dislocation,; {These regions, whose shorlest dimension 1~. expected to be ~)l order 2l.~ q(~ A [9], could involve stacking faults or partial edge dislocations, but other kinds of anharmonic ,,tress relief are possible as well. i The layer bucklirlg m turn disorders the oxygen vacancies on the Cu(), chains, w h i c h q u e n c h e s the gap a m p l i t u d e ]..lib) t near Ihc~,e regmus, producing locall) normal-metallic resistivi b pet 1" When Zn impurities are added, the gap I A ( b ) I is suppressed Iocall', nean each impurity and its average value ~s also reduced, for inslance b? scattering by magnetic moments associated with the m~purme.s ,\~ the same time, howe,.er, the random strain fields associated with lilt' Zn unpurities prevent the accumulation of long-range stress due I . interlayer misfit, so that the volume fraction of nodal { normal-metal he) regions decreases The end result is that the tov,-lemperature anomaly with AA a "1" is suppressed by the addition ol Zn mlpurilies III cegl~|ln rcglony, 'ahlch a n h a r n n l n l c a l l }

Most readers of this journal will have no difficulties in understanding and accepting this nmchanism, as il employs ideas which, although unfamiliar to most theoretical physicists, are common knowledge to material scientists. However, they will still be curious to knm~ how the second question is answered. What happens when a small amount o f Z n ( - 1%1 is alloyed mtothe Cu sites that eliminates the linear T term? We believe that point defects such as Zn locally relieve tile misfit. possibly by developing a local oxygen-coordination configuration that is no longer described by bonds paral[el to the Cartesian axes. (Recall that CuO has the octahedral NaCI structure, but that ZnO is tetrahedrally coordinated.) As a result locally T~. is suppressed, but at the same time long-range stress accumulation is also suppressed and the gap, although reduced, has many fewer nodal regions in r space. This is the real meaning of the experimental data [ 51. not d wave pairing It is illustrated in Fig. I. The real justification for the model shown in [;ig. i

J.C. Phillips/ Physica C228(1994) 171-174

is quite general, and as the underlying theoretical principles are well established, it needs no detailed justification. However, in a field with 35 000 papers it is easy to find many experimental results which are consistent with the structural model illustrated in Fig. 1. We mention only one, taken from the current literature. The strongly buckled normal regions postulated for CZn= 0 obviously reduce the resistivity anisotropy between the more resistive c-axis and the more conductive ab planes by providing regions of higher conductivity along the c-axis. When the volume fraction of these normal regions is reduced by Zn impurities which relieve stress locally, the c-axis resistivity should increase, and in fact this is just what is found experimentally [ 11 ]. In this connection we note that a very similar phenomenon occurs in connection with chemical trends in the normal-state resistivity p(T), which is "anomalously" linear in T (rather than T 3, for example) over a wide range of temperatures when Tc is maximized. When spatial inhomogeneities are ignored, the linearity of p(T) can be explained [ 12] only by assuming that the density of ballistic states Nb(EF)=0. This is another absurd result, because it is clear that any effective medium model which assumes Nb(EF)=0 will reduce T~, rather than enhance it. This problem disappears when proper allowance is made for spatial inhomogeneities [ 13 ]. The problem of the linearity of AA(T) is analogous to the problem of the residual magnetic relaxation rate which does not go to zero as T ~ 0 , but instead saturates. The saturation is explained prosaically [ 14] by local heating near spatial inhomogeneities. Indeed we believe that all of these T << T~ "anomalies" are termed such only because it has been assumed that a crystal with a sharp superconductive transition must be spatially homogeneous. This assumption is based on logical confusion between the conditions necessary (which it is) and sufficient (which it certainly is not). Indeed spatial inhomogeneities (including even phase separation on a submicroscopic scale < 50 ,~) have often been proposed as the explanation for the disappearance of superconductivity in Laz_xSrxCuO4 for x>0.2. These explanations have been examined for this "simple" structure (only seven atoms/cell) in many extensive studies, but with inconclusive results [ 15]. After so much effort one must necessarily conclude that the burden of proof in any experiment rests on those who assume homogeneity, especially near the

173

sample surface and especially when this assumption is not even stated explicitly. We also note that the complex functional behavior of p(H, T) in the transition region is best described by the Tinkham-Josephson network model [ 16], not only for granular samples, but also for very high-quality single crystals as well (ATe~0.14 K) [17]. The specific heat and magnetization in the transition region of high-To cuprates also behave qualitatively differently from low-To superconductors because of spatial inhomogeneities [ 18 ], and these qualitative differences occur not only in granular samples but also in single crystals. In other words, spatial nodes in the gap are intrinsic to high-quality single crystals but, unlike k space nodes (d wave pairing), while they may reduce T~ by a factor of ~ 2, they certainly do not reduce it by a factor of order 102.

Acknowledgement I am grateful to D.R. Hamann for stimulating my interest in this problem.

References [ 1] J.G. Bednorz and K.A. Miiller, Z. Phys. B 64 (1986) 189. [2] D.A. Wollman, D.J. Van Harlingen, W.C. Lee, D.M. Ginsberg and A.J. Legget, Phys. Rev. Lett. 71 (1993) 2134. [3] C.-R. Hu, Phys. Rev. Lett. 72 (1994) 152C. [41 P. Chaudhari and S.-Y. Lin, Phys. Rev. Lett. 72 (1994) 1084. [5] W.N. Hardy, D.A. Bonn, D.C. Morgan, R. Liang and K. Zhang, Phys. Rev. Lett. 70 (1993) 3999. [6] R. Liang, P. Dosanjh, D.A. Bonn, D.J. Baar, J.F. Carolan and W.N. Hardy, Physica C 195 (1992) 51 ; W. Hardy, Bull. APS 39 (1994) 111; K. Zhang, D.A. Bonn, R. Liang, D.J. Baar and W.N. Hardy, Appl. Phys. Lett. 62 (1993) 3019. [7] J.B. Goodenough, Supercond. Sci. Tech. 3 (1990) 26. [8] F.C. Frank and J.H. van der Merwe, Proc. Roy. Soc. A 198 (1949) 205. [9] J.M. Tarascon, P.F. Miceli, P. Barboux, D.M. Hwang, G.W. Hull, M. Giroud, L.H. Greene, Y. LePage, W.R. McKinnon, E. Tselepis, G. Pleizier, M. Eibschutz, D.A. Neumann and J.J. Rhyne, Phys. Rev. B 39 (1989) 11587; H. Budin, O. Eibl, P. Pongratz and P. Skalicky, Physical C 207 (1993) 208. When suitable large crystals are available, the most powerful tool for observing layer buckling is ion channeling, which reveals large changes in the degree of buckling at T~ which are not observable by diffraction; see R.P. Sharma, F.J. Rotella, J.D. Jorgensen and L.E. Rehn, Physica C 174 (1991) 409;

[ 74

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J.C. Phillips, in: Lattice Effects in High-7~: Superconductors. eds. Y. Bar-Yam, T. Egami, J. Mustre-de Leon and A R . Bishop (World Scientific, Singapore, 1992) p. 3 [ 10] J.C. Phillips, Phys. Rev. B 42 (1990) 8623: ibid., 43 ~ 1991 ) 11415. [ I 1 ] K. Semba, A. Matsuda and T. lshii, Phys. Rev. B 49 ( 1994 ! 10043. [ 12] C.M. Varma, P.B. Littlewood, S. Schmitt-Rink, E. Abrahams and A. Ruckenstein, Phys. Rcv. Lett. 63 (1989) 1996: PB. Littlewood and C.M. Varma, Phys. Rev. B 45 ~ 19921 12636; ibid., 46 (1992) 405. This model is often called the marginal Fermi-liquid model ( M F L ) because Z(0) 0

I I 3 ] J.C Phillips, Phys Roy B d . 6 i 1 4 9 2 ) 8542 114 ] A. Gerber mid J.J.M. Fr~mse, Phys. R e v LelI. 71 ! 1'49~, ) 1895 [15] P.G Radaelli, D.G Hinks, A W Mitchell, B.A Huntcl, ,1 i Wagner, B. Dabrowski, K G Vandervoort, H K Viswanathan and J.D. Jorgensen, Phys Re', B 49 I 1994 ) 416 :~ F¢3r YBC( '~ see A . N Lavrov, Physica (" 21t~ (1993) 36 161 M, Tmkham. Phys. Re,. [,cll ~,1 {1988) 1658 171 t].A. Blackstead. Phys R e v B 47 t 1993 ) 11411 : u.lem, Physlca (" 209 (1903) 437, R Kleiner and P Miiller, Phy~, Re,, B 49 ( lqq~4i } ~2 I 8 ] J C Phillips, The Physics ofHigh-7~ %uperconduclor,',, Chaplcl X ( Academic, Boslon, 198 (} t