Infrared properties of high Tc superconductors

Physica C 185-189 (1991) 5 7 - 6 4 North-Holland

INFRARI!!)

I ' R O I ' I ! R ' I ' I F . S O F I I1(;I I "1c S I J P ! ! R ( ' ( ) N I ) I J ( : f O R S

Z. SCIlI.I:.SIN(;F.R, I.. i). Rotter, R. T. Collins, F. lloltzberg, C. Feild, IBM Watson Research (:enter, Yorktown lleights, New York 10598 11. Welp, (;. W. ('rabtree, .I.Z. I iu*, Y. F a n g and K. G. Vandervoort Materials Science Division, Argonne National I.ab, Argonne. Illinois 60439 * present address, Physics Dept., University o f California, l)avi.~, California, 95616

Over the past several years a coherent phenomenology o f the high "!"c cuprate superconductors has begun to emerge. Infrared measurements have contributed several important ingredienls to this picture including: I j the inference o f a scattering rate that is linear in frequency For o~>'l', and of order (,~, -- 2) a characteristic energy scale in the superconducting state ofSOO c m - v (60 meV), which can he interpreted as a superconducting pair excitation threshold or energ} gap, and -- 3) evidence for very unusual temperature dependence in the vicinity of T c. An attempt to describe these aspects o f the data is presented here.

l h c subject of cuprates at half-filling and low doping

I. I N T R O I ) I J C T I O N

has bccn discussed by Professor 11chida on Monday at Since

the

discovery

of

superconductivity

in

I.a2_,BaxCuO 4 in 1986(I), a great deal of effort has

thi~ meeting, and also by Dr. Sawatzky on Friday.

i

will summarize thi~ aspect only very briefly. At half-

been pitt into the study o f fundamental properties of the

lilling the

cuprates. A primary goal o f this work is. o f course, to

electron-electron

understand why certain cuprates are superconducting

comh~tivil~ k roughly zero up to a charge transfer gap

at

Infrared

typically in the vicinity of 2 eV (16,000 c m - J). With

spectroscopy, which covers the energy range from IO to

doping the strength o f the charge transfer excitation di-

IO,OOO K in which the characteristic energy scales rele-

minishes, and conductivity below .-, 2 eV increases cor-

vant to superconductivity are expected to lie. can be

respondingly. Strong hybridization effects appear to be

very high

temperatures

(~100

K).

cupratcs

are

insulating due

interactions.

to

The

strong infrared

expected to provide a very significant probe o f funda-

relevant to understanding the rate at which the laCe-

mental properties.

grated

The ellicacy of infrared measure-

infrared

(0,<2

eV)

conductivity

grows

ments was demonstrated in the study of conventional

(Sawatzky), which is quite fast at low doping.

superconductors(2-6), particularly in the early studies

cuprates thus seem to be best classified as charge

The

o f the energy gap(2-5). To date, there are hundreds of

transfer insulators with strong hybridization.

papers on the infrared properties of cuprates. My goal here wiii not be to present a summary o f this work, but

At low doping, i.e. x
instead to try to capture the essential aspects o f the in-

frared conductivity typically has a local minimum near

Frared conductivity o f the cuprates, and to describe

¢,~ f ) , grows with frequency to a maximum between

these aspcct~ as simply as possible.

In fact, I believe

about 2()fit) and 8000 c m - 1 and then decreases slowly

infrared properties can be

with f,, up to the remnant charge transfer threshold.

described quite simply, particularly in the composition

I b i s bcilavior is clearly seen in the La 2 _ ,Srx(:uO a data

range

of l lchida et a!.(7.8), and in data from Y doped

that the

phenomennloKV of where

optimal,

superconductivity occurs.

or

nearly

optimal,

B i 2 S r 2 ( ' a ( ' u 2 O r _ ~. ~amples o f Terasaki et ai.(9.10).

0921-4534/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All fights reserved.

58

Z Schlesingeret aL / lnfrared pmpenies of hi&ll Tc superconductors

This low doping regime has also been examined by Tokura etal. for the electron doped superconductors, and most recently by Thomas ct al. (11). Possible reasons for the form of a(a)) in this low doping regime, including aspects of the correlated band.structure, and suppression of d.c. conductivity by strong localization effects have been discussed by others at this meeting (e.g. Uchida, Sawatzky, []anke). In this talk, ! will concentrate instead on the moderate doping (#~.t5-.25) regime where high Meissner fraction superconductivity occurs, and where the phenomenology of the conductivity seems to be rather simple. I will try to demonstrate this simplicity of form as well as the highly unusual nature of the infrared response.

,--. 4000 '7 t= Cji '7 vca 2000 :3 10

i

o) 1 "

j

twinned

0

.--,. 4000

'b)

're !

vc=

untwinned

2000

a OX~S :3

,:7

Much of the infrared work on cupratcs has involved YBa2('uaO 7 _ y, which is a very good material to study because of the apparently high degree of electronic homogeneity. Studies of this material can bc complicated by the presence of conducting chains. Measurements of twinned cD'stals of YRa2CuaO 7_y(12-18) yield a conductivity that involves contributions from both chains and planes. In figure la the normal state conductivities measured for three twinned crystals with Tc's of 90, 80 and S0 K, respectively, from Orenstein et al.(lS) are shown. For the samples with T¢~80 K and .50 K, the conductivity exhibits a local maximum in the 1000 to 4000 cm-~ range, in addition to the peak at r,=0. In parts b and c of figure l, wc show the conductivity of several untwinned crystals of YBa2Cu30 7 _ y with similar Tc's (92, go, and 56 K) from Schlesingcr et al.(19) and Rotter et al.(20). In part (h) the infrared radiation is polarized along the ] axis, tht,s one obtains the pure conductivity of the C u e 2 ~lanes: whereas in part (c) the polarization is along the b axis (parallel to the Cue chains) and, like the twinned data, is enhanced due to the presence of the chains. One thus finds that for the pure C u e 2 planes response, tne conductivity well above Tc has a very simple form in YBa2Cu30./ _ y, with no local maximum for ~,~
i

0

i'

In principal, two structural aspects are of potential relevance to understanding the a-b anisotropy of ~(ro)

'0

k.

E "7

v

STAI"F.

cm

,.-..4000 7

"',,

2000

v

2. N O R M A l .

untwinned b axis

:3 b

i

0

r

,

4000

0

8000

-t)

FIGURE ! Thc normal state conductivity (at "f~lO0-200 K) of twinned YBa2Cu307 _y crystals (aL and the resolution .

.

.

A

A

of the conducuvlty rote a and b components, (b) and (c)0 is shown. The data in (a) is from ref. 18; the data in (b) and (c) is from rers 19 & 20. The Tc's for these samples arc approximately 90 K (dotted curve), 80 K (solid curve) and 5.5 K (dashed curve).

in YBa2Cu3~) 7 _ y. YBa2Cu30-/ _y has chains oriented parallel to b, and the in-plane Cu-O bond length is about 2% longer in the b direction than in the ~ direction. Rather generally, a longer Cu-O bond length would lead to a lower conductivity, thus the observed anisotropy is opposite in sign to that expected from the bond length difference. Instead, both the higher A conductivity along h, and the greater complexity observed in this direction, indicate that the copductivity is enhanced by the presence of chains along b. Of central importance, however, is that the conductivity along the ,~ dircction is quite simple for all values o f T c considered here (Tc>55 K).

Z

$chl~in~r et aL/ lnfrar~ ~

of high T¢ ~

~

One might ask whether the same simple form is followed in other high T e superconductors. To address

stale data.

this qucstion, in fig 2 the conductivity in the no.,'mal

conductivity u~ing a conventional [)rude term ~nd a

~tate for l,a~_ xSrx('uO4 (x~O.15), Bi2Sr2(Ta('u20~_ ~.( 1"c',,90).and YBaiCu~O ? _ y (Tc- 92 K and Tc= I~0 K)

often associates the D r u ~

are shown. The l.a a _ xSrxCuO4 data is From Uchida et

contribution to e(m), while tim Lortmtz oscillattxs are

al.(8), the Bi2Sr2CaCu20 ~ _ y data is from unpublished

associated with interhand excitations. One can indeed fit the normal state conductivity for t~.SOO0 o n - I us.

transmission measurements of Mandrus et al. (Stoneyhrook), and is equivalent to the Terasaki data(IO). The YBa2CutO- ~ _ y data are from Schle~nger et al.(19) and Rotter et al.(20), respectively. One sees

that for all these samples the Form of the conductivity is quite similar and quite simplc. On a log-log plot, Otn0~0 can hc sccn to fall like I/mn, with n of about O.7-1. This is a much slower rate of decrease than the

l.et us now consider interp~tat:on, of the normal Onc

approach. Ix~s b~x~ to fit the

~cquence of I drone/ o~cillatot~, in this appro.'tch one

m'm with the intrttmnd

ing a Drude term and 3 additional l,orentz oscillators. Such a fit. using parameters very .~innilarto thole o1" Kamaras cl al.(21) is ~hown in figure 3. Given the number o f parameters available (eleven). it is not sur. prising that this provides a reasonably good fit to the

data.

The additional step of collapsing the (entire)

Drudc tcrm to a Dirac ~S-function at m " O

to fit the

conventional Drudc form. for which n = 2 for frequcn-

~upcrconducting

cies greater than the scattering ratc.

considcrcd( 21). does not work w~il (dashed line. figure

!

3).

~_ 4000 'EE T v

i

o) 4000

Lot.&sSr.ssCuO4

2000

" i

:3

!

0

v

2000

I

b)

c~ v

Bi2Sr2CaCu208_),

's

0

b

2000

3 v

0 0

40O0

c)

E Ls

I

J

been

b

:3

I

i i

ha.~ ako

E c.)

4000 - ? E o "T

~tatc data. which

500 1000 15002000

-1)

YBa2Cu307_y

2000

:3 b

0

0

3000

6000

FIGURE 2 The normal state conductivities of l.a I RsSr ! s(TuO,t (a). Bi2Sr2('aCu20 ~ v (h). and YBa2Cti~OT- V (c) are shown. --" " - •

F I ( H ]RF..3 Attempts to fit the normal and superconducting states using a sequence of I.orent?- oscillators and a Drude tr.rm i¢ e h n ~ v n (~ffer Kamaras et al.(21)). The dot[da~he[i c"~':.e is "the fit to the normal s~ate data (,Wr,er solid curve). The dashed curve i~ a (failed) attempt ~o fit the q~perconducting data hv reducing the width cff the Drude term to O. i.e., collapsing it to a zero fre quency ,S-function. The data are from both refleetivity(19) (solid curve~) and ab¢orptivity(27J (dotted curve), a~ discuesed in the following ~ection (~ee aI~o fig 7).

Z Schlesinger et ag / Infrared properties of high T c superconductors

60

Another approach is to treat all the conductivity below, For example, ~2000 cm- i as a single entity, and to then represent the electronic response in terms of a Frequency dependent mass and scattering rate, as shown in fig. 4. One then finds that the scattering rate is proportional to the frequency for to>T (rel'. 19). This approach reveals a fimdamental relationship between the temperature dependence of the resistivity (linear in T), and the frequency dependence of the scattering rate (linear in ¢,). l'his approach also allows one to readily see a connection between the linear scattering rate as a Function of frequency (energy) and a linear photoemission linewidth as a function of energy, which has also been widely discussed(22-24). One probes single particle response, while the other probes twoparticle response, but both appear to be reflecting the same physics. An apparently related phenomenon is the broad electronic background observed in Raman scattering (23). Together these measurements present a coherent picture of a highly unusual (non-Fermi liquid) normal state phenomenology.

_-'-- 1600

For the Tc-,-90 K superconductors, the phenomenology of the normal state can be summarized quite simply. At o~--0, we know from d.c. resistivity measurements that nln(¢O ) is proportional to the I/T. At higher frequency the conductivity drops with frequency like I/con, with n~-0.7-1. The temperature dependence of O'ln(e) ) iS primarily confined to the frequency range fo<2kT. (For T = 150 K, e. g., this means m<200 cm-1.) These essential aspects of the normal state conductivity are illustrated in fig 5. Finally, we emphasize that unlike conventional metals, where the scattering rate establishes a characteristic energy scale in the normal state, the cuprates with To~90 K show no characteristic energy scale in the normal state, other than kT.

-"" 8000 I

4000

I

E

%. 800

j.=o 0

I

0

I

0

2

Ooo

I

1000

I

(a (cm -1)

2000

o0 o0

"E

00000000( 1 !

0

1000

co (crn-b

2000

FIGURE 4 Scattering rate (renormalized) vs frequency is shown for I al RsSr--CuOd (diamonds), Bi-Sr~('aCu,O~ . (triangles) an~Ba2(.u307 (odes). Also shown m ~art (b) is the mass enhancement as a function of Frequency for YBa2Cu30 7.

FIGI.IRE 5 Normal state temperature and Frequency dependence of the infrared conductivity (schematic) at I00 K (solid), 200 K (clashed) and 300 K (dotted). At low co (<2 kT), ~/n(a~) increases with decreasing T. The sum full'is satislicd by a corresponding very. modest decrease in nln(Cn ) extending over a very wide frequency range (3 kT
Z. $chlesingeret a£ / Infrared properties of high T¢ superconductors 3. S! II~I!R(?ONI)IJCTIN(; STATE For the "l'c~q0 K superconductors, a characteristic energy scale begins to emerge near T¢, and is quite evident deep in the superconducting state. This can be seen both in ratios (fig 6) and in the absolute conductivity (fig. 7). Figure 6 compares reflectivity, transmission and conductivity ratios (superconducting state divided by normal state), for conventional and cuprate superconductors. These data are quite suggestive (of a superconducting energy gap), in that, for cuprates with "f¢-,,90 K, the changes in the low frequency spectra associated gSth superconductivity are quite similar to those seen in conventional superconductors(2-5) and Ba I _ xKxBiO3(25).

1.02

,

I

.

,Lgl~lVand Nb

61

From the ratios shown in Rg 6 characteristic energies corresponding to about 2A/kTc~4 have been inferred for the conventional superconductors. Ph, V, and Nb (2-S). Frnm the 1'c~90 K cuprates, however, the characteristic energy inferred from these ratios is abo~ t 500 cm- t. which corresponds to 2A/kTc~g. (This is where the conductivity threshold occurs.) As an interesting side-issue, we note that the displacement of the peak in 'l's[l"n to higher frequency than 500 c m - t (,-,600-700 cm-~) can be shown to result from the unusually slow decrease of etl(n~) in the normal state. This effects a2(o 0 (through causality) in both the normal and superconducting states and causes the peak in TslTn to occur above the frequency of the conductivity threshold(26). This is different from conventional superconductors where the peak in TstTn occurs very close to 2A (3).

1.04 [ ~ t ' ~ 'fBa;tCu307

\

o~

!

4000 I

1.00 0

15

30

45

0

500 10(30 1500

E U

7

pbd~ P

1.75

1.50

2000

1.50 1.25

b,-

~ 1.25

1.00 .75

1.00

0.75

20

40

0 i

4000

5OO 1000 1500

60

i

,

twinned

(b)

I I

0.9 Pb'

,~,b~,~ 101~02Cu30~'7..

t/t 0.0 3"

0

, 0 20 40 60 0 oJ (cm -~)

500 1000 1500 to (cm-')

E U

2000

0 I

0 FIGURE b Comparison of chan~es due to superconducting transition in certain conventional superconductors(3-5), and cuprates with Tc~90 K. The YBa2('u307 refelctivity ratio is from references 12, 16 and 17. The Bi2Sr2CaCu20 r . transmission ratio is from unpublished data o r - ~ a n d r u s et al.. The YBazCu307 conductivitv ratios are from untwinned crystats using the reflectivity (solid) and absorptivity (dotted curve) data of Schlesinger et a1.(19) and Pham et a1.(27).

1000

2000

(cm-1) FIGURE 7 a) The conductivity of the CuOzplanes in YBa~('u~O7 m' the normat O1,ppe,. .,-,urve .. leO K) and superconducting-" " state (30 K) are shown from a untwinned YBa2Cu30 7 cr3stal(19) (part a). The dotted curve is from absorptivity data (27). In (b) the same quantities are shown for twinned YBa2Cu307 (17,28).

Z, Schlesinger et a L / Infrared properties of high T c superconductors

62

Figure 7 shows superconducting state conductivities obtained from refleetivity(19,17) and from absorptivity measurements(27,28). In part (a) the data are the pure

to al(o0 at the gap frequency(21). This point of view does not seem to have any relevance for the cuprates, simply because the normal state al(a 0 does not fall so

conductivity of the CuO 2 planes, as measured in an untwinned crystal(Iq,27), while in part (b) conductivity

rapidly, and thus there is a great deal o f conductivity even at 500 c m - i as seen in fig 7. In fact there is much

data from a twinned crystal(17,28) are shown. One can

more comluetivity at ~500 c m - ~ than one would expect based on a conventional Drude picture, and the changes

see that significant progress has been made in this low frequency range by studying untwinned crystals, in that the conductivity is now getting much closer to zero in

in the conductivity below T e are in fact quite large, as seen in fig 6 and 7. These changes cannot be explained

the superconducting state than it did for the twinned crystals. In part (a), the solid line is from reflectivity

by collapsing a Drude term to a Dirac ~'~-function, as

data(W) and the dotted curve is from absorption

shown here in fig 3.

measurements(27). The data are similar in that both show clearly the conductivity threshold at ,,-500 c m - 0

acknowledged in the Erratum for reference 21, and as

and both show no evidence for any other characteristic

I believe that the perception o f controversy in the infrared field may be significantly greater than the real-

energy scale within the range o f the data (down to --,80

ity. Often the disagreements between dilYerent groups

cm- 0 For absorptivity).

are based in semantics rather than real differences in dala or physics issues. At this meeting there seems to

From the reflectivity measurement the level of the conductivity is consistent with zero below 500 cm- ' in

be widespread agreement that the way to describe the

the superconducting state. From the absorption measurement a conductivity level o f about 20°,'0 of Crln(O)) can be inferred. It is not clear at the present time if this

of a scattering rate that is linear in fo(19). This point

absorption in the superconducting state is intrinsic, or

YBa2Cu307 _ y and Bi2Sr2('aCu2Og _ y data. This approach has also been adopted by Batlogg (AT&T) in his summary of this conference and in a recent Physics Today article.

iFit is due to poor surface quality. The Maryland group is currently working on improved surface preparation and measurement techniques to address this important question. To date, the crystals which have been studied have had as-grown or polished-in-air surfaces, which are expected to be less than

ideal.

Difficulties with

tunneling and photoemission measurements due to surface quality, especially with YBa2Cu307_y, are well known. To some extent one can get away with studying less than ideal surfaces with infrared because the penetration depth is so large (~150 nm), however, with high precision measurements the issue of ~urface quality becomes increasingly relevant even for infrared measure-

ments. People sometimes ask if it is true that the cuprates are "too clean to see the gap". "l'his idea is predicated on the expectation that the intraband contribution has a conventional Drude form (falling like I/,~2), and that there is there[', e no significant intraband contribution

normal state data for good superconductors is in terms of view was presented by Uchida on Monday for 1.al.l~sSr.15CuO4,

and in the present

talk for the

Regarding the energy gap controversy, I would like to quote from the recent Phys. Rev. B article( I g) on inFrared properties by Orenstein, Thomas, Millis, Cooper, Rapkine, Timusk. Schneemeyer, and Wasvczak, which states that "'the comparison qf one- and two.particle .wectroscopies strongly suggests the existence of a gap o f magnitude 50-60 me It b~ superconductors with Tc~90 K." This is essentially identical to our point of view regarding the gap.

in our work we have found that for

superconductors with To~90 K, there is an absorption threshold at ~60 meV (500 c m - i ) , which can be readily interpreted as an energy gap or pair excitation threshold in the superconducting state. A similar point a view is also taken bv Renk ct a1.(29), who, in very careful farinfrared and microwave studies of YBa2Cu307 _y films, find "'..eridcnce .fi, r a superconducting gap at 2A/kTc'--7

Z, $chlesinger et at / Infrared properties of high T¢ superconductors

63

(",55 nwV)..", and "..no other feature that may he due to a second energlJ gap at lower .frequency. as suggested earlier.".

similar temperature dependencies. This comparison has also been made recently for reduced "f, (~60 K)

The absence of evidence for a lower gap has also been found in the absorption studies o f Pham, Drew et

sual. Possible implications o f these data including their relationship to a normal state spin-gap scenario (dis-

a1.(27,28) and of Miller, Richards et al.(30).

cussed by Fukuyama, l.ee, Rice and other~, at this conference and at the Toshiba school in Kyoto), are

For the

direction perpendicular to the CuO 2 planes however, there is evidence for a lower characteristic energy scale in the superconducting state(16), which is roughly about 10t) -200 c m =. l'hus far the nature, existence or magnitude e r a superconducting gap For the chains, remains an unresolved issue.

Some Raman data from "124"

(lleyen et a1.(31)) suggests a very low characteristic energy (~lO0 cm- )) for the chains.

YBa2('u.a() 7 _ y (Rotter et al.(20)), where the temper. aturc dependence of them quantities is even more unu-

discussed in reference 2t). t)verali, much of the infrared, N M R and neutron data suggest a highly unusual phenomenology above and below "rc, in which the o n ~ t o f phase coherence in euprates may lie somewhere betwcen the gap opening transition of BCS theory, and Bose condensation of preformed pain.

Af'KNOWI.I!I)(;15MI!NTS We have discussed so far two aspects of the infrared data. One is the normal state conductivity which drops unusually slowly as a function of t,) and can be repres-

The attthors acknowledge valuable conversations with P. W. Anderson, II. Fukuyama, M. V. Klein, D.

ented in terms e r a scattering rate linear in at. ]'he other is the ,~uperconducting state conductivity, which exhib-

'l'akigawa, S. Uchida, C. M. Varma and R. li. Walstedt.

1 I. I.ee. T. M. Rice, D..I. Scalapino. ('. P. Slichter, M.

its an energy scale o f ~500 c m - 1 which is unusually large compared to T c. (For "1"c~90 K, 2A/kTc---8.) For the t;uO 2 plane response, this is the only characteristic energy scale in the infrared data, thus if one believes

RFI:!!RI!N('!!S

that there is an energy gap, it is almost certainly asso-

2.

ciated with the 500 c m - ~ (60 meV) feature.

I.

Compar-

isons to data from conventional superconductors (fig

3.

6) show that this feature presents itself in very much like

4.

an ordinary superconducting gap. 5. A filrther aspect of the infrared data which we have

6.

not been able to discuss here due to space limitations is the temperature dependence of this gap feature, in particular one finds that this is quite unusual in that the gap goes away near "I"c by "filling-in"(19), but does not

7. 8. 9.

collapse to lower energy a,~ in the convc:~tional B('S theory. This has been discussed in references 17 & It). and in more detail in ref 32 antl 33 where a two-fluid approach has been considered.

In ref 33 comparison

has been made between the temperature dependence of the infrared conductivity, and that of the relevant planar NMR (or N Q R ) relaxation rates.

These two

quantities (as well the Knight shift) have remarkably

I0. I I. 12. 13.

J. (i. P,c,;,lorz and K. ,~ M~dter, Z. Phys. B6d, 189 ( I q~6) R. I!. (;lover and M. Tinkham, Phys. Rev.lOZl. 8d4 (1956), Phys. Rev. IOS, 2,33 (1957) I) M. (;insherg and M. Tinkham. Phys. Rev.llg, 99O ( 1960} P. I.. Richards and M. Tinkham, Phys. Rev.ll0, .ST.~ (19
Z. Sc.hlesinger et at / Infrared properties of high Tc superconductors

64

14. R. T. Collins, Z. Schlesinger, F. IIoltzberg, P. Chaudari, and C. Field, Phys. Rev.B. 39, 6571 (1989). 15. J. Schutz.mann, W. Osc, .l. Keller, K. F. Renk, B. Roas, i.. Schultz and G. Saemann-ischcnko, Europhysies Lett. 8, 679 (1989) 16. R. T. Collins, Z. Sehlcsinger, F. ltoltzberg and C. Field, Phys. Rcv. Lett. 63, 422 (1989). 17. Z. Schlesinger, R. T. Collins, F. lloltzberg, C. Fcild, G. Koren and A. Gupta, Phys. Rev. B41, 11237

(199o)

|g. J. Orenstein, G. A. Thomas, A. J. Millis, S. L. Cooper, D. II. Rapkine, T. Timusk, [.. F. Schnccmeyer and J. V. Waszczak, Phys. Rev. B42, 6342 (1990) 19. Z. Schlesin~er, R. T. Collins, F. l[oltzhcrg,C. Feild, U. Welp, G. W. Crabtree, Y. Fang and J. Z. l.iu, Phys. Rev. l.ett.6$,801 (1990) 20. I.. D. Rotter, Z. Schlesinger, R. T. Collins, F. lloltz.herg,C. Feild, U. Welp, G. W. Crabtree, Y. Fang, K. G. Vandervoort, S. Fleshler and J. Z. Liu, submitted to Phys. Rev. l.ett. 21. K. Kamaras, S. I.. l[err,C. D. Porter, N Tache, D. B. Tanner, S. Etemad, T. Venkatesan, E. Chase, A. Inam, X. D. Wu, M. S. Hegde, and B. Durra, a) Phys. Rev. l.ett.64, 84 (1990): b) Erratum, ibid, 1962 (1990)

22. P. W. Anderson, in Strong Correlation and Superconductivity, edited by I!. Fukuyama, S. Mackawa and A. Malozamoff (Springer-Verlag, Berlin, 1989) 23. M. V. Klein, ibid 24. C. M. Varma, P. B. l.ittlewood, S. Schmitt-Rink, E. Abrahams and A. E. Ruekenstein, Phys. Rev. l.ett. 63, 1996 (1989); 25. Z. Schlesinger, R. T. Collins, J. A. Calise, D. J. l links, A. W. Mitchell, Y. Zheng, B. Dabrowski, N. E. kickers, and D. J. Scalapino, Phys. Rev. B40, 6862 (I989) 26. R. I". Collins et al.,unpublished 27. F. Pham, M. W. l.ee,D. IL Drew, U. Wclp and Y. Fang, prcprint 2g. 1". Pham, II. D. Drew, S. II. Mosely and J. Z. [.iu, Phys. Rev. B41, l16gl ([990). 29. K. F. Renk et al.,preprint 30. D. Miller, P. I.. Richards et al.,preprint 31. E. T. I[cycn ct al.,this conference 32. D. van dcr Marel, M. Bauer, E. H. Brandt, II.-U. ![ahermeier, W. Koenig, and A. Wittlin, Phys. Rev. B43, 8606 (I 99 I) 33. R. T. Collins, Z. Schlesinger, F. Holtzberg, C. Feild, U. Welp, G. W. Crabtree, J. Z. l.iu and Y. Fang, Phys. Rev. B43, 8701 (1991)