Surface State and Normal Layer Effects in High-& Superconductors

I "2 'W

p i E, cz j \j ED Richard A. Klemm and Marko Ledvij* Materials Science Division

Argonne National Laboratory Argonne, IL 60439

Distribution:

1-2. M. J. Masek 3. B.D,Dunlap 4. G. W. Crabtree 5. A. A. Abrikosov 6. Editoridoffice 7. Authors

and

Samuel H. Liu Department of Physics

University of California at San Diego La Jolla, CA 92093-0319

31-!oQENG3& Accordi ry. the U.S. Government retauw a nonexclushrs. &-fre license to publish or

published form of this contrbution. or alkw we

January, 1996

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsi- bility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Refer- ence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recorn- mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

Invited paper for the Conference on Oxide Superconductor Physics and Nano-Engineering 11, January 27-February 2, 1996, San Jose, CA

To be published in the Proceedings of the SPIE Proceedings, Volume 26%/7

This work is supported by the Division of Materials Sciences, Office of Basic Energy Sciences of DOE, under contract No. W-31-109-ENG-38,

DXSCLATMER

Portions of this document may be illegible in electronic image products. Images are produced from the best available original document

Surface State and Normal Layer Effects in High-Tc Superconductors

Richard A. Klemm and Marko Ledvij" Materials Science Division

Argonne National Laboratory Argonne, IL 60439

and

Samuel H. Liu Department of Physics

University of California at San Diego La Jolla, CA 92093-0319

mntractor of the U.S. Government under contract No. W- 31-109-ENG-38. Accordi ly. the, US. Government retains a nonexclusive. roy#y-free llcense to prWih or

January, 1996

/sm

Invited paper for the Conference on Oxide Superconductor Physics and Nano-Engineering 11, January 27-February 2, 1996, San Jose, CA

To be published in the Proceedings of the SPE Proceedings, Volume 2696/7

This work is supported by the Division of Materials Sciences, Office of Basic Energy Sciences of DOE, under contract No. W-31-109-ENG-38.

Surface state and normal layer effects in high-T, superconductors

Richard A. Klerntn and Marko Ledvij’

Materials Science Division, Argonne National Laboratory Xrgoiine, Illinois 60439 U S A E-mail: richard9rlemmQqmgate. anl. gov

Samuel H. Liu

Department of Physics, University of California at San Diego La Jolla, CA 92093-0312 USA e E-mail: sliu@sdphul .ucsd. edu

ABSTRACT

in addition to the condilcting Cu02 (S) layers, most high-T, superconductors also contab other conducting ( N ) hyers, which are only sgperconducting duL to the proximity effect. The combination of S and N layers can give rise to complicated electronic densities of states, leading to quasilinear penetration depth and NMR relaxation rate behavior a t low temperatures. Surface stat- can also complicate the analysis of tunneling and photoemission meas Jrements. Moreover, geometrical considerations and inhomogeneoilsly trapped A1.x are possible explanaiions of the paramagnetic Meissner effect and of corner and ring SQUID experiments. Hence, ail of the above experiments could be consistent with isotropic s-wave superconductivity within the S layers.

Keywords: superconductivity, proximity, order parameter, surface states, normal layers, penetration depth, pho- toemkion, SQUIDS, Meissncr effect, trapped flux

-

1. iNTRODUCTION

Gecently, there has been a great deal of interest in the symmetry o=* the superconducting order parameter (OPj - - in th: layered high transition temperature T, cuprates. Most studies have been discusscd in terms of an OP A(k,T) of d , ~ ~ z - w a v e [A(k, 7’) = A&?)(&: - &,”) = A&?) cos 241 or of s-wave [A(k,T) = A,(T)] symmetry, or of linear mixtures of the two competing OPs in ortharhombic crystals. Of the -c.aterials studied, by far the largest number of experiments have been performed on YBa2Cu307-8 (Y3CO). In pzrticular, tunneling,l-* YBCO/Pb Josephson tunneling along different YBCO ~ u r f a c e s ~ - ~ and corners,8-’ the temperature T dependence of the penetration depth,’O YBCO/YBCO grain boundary junction experiments in various geometries,11*12 neutron ~cat ter ing,’~ nuclear magnetic resonance (NMR) or nuclear quadrupole resonance (NQR) l/T1 (TI and Knight shift measurements14 below T,, low T measurements of the magnetic field H dependence of the specific heat,15-16 the Raman scattering inten~ities,’~-’~ the angular dependence of the non-linear magnetic torque” with H I E , and the angular dependence of th=. in-plane magnetothermal tra11sport20 have l~een made. While some of these experiments were interpreted in terms of the above d-wave OP, others were interpreted in terms of an s-wave OP, and the present situation is that there BS really no cansens*:s among the experimestal results.

In BiaSraCaCu?Oa+a (BSCCO), experiment; made with tunneling,’’ angle-resolved photoemission spectroscopy (.ARPES),’”-”5 Raman scattering26 low T specific heat,”,’” penetration depth,” and magnetic flus espulsion (Ifeiss- ner e f l e ~ t ) , ~ ~ , ~ ’ gave resulk for the OP that wer;. also inconsistent. Similarly, in La?-,Sr,Cu04 (LaSr214), peiietra- tion depth r n e a s ~ r e m e n t s , ~ ~ Raman s~a t te r ing?~ and polarized neutron scatterin$‘ led to inconsistent results €or the OP. Although single crystals of HgBa2CuO4 (Hg1201) are not yet available, NMR3’ and point contact on polycrystalline samples have led also to different conclusions regarding the OP. To date, only one rather inconclusive esperiment relevant to the order parameter is -.-.ailable for the tetragonrJ Tl?BazCuOG+h system3‘.

However, in Ndl s5Ceo 13Cu04 (XCCO), penetration depth X and sL.-face impedance experiments3” are quantita- tively in agreement with the Bardeen-Cooper-Schrieffer (BCS) theory of an s-wave superconductor, and point contact tunneling experiments3’ are at least qualitatively consistent with that interpretation. Thus. escept for SCCO. in all of the materials studied to date. no consensus has been obtained as to the symmetry of the OP.

Here we argue that intrinsic and/or extrinsic complications are present in many. if not most. of the materials studied. In particular, we shall esamine the intrinsic properties of surface states and normal layers. which can greatly complicate the analysis of many experiments. In addition, extrinsic effects arising from specific sample geometries.

The submitted manuscript has been authored by a contractor of the V. S. Government under contract No. W-31-104ENG-38. Accordingly. the U. S. Government retaim a nOnexclUdVe. royalty-free license to publish or reproduce the published form of thor contribution. or ailow others to do so, for i U. S. Government pwposes.

inhomogeneous stoichiometries, and inhomogeneously trapped flux can explain the apparent phase shifts observed in some superconducting quantum interference device (SQUID) and junction experiments. Hence, we shall conclude that even isotropic s-wave superconductivity cannot be ruled out by the experiments to date.

2. THE SN MODEL

In LaSr214 and NCCO, the evidence is pretty strong that the only conducting layers in the crystals are the CuOz layers. However, the presence of spin fluctuations in LaSr214 can cause coinplications in the analysis of many physical properties (such as the Raman scattering). In YBCO, on the other hand, in addition to the two conducting Cu02 planes within a unit cell, there is overwhelming evidence that the CuO chains are also conducting. This is -- true both in the normal state, as evidenced by the resistivity measurements on ujktwinned single c r y s t a l ~ ~ ~ and by direct observation of the chain Fermi surface in positron annihilation experime~lts ,~~ and in the superconducting state, as evidenced by measurements of the in-plane anisotropy of the penetration depth in untwinned by point contact tunneling directly on the chain sites,43 and in neutron scattering indications that the chains exhibit a supercondccting gap.44 In BSCCO, the situation is less ckar. Local density approximation (LDA) cdculations4' predicted that the BiO layers ought to be conducting, but the la& of a linear term in the h w T sDecific suggests that they might not be in the bulk. Moreover, point contact tunneling on the tup biO surfa;e2' indicated that the top BiO layer band lies above the Fermi energy EF by about 60-80 meV. This small Bi-0 energy gap is likely sample dependent, since overdoped samples of BSCCO a p e x to exhibit normal state resistivities along the c-axis which are suggestive of metallic behavior.46 As i t k well known that BSCCO is stable with a large range of stoichiometries, it is therefore likely that the BiO layers are spatially inhomogeneous, with conducting islands within

- semiconducting regions. In addition, structural transitions associated primarily with the BiO layers are known to be present in a number of BSCCO-type corn pound^,^^-^^ with many phase transitions occuring over the temperature range relevant for supe rcondu~ t iv i ty~~ and the overall structure is most probably m ~ n o c l i n i c . ~ ~ * ~ ~ The situation in

- iIg1201 is somewhat similar, as suggested by NMR and point contact tunneling e ~ p e r i r n e n t s . ~ ~ ~ ~ ~ LDA calculations predicted that the Hg-0 layers were above EF, but gave widely different values for the gapp50*51, varying between 1.2 eV and 0.26 eV. Hence, it is quite possible that the Hg-0 chains have b a d s which lie very close to EF, and

- inhomogeneous oxygen concentrations might lead to regions of both metallic and semiconducting HgO chains layers. ' Thus, we have modelled these high-T, superconductprs as SN multilayers. For simplicity, we assume only one

CuO2 (S) layer and one nominally normal conducting ( N ) layer per unit cell, which becomes superconducting only Secause of its proximity to the S layers:. For simplicity, we assume zoherent interlayer hopping parmaeters 51 and 52 across the insulating barriers of thickness ti and d' = s - d. The H;zmiltonian is thus taken to be H = Ho + V , where

-

--

--

are the single quasiparticle Hamiltonian and the pairing interaction forming either s-wave pairs with Xk,kl = A0 or dZ2-,,2 pairs with &k' = 2x0 COS28k cos 28kJ within the s ( n = 1) layers for energies within w11 of EF. In Eqs. (1)

the jth unit cell, and we have set h = c = k~ = 1. The model described in Eqs. (1) and (2) is pictured in Fig. l(a). The &(k) represent the relevant (metallic, or nearest to E F ) quasiparticle energy bands on the different layers, relative to E F . This general model is a simplification of a more complicated one,52 but contains all af the important phvsics with many fewer parameters. Here we consider two versi0.s of this general model.

and (21, +jna(k) [djno(k)] t annihilates [creates] a quasiparticle with spin (T and wavevector k within the nth layer in

2.1. The SN model with equal Fermi surfaces

In Model (A): we take

2.0

1.5

w' 1.0

' 0.5

( .

0.0 9.

t ,

,87 0.92 0.9 k a h

7

- Fig. 1. (a) Schematic view of the two-layer system, with pairing in the S layers, and hoppings J1 and J2 between the S and N layers. (b) Quasiparticle energy dispersion along the direction 6 = 60' (see inset), for YBCO Model (B) with dimensionless parameters t = t' = 25, p1 = p2 = 20, tar = 2, and t 2 y = 25, relative to TCo, as a function of !kla/z. Dashed: normal state. Solid: A = 1.6 (T << Tc). In inset, dashed (solid) curves are normal state Fermi surfaces with JI = J2 =- 0 (J1 = J 2 = 0.5).

where 0 = m1/m2. This model is chosen for simplicity, as the two layers -Save identical Fermi surfaces in the absence - of inkslayer hopping. The parameter p can simulate both the number of and the effect of strong correlations within the S layers, which typically require53 p x 5. Since the Fermi surfaces of the S and N layers in Model (A) are identical, the proximity coupling between these layers can be extremely ctrong: The low-T dependence of properties - depending upon the quasiparticle density of states (DOS) will behave a3 T'12 for J1 = Jz, unlike the experiments. We therefore choose J1 # J2, which splits the bands, weakening the proximity coupling. This approach is also useful in describing surface states. This model can describe the c-axis versus a - b plane X acisotropy, but cannot describe-- any in-plane X anisotropy.

2.2. The SN model w i t h planes and chaims -

In Model (B), we 'assume the quasiparticle dispersions are given by

We generally take pl = p? = EF. This model czil closely approximate the Fermi surface of YBCO, with quasi-two- dimensional S layers and a quasi-one-dimensional N layer. The parameters must be chosen to be consistent with ARPES measurements and/or LDA calculatious. In the inset of Fig. l(b), such choices were made. Note that in Model (B), the Fermi surfaces can only intersect at a finite number of points, so the proximity coupling is much weaker than in Model (A). Hence, one can choose Jl = Jz, a t least with regard to bulk properties. Nevertheless. it is clearly seen in Fig. l(b) that the the energv gap is zero above T, and lies on the Fermi surface. However, below T,. the gap is non-vanishing, but its position moues 08 the Fermi surface! Hence, a determination of the actual energy gap function and the OP is greatly complicated by the presence of normal layers.

2.3. Bulk Properties

The specific heat CV is a fundamental, bulk property of a solid. In ordinary superconductors, one expects Cv(T) - T3 as T - 0 from phonons. In YBCO, however. in addition to a Schottky anomaly due presumably to

Cu+* S = spins, Cv(T) - y(0)T + pT3. The 7(O)T term is obtained when a finite portion of the Fermi surface is gapless. From the inset of Fig. l(b), the chain band is gapless where the bands are well separated. Hence, Model (B) can explain the yT term generally observed in YBC0.15*16 Paramagnetic impurities arising from oxygen vacancies on the CuO chains could also explain it.43 If the OP had line nodes, CV(T) should also have an crT2 term. However, no aT2 term was observed in YBCO." While rather strong Hilt dependence of y was o b s e r ~ e d , ' ~ ~ ' ~ few data points at low H were taken, and the H = 0 datal5 were adjusted to y'(O)T + aT2 + p'T3, by assuming y(H)-y'(O) oc H1I2 for a d-wave superconductor, with acorresponding (non-observed) aT2 term at H = 0. Without making this assumption, the data are also consisteat with 7 ( H ) = ~ ( 0 ) t 71H - 72H2, which could be consistent with s-wave superconductivity. Hence, the significance of these CV(H < 2") data is presently unknown. Moreover, the non-:inear H dependence of the transverse magnetization at various angles with H I2 in the Meissner state has been studied on disk-shaped untwinned YBCO singie crystals, and no evidence for nodes of the OP was ob~erved.~'

We remark, however, that the low-T, H = 0 specific heat in BSCCO exhibits neither a y(0)T term nor an aT2 could prove useful. The linear T dependence of the penetration depth2' and the ARPES appear to suggest that the gap might have nodes, but the specific heat contradicts this interpretation.

The T dependence of X in twinned YBCO sin& crystals has been studied,1° and the low-T behavior was found - to be consistent with Model (A) for either s-wave or d-wave s~perconductivity.~~ In that calculation, it was shown : that fitting the in-plane X a b ( T ) with either OP form led to distinctly different predictions for the out-of-plane X,(T). However, both types of behwior were observed in YBCO and in YBa2Cn408, confusing the i s s ~ e . ~ ~ ~ ~ ~ To further-: elucidate the nature of the chains, data on untwinned YBCO have recently been taken.57 These data showed linear j A,(T) and Xb(T) 1ow-T behaviors, and X,(O) and Ab(()) differed by about 50%57 or more.' We tried to fit these data 1 qualitatively by employing Model (B):a as did Atkinson and C a r b ~ t t e . ~ ' It is difficult to fit the data with either s-T or d-wave superconductivity. While the d-wave model readily fits the linear X,(T) and &(T) low-T behaviors, the difference in their magnitudes is very difficult to fit, except for some Fermi surfaces similar to those predicted by the : LDA. These difficulties are only slightly more pronounced for s-wave superconductivity. We chose the parameters-' listed in the caption of Fig. 2. In Fig. 2, the resuits for our calculatiovs of Xa(T), X b ( T ) , and &(T) for s- and '

d-wave superconductivity are shown, and are all qgalitatively consistent with the data.56*s7 Hence, we conclude that . the in-plane anisotropy &,(o)/&(o) and the rather linear X(T) behaviors zbserved at low T can be explained withf realistic models of either s- cr d-wave superconductivity.

This fact strongly suggests that BSCCO is nodeless, an& that specific heat measurements with HI12 -

T / T C 0.0 0.2 0.4 0.6 0.8 1 .o

T / T c

Fig. 2 . Plots of AZ(T)/A:(To), Af(T)/Af(To), and Az(T)/Xz(To) versus T/Tc (solid curves) for Model (B) u-ith the dimensionless parameters t = 25, t' = 20, p1 = pz = 15, tZr = 8, t z y = 25, J1 = 1.5, Jr, = 0.5. relative to Tco, and To = O.OITc. (a) s-wave pairing, Dashed curve: standard BCS model. (b) d,Z+ pairing. Dashed curve: standard d-wave model.5d

3. SURFACE SENSITIVE PROPERTIES

Two of the most often cited classes of experiments relevant to the OP symmetry in the cuprates are tunneling and ARPES. In YBCO, ARPES experiments above and below T, have not generally been successful in observing the quasiparticle energy gap, and did not observe the CuO chain Fermi surface either. Moreover, SIN tunneling between YBCO and a normal metal have generally shown quite gapless behavior.' In addition, c-axis YBCO/Pb Josephson junctions have led to pr*-ducts IC&, of the critical current I , and the normal resistance R,, well below thc standard Ambegaokar-Baratoff (AB) r e s ~ l t . ~ - ~ The combination of the above strongly suggests that there is some sort of normal top surface layer of YBCO, even below T,.

3.1. Bilayer model

In Model (C), we treat YBCO as a bilayer, with an N layer on top of an S layer,6o as pictured in Fig. 3(a). In -

c-axis Josephson and SIN tunneling, the conventional superconductor St is situated on top of the N S bilayer, with an insulating ( I ) junction in-between, leading to an overail S'INSjunction, with a tunneling matrix element Tq,k across the I junction. We assume the N aad S layers have idenrical Fermi surfaces, but different pairing interactions. In -- addition, the N and S layers are weakly coupled with effective hopping energy J . In Model (C), we have calculated I,& as a function of J/Tco, assuming s-wave superconductivity in both the S and St superconductors, where

-- T,o E T,(J = 0). Our results relative to that of AB are shown in Fig. 3(b). In the iimit of large coupling, IC& - approaches the AB limit. For finite coupling, it is always.less than the AB limit, as observed in experiment^.^-^ IcR,,/IcR,(AB) is about 0.2 in untwinned single crystals, but it is smaller in twinned samples. In (heavily twinned)

- thin films with the number of twins per junction Nt > lo5, the ratio is decreased by about a factor of lo2, suggesting -- that the coupling decreases more slowly with Nt than Ng-"2. Clearly, these data can be explained from purely s-wave superconductivity, in which the twins alter the low-energy density cf states of YBCO in the superconducting state. It remains to be seen whether these data can also be explained by a pure d f s state in YBC0,61 or whether surface and normal layers as we have considered are also required to explain the data. This is especially true in view of the gapless S I N tunneling behavior observed in YBCO,' as discussed ir the following.

-

-

I

I _ _ N S

J

0.0 c

0.0 0.5 1 .o 1 .>

JfL Fig. 3. (a) Schematic view of Model (C). (b) Plot of IC&, relative to the Xmbegaokzr-Baratoff result. as a function of J/T'o, for Model (C).60

3.2. Surface states

In addition to the spatial variation of the pairing interaction, other types of intrinsic surface effects are possible. In a n S-\- multilaver, it matters whether an S or an .V layer is on top. In the S surface case, the top S layer Tc (and the corresponding gap) is higher than in the bulk, as it is decreased from Tco by its proximity to only one adjacent

.V layer.62 Conversely, when the N layer is on top, it is less superconducting than the S layers in the bulk. These differences are enhanced by the presence of surface sfates . Of these, the simplest are of the Shockley

type, for which the atomic positions, electrostatic potentials, and pairing interactions do not vary spatially, except for the introduction of the vacuum at the surface. Such Shockley states were recently predicted to occur in NCCO in LDA calculation^.^^ We consider a simple extension of Model (A) in which &,I = €02, J1 # 5 2 , and take /3 = 1 for simplicity. This is a simplification of a more general model of three or more layers per unit cell, for which two or more effective hoppicgs x c u r naturally. For the effective two-layer systems, we then have two models. l a Model (Dl) , we assume the layers end interlayer hoppings are ordered from top to bottom according to S J ~ N J ~ S J L ..., and in Model (D2), we have N J ~ S J ~ N J I .... In the normal state above T,, these models are equivalent. It has been showp62 that a band of surface states can exist if J l / J z < 1. For inequivalent J,, values, the two Fermi surfaces are split by the hopping, and the surface states lie halfway in-between the Fermi surfaces. The surface charge density is

_. localized near the surface, and decays and oscillates with the distance from the surface. Hence, the largest elecaronic - density occurs on the top layer.

For T < T,, the role of surface states can be very complicated. When an N layer is on top, the enhanced charge density due to the surface state causes the superconductivity to be suppressed on the surface. In Fig. 4(a), we have pictured the S I N tunneling DOS expected for this case of Model (D2). Note that the DOS is very gapless, with- a zero-bias conductance (or central DOS) which is a large fraction of the normal state value. This is exactly as observed in S I N tunneling experiments on YBCO.'** Hence, the excellent agreement strongly suggests that the top surface of YBCO is normal. This conclusion is alsc supported by the fact that numerous workers have been unable to observe a reliable superconducting gap in YBCO in ARPES experiments.

1 6

.-

i 4 - 3 - 2 - 1 0 1 2 3 4

Fig. 4. (a) Density cL states N,(w), re.dtive to t,.e norma. state value X f O ) , for t he Model (D2) with the *V layer on top, as a function ofw/Tco, assuming'~ J3 = 2J1 = O.tiT,, and S = 1. (b) Schematic view of the charge density of the surface states for Model ( D l ) with the S la?-er o n top. and with Jl(k) given by Eq. (5 ) .62

On the other hand. when the top layer is an S layer, the enhanced electronic charge density associated with the surface state will make the superconductivity appear to be more pronounced than it is in the bulk. Since the gap on the surface is larger than in the bulk, surface sensitive measurements will favor this enhanced surface gap. In BSCCO, for example, it is possible that the top BiO layer could be a narrow gap semiconductor. as evidenced by scanning tunneling microscope measurements.21 In that case. if the internal BiO layers are nominally S layers. the top surface'layer would be an S layer, and surface states could complicate the analysis. Furthermore, from LD-A

calcuLAons,45 the interlayer hoppings depend strongly upon the intralayer wavevectors k. One scenario consistent with the LDX would be for Jl(k) and J?(k) to satisfy

Jljk) 52 + 6 J - J'I C O S ~ , U - C O S ~ , U ~ . (5) where 5' > 0. In the case 6 5 = 0, J1 < 5 2 except at R , = fk,, at which points the spectral weight of the surface states (and the apparent superconducting gap on them) vanishes. This is pictured in Fig. 4(b). If 25' > 65 > 0, the spectral weight of the surface states (and their gap function) vanishes over a finite region of the Fermi surface, as claimed in some recent experiment^.^^^^' For different 6 J values, the surface states could vanish completely, or lead to an apparent nodeless but anisotropic gap function. 'rhus, even an isotropic s-wave surperconductor can appear to be highly anisotropic, appearing to exhibit nodes or even finite regions of vanishing gap in ARPES experiments, due to the presence of surface states.

Another possible explanation of the ARPES experiments in BSCCO arises from a detailed analysis of the ARPES data on NCCO, for which the group symmetries of the various electronic Cu02 bands in the vicinity of EF predicted . by LDA are and for which the polarization dependences of the experimental collection directions were reported in detail.65 It has recently beer. argued that in the vicinity of the M point in NCCO (roughly equivalent to the X or Y points in YBCO, or the by the LDA, with a different symmetry than that along the I' - X (or r - S in YBCO) direction6' predicted in strong coupling calculations. This band is observable in ARPES experiments because the surface breaks the matrix element selection rules which ordinarily would require the elecironic states to be even under reflections about the. plane containing a CuOz layer (parallel to the sample surface). When the most important planes contributing to the scattering intensity lie on or near to the surface, this symmetry is broken, and these states are allowed. It is noteworthy that these states are quasi-one-dimensional in the real space representation, so that they are susceptible to charge density wave formation and structural transitions, such as the Martensitic transitions in the A15 compounds. Evidence for charge density wave transitions associated with the chains (which are most important in the vicinity of the Y point in the Brillouin zone) have been r e p ~ r t e d ~ " > ~ ~ in YBCC, and may be r e s p ~ n s i b l e ~ ~ - ~ ' for the behavior - in the vicinity of the M (BiO plane) regim in BSCC0.66 In addition, a recent report24 that the ARPES observation of the apparent opening of the quasiparticle gap occurs at a temperature Tg > T, is intriguing. In oxygen deficient BSCCO, T, decreases with oxygen deficiency, but Tg does not. This strongly suggests that the 'gap' observed in- ARPES experiments may in fact be unrelated to the superconducting gap. A recent ARPES measurement66 on thin films of BSCCO elucidated that the shift in the quasiparticle dispersion occurs over a wide range of wavevectors in the vicinity of the % point in the Brillouin zone. In fact, those authors showed that the 'gap' actually was maximal at g , 08 the Fermi surface! This is ceI-tainly not what would ordinarily be expected for a superconducting gap. Hence, further experiments on underdoped BSCCO ought to be carried out to determine if Tg and T, are really independent of each other, as currently suggested.24

paint in BSCCO), the band consistent with the data could be that predicted ..

4. INHOMOGENEOUSLY TRAPPED FLUX

The paramagnetic Meissner effect (FME), also known as the Wohlleben effect, occurs when the field-cooled (FC) magnetization is positive3' below T,. This has been seen in melt-cast polycrystalline samples of BSCCO, and in one single crystal of YBC0.67 The PME in polycrystalline BSCCO was claimed to be a feature of d-wave supercond~ctivity.~~ However, the effect bas recently a1.m been seen in Nb disks.6" Those authors showed that the effect was intimately connected with the surface properties, as polishing the surface caused the PME to vanish. They also found that the zero-field-cooled (ZFC) magnetization exhibited a knee just below T, prior to polishing, which disappeared after polishing. Hence, they attributed the effect to the surface having a lower T, than the bulk. Independently, at Argonne we have reproduced their main results in two samples6' taken from stock BV, pictured in Fig. j(a). However, in two other samples taken from stock KG, a slightlv different effect was observed. In Fig. .J(b), data taken on a S b disk are shown, both before and after polishing the top and bottom surfaces6' It is seen that the FC magnetization dips diamagnetically just below T,, and then becomes paramagnetic at lower 5". After polishing, the effect disappears. However, the ZFC magnetization results in a lower T, after polishing, so that the surface initially had a higher T,. Evidently, the PME is observed when the sample surface has either a higher or a lower T, than the bulk value. This is not yet understood. but there is compelling evidence that inhomogeneously trapped flus combined with inhomogeneous surface stoichiometries are mainly responsible for the PNE. \Ve note that the cuprates are notorious in exhibiting inhomogeneous oxygen stoichiometries, especially near to surfaces6' and/or grain boundaries. In any event, the observation of the PME in S b clearly shows that the effect is unrelated to d-wave superconductivity.

I

0 . 6 0 . 2 -

I

0.4 1 5 0 . 2

0 f 0 T- v

E - 0 . 2

-0.4

-0.6

0

- A 3

$ -0 .4

? 0 T ‘E -0.8

- 1 . 2

1 ---+--t-.-t I :- ZFC in 0.0‘ Oe ----”.-,

A I I I 1 I

I I

h

3 0.1 E al

0

E -0.1

h

2 Q,

0

‘r -0.4 0 l- v

E -0.8

-1.2

I 1 FC in 1 Oe

8.8 3 . 9.2 9.4 9.6 8.8 9 9.2 9.4 9.6

T {K) T (Ki)

Fig. 5. Plots of M(T) of a Nb disk in a perpendicular Circles (triangles): Data taken before (after) polishing top and bottom surfaces. (a) Sample from stock BK. Upper: FC in 4 Oe. Lower: ZFC in 0.01 Oe. (b) Sample from stock KG. Upper: FC in 1 Oe. Lower: ZFC in 0.01 Oe. Inset: ZFC curves for another sample from stock KG.

-.

. Since the PME is most likely due to sample Tc inhomogeneities and inhomogeneously trapped flux, one might wonder whether such problems might also help to explain the SQUID experiments that have been widely cited as ‘smoking guns’ for d-wave supercond~ctivity.~-’*~~ Of these, flux trapping problems appear to be the strongest in the corner SQUID experiments,”.’ especially due to the sample corner^.^^*^^ In that latter e~pe r imen t ,~ a corner junction was made on a rather flat YBCO sample in a perpendicular magnetic field, and the I,(B) curve was recorded. The appearance of a dip in the low-field region of I,(B) led the authors to claim evidence for d-wave superconductivity. However, such a dip has been seen in S N S junctions prepared with conventional material^,^^ provided that a voTtes was trapped near to the center of the junction. This was explained by a *-phase shift arising from a monopole vortex73 entering the junction from one of the S layers and exiiing the junction in all directions within the iV layer. A ?r-phase shift in the critical current was also predicted by those authors73 for the interesting case of a dipole vortex consisting of two monopole vortices, with a ‘jog’ of the vortex within the N layer. Using this model. the locations of a dipole vortex inexplicably pinned near to the center of the SNS junction and of a moveable monopole vortex were precisely determined. When the monopole was located near to the center of the junction, the dip in I,( B ) a t B = 0 was so pronounced that I c ( 0 ) vanished!

More recently, such a dip has also been seen in a c-axis YBCO/Pb junction. in which one f l u s quantum was deliberately trapped in the j~nc t ion . ’~ In corner SQUID experiments,’.‘ the junctions were prepared as symmetrically as possible about the sample corner. Since magnetic flux naturally prefers to be pinned at sample corners both in conventional and cuprate superconductors,i4 it is highly likely that flux will be trapped at the YBCO corners in such SQUID experiments. As the corners are the central regions of the junctions. this situation is entirely analogous to that observed in conventional SXS junctions.“ Hence. it is quite likely that inhomogeneously trapped magnetic flus could explain the corner SQUID experiment^.^*^ Further experiments should thus be made to prove explicitly whether or not the results of those corner junction experiments’,’ are actually due to inhomogeneously trapped flux.

lyhether such a scenario could possibly explain the YBCO tricrystal ring esperiments” and the somewhat

._

more convincing Maryland \-BCO/Pb square SQUID experiments,7 remains to be seen. One interesting possibility is that a single flux quantum might lie entirely within the ring or SQUID, making its observation by a moveable SQUID microscope held in a fixed angular configuration difficult. If the hidden vortex exhibits a sideways jump at one of the junctions due to inhomogeneous flux trapping, an effective x-phase shift could occur,73 leading to a spontaneous appearance of a half-integral flus quantum contained within the ring. In any event, such experiments mmt be reproduced in another laboratory, as the results are not obviously compatible with those of c-axis Josephson t ~ n n e l i n g ~ - ~ and H I 2 magnetic torque experiment^.'^^^^ While the possibility remains that s - d mixing might be Compatible with all of the experiments on YBCO, the fact that an s-wave component of the OP has now been established by two experimental groups3-$ indicates that if nodes are present in untwinned YBCO, they most likely do not occur at 45’ from the Cu-0 bond direction in the CuO2 planes. This point is an interesting one, since it could very well mean that the tricrystal ring experiments12 on YBCO are actually incompatible with the c-axis Josephson tunneling experiments. It would be most interesting to attempt to reproduce the Maryland YBCO/Pb SQUID experiments7 with untwinned YBCO thin films.

5. SUMMARY

The high temperature superconductors are complicated materials. There are intrinsic structual complications, such as conducting chains as well as planes, which occur in YBCO and related materials. In addition, there are extrinsic problems, such as axygen inhomogeneities, which lead to local variations in T, and probably to local regions of conducting and semiconducting additional layers (such as the BiO layers in BSCCO). In addition, there are structural phase transitions, such as charge density wave transitions, and other more subtle transitions, which can greatly complicate the analysis of the available data. Furthermore, magnetic flux is extremely difficult to eliminate from these materials, and i t prefers to trap near the sample corners. The combination of these complications is really pretty hard to overcome. In essence, the svmmetry of the order parameter in the cuprates remains a mystery.

6. ACKNOWLEDGMENTS

The authors would like to thank J. W. Allen, R. C. Dynes, K. Gofron, A. M. Goldman, N. E. Phillips, and- B. W. Veal for useful discussions. This work was supported by the U. S . Department of Energy, Division of Basic Energy Sciences, under Contract No. W-31-109-ENG-38.

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