Thermal fluctuation of the order parameter symmetry in high Tc superconductors revealed from the penetration depth measurement

Solid State Communications,Vol. 105, No. 3. pp. 155-159. 1998 Q 1997 Elsevier Science Ltd Printed in Greet Britain. All ri ts reserved 0038- 1098l9f s19.OOt.00

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PII: soo38-1098(97)10098-9

THERMAL FLUCTUATION OF THE ORDER PARAMETER SYMMETRY IN HIGH T, SUPERCONDUCTORS REVEALED FROM THE PENETRATION DEPTH MEASUREMENT Li Jui Chen and Juh Tzeng Lue Department of Physics, National Tsing Hua University, Hsinchu, Taiwan (Received 22 August 1997; accepted 26 September 1997 by T. Tsuzuki)

A dielectric microwave resonators operating from 20 K to 70 K has been used to measure the temperature dependence of the penetration depth A(7) for the high-T, superconducting YBa2Cu307-6 and T12Ba2CaCu207 thin films. A T* dependence occurs at low temperatures and an exponential dependence at high temperatures. An impurity scattered d-wave with admixture of s-wave due to thermal fluctuation is proposed for the pairing states of those high T, superconducting films. 6 1997 Elsevier Science Ltd Keywords: A. high T, superconducting films, C. order parameter, E. microwave penetration method.

Although a number of theoretical investigations have proposed that d-wave symmetry of the pairing state occurs in high T, superconductors [ 1, 21, there is presently no real consensus on this issue [3]. A second intriguing possibility is the proposal of the s and ds _Y2 mixed waves [4-61. Experimental studies on the change of penetration depth X(T) for a high quality YBa2Cu307_a (YBCO) single crystal in low temperature limit indicated a strong linear dependence [7], which are concluded to be a clean d-wave superconductor with line nodes on the Fermi surface. Recently, a parallel plate microwave resonator technique for measuring YBCO thin films shows a T* dependence on the X(T) between 10 and 25 K, accounting from impurity or defect scattering of the d-wave superconductor [8]. A model of a small admixture of an isotropic s-component to the dg -9 wave which does not increase the number of nodes but merely displaces the node away from the original 45” angular position of the node [9] and a s-wave component induced around a vortex in dg _y2 wave with a distribution function of a four-lobe clover [6, lo] are proposed. Other experiments 11l] have indicated that the order parameter in high T, superconductors is highly anisotropic. However, these experiments have conflicting features. Recently some important works by Jacobs’ group [12] suggested that the temperature dependent R,(T) and A(Z) can be explained by a weak-coupled dg _,,I order parameter in the form of A(T, VP)= can Ad(T) cos (2p)which satisfactorily fit the

experimental data by a modified energy gap A,,(O) = 2.16 kT, in a wild temperature range with respect to the crossover from the d- to s-behavior. There seems no incontrovertible evidence to determine the symmetry of the order parameters without ambiguity [9]. (a)

sapphire

coupling

loop

le

cooler @I

Dielectric

Rod 7

HTSC films

Fig. 1. (a) Structure of the dielectric resonator composed of HTSC films and dielectric material (sapphire). (b) The TEai, field pattern of this dielectric resonator.

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THERMAL FLUCTUATION IN HIGH ?‘, SUPERCONDUCTORS

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Vol. 105, No. 3

1.500

1 .ooo

,” s u 0.500 .-5 -w 0 Q) u2

0.000 c.++.ea 70 K s 67 K 65 K o+++a 64 K 63 K ,111111111,111111111)111111111111l”””l””l””l~”’~“= 28.78 28.77 28.76 28.75

-0.500

frequency

60 K 50 K 40 K 35 K 20 K

28.79

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Fig. 2. The resonant frequency increases as the sample temperature decreases resulted from the contraction of the penetration depth and the cavity size. 600.0

, 4

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.

---

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egperimental data T fitting (low temp. GC eq. fitting MB eq. fitting

region)

11

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I’

1

50.0

“““‘I”“““’

60.0

7c 0

(K)

Fig. 3. The calculated AA(Z’)and theoretical fitting for the data from the Tl-2212 superconducting film, the inset is the SQUID data.

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THERMAL FLUCTUATION IN HIGH T, SUPERCONDUCTORS

In this work, we attempt to measure the temperature the s I I reflection signal. The whole cavity is cooled down dependence of the penetration depth X(2’)for the high T, from room temperature to 12 K by a closed-cycle helium YBCO and TlzBa2CaCu207 (Tl-2212) thin films by a refrigerator. As the temperature decreases, the resonant microwave dielectric resonator. This X(T) measurement frequency shifts to a higher value predominantly due to yields information regarding the pairing states in the the reduction of penetration depth of thin films and material. This experiment clearly reveals that A(T) copper wall and is plotted in Fig. 2. Meanwhile, the follows the d-wave symmetry at low temperature coupling between cavity and transmission line change regions and becomes more prominently to be fitted by from undercoupled to overcoupled resulting from the the BCS symmetry at high temperatures near the critical increase of the Q-value of the cavity. temperature T,. It seems plausible that the pairing state is To extract the change of penetration depth from the fluctuated from a pure d-wave to a mixed s- and d-wave frequency shift, the formula derived from the Slater shape perturbation theory is given by [ 161 and then approach to a pure s-wave as temperature increases. 6w 2&w.Ap + &AX + A2/2)] -= To explore the surface resistance R, and the change (1) W wo of magnetic penetration depth AX(T), a dielectric microwave resonator [ 13-151 consisting of a small sapphire where Ap(7) and &z(T) are the size change of the copper rod sandwiched by two high T, superconducting films is cavity in the radial and azimuthal directions, W is the constructed as shown in Fig. l(a). The cavity is prefer- total energy stored in the cavity, including those stored entially excited by the fundamental TEoi I mode by which inside and outside the rod, gs and gw are two constants the EM fields are mostly confined in the sapphire rod due related to the slight change of stored energy respectively, to its high dielectric constant, while with low current loss on the film surface and copper wall due to cavity on the outside copper wall, resulting in a high Q-value as contraction. In the case of local limit that the superconducting shown in Fig. l(b). The input antenna is a current loop coherence length E is much smaller than the London connected to a HP 8510 network analyzer by a coaxial penetration depth X, i.e. 5 < X, the AA(T) calculated by transmission line and 2.4 mm connectors for detecting

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1 I I I1

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20.0

I,,,,,,,,I,

,,,(I,,,

25.0

Temperature

I,,,,,,r

,I,,,,,

30.0

(K)

35.0

Fig. 4. The same data of the above sample but stored for two months in a dry box.

4( 0

THERMAL FLUCTUATION IN HIGH T, SUPERCONDUCTORS

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Vol. 105, No. 3 1

l .0.. AAAAA

virgin film exposed in air T* fitting MB fitting

(low

for

12

temp.

h region) :

~300.0 f

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x

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32.00

34.00

Temperature

36.00

38.00

40.00

(K)

Fig. 5. The AX(T) of the YBCO thin film. The magnetization shows that it contains less impurities or defects than the TIT2212 film. Mattis and Bardeen (MB) [17, 181 for a s-wave (BCS) pairing states excited by a finite energy, is given by NT)

--

X(O)

3.33

0 +

112

exp ( - AL?,

(2)

where A = aT, is the energy gap at 0 K, which is equal to 1.76T, as derived by Miihlschlegel [19] and A)\(T) = X(T) - h(O). MB equation is appropriate for most pure elemental and Al5 superconductors. However, in a MB fitting of AA(T) for high T, superconductors (HTSC), (I!may span a range from 0.4 to 3 and does not reveal any definite value in some experiments 120, 211. Another possible mechanism is the Gorter-Casimir (GC) relation 1221derived from the two fluid model as given by

3$

[l-(;)4]-“2.

(3)

However, the GC relation is closely related to the BCS theory [ 18. 231. If there are line nodes on the Fermi surface, AA(T) is calculated to be proportional to Tp [24],

in which p = 1 for the simplest form of a gap with the d-wave. An impurity or defect scattering can change the T dependence to T2 [S, 25,261. In general, powers of T, T2, T3, T’ are possible depending on the type of nodes and the orientation of the applied fields with respect to the crystal axis [24, 261. The experimental results of the temperature dependence on the change of the penetration depth A.X(T)= X(T) -X(20K) for the T12Ba2CaCu207 thin films prepared by laser ablation on LaA103 substrates is shown in Fig. 3. Below 60 K, the measured data can be fitted satisfactorily by the T2 law. However, above 60 K, only GC or MB equations can yield better agreement. We have inserted the magnetization data measured by the Quantum Design MPMSS SQUID in the same figure for manifesting that the film contains some defects or impurities. The sample stored in a dry box for two months was measured again for comparison. We observed that the transition temperature for the s- to d-wave state is lowered down from 60 K to 32 K as shown in Fig. 4. This implicitly addresses that the superconducting films with impurity phases are much

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unstable to be readily fluctuated from their original d-states. Another AA(T) plot for a YBCO film with an on-set critical temperature near 90 K (Fig. 5) also shows the same trends but yield a transition temperature near 36 K. This YBCO film exposed in air for 12 h was measured again and we observed that the transition temperature from d- to s-wave was further decreased for this chronically aged film. This gives us another evidence that the decrease of transition temperatures is due to the increase of impurities or defects from the magnetization curve. In light of the different temperature dependence of AX(T) which are different from those measured for a high quality single crystal YBCO 17, 81, it seems need a close scrutiny of the extrinsic effects on the pairing state. For a high quality, high T, single crystal, the temperature dependence on Ah(T) is linear from 3 to 25 K. A perfect thin film or common quality crystal, this temperature dependence will follow T*. For films containing an impurity phase or many defects, Ax(7) is proportional to T* in the low temperature region and exhibits exponential dependence at high temperatures. A power law dependence (i.e. AX(T) m Tp) can be derived from the d-wave states for superconductors with tetragonal or orthorhombic symmetry and a Fermi surface that has spherical or cylindrical topology with line nodes in the gap [25]. As the magnitude of impurity or defect scattering increase, the d-wave pairing state can change the temperature dependence from T to T*. At high temperatures, the thermal fluctuation will violate the pure d-state into mixed d$ _,,z and s-like and then to pure s-like as the temperature increases further. Our results are compared to the works of Jacobs et al. [12]. In the three suggested effects, we suggest that fluctuations are dominant because in our fittings, the use of a modified gap function does not exhibit better agreement. Moreover, following Jacobs’ approaches, the low temperature slope d[A,X,(T)/d7’J is expected to be X,dO>In (2)/A,,(O) and &(O) = 2.16kT,, which yields a X,,(O) longer than 500 nm from this experimental data. However, a direct extrapolation of Fig. 5 implies a more reasonable value of b(O) = 270 nm, showing that the strong-coupled d-wave model is not useful to explain our data. A recent t-U-V (hopping, repulsive on-site and attractive at distance) [271 Hubbard calculation, which leads to the result that the binding energy for the d-pairing state is lower than that for the s-state, strongly supports this assumption. Acknowledgements-This work was supported by the National Science Council of the Republic of

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China under Contract No. NSC86-2112-MOO7-002. The authors are indebted to Dr H.C. Lai in Industrial Technology Research Institute and Prof. K.H. Wu in National Chiao Tung University for providing the films. REFERENCES Schulz, H.J., Europhys. Letr., 4, 1987, 609. : : Gross, C., Joynt, R. and Rice, T.M., Z Phys., B68,

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