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Far-infrared optical conductivity of YBa2Cu3O7 − χ thin films
ELSEVIER
Physica C 341-348 (2000) 2197-2200
www.elsevier.nl/Iocate/physc
Far-infrared optical conductivity of YBa2CuaOT-x thin films Hajime SHIBATA a, Shinji K I M U R A ~, Satoshi KASHIWAYA~, Shigehiro UENO a'b, Masao KOYANAGI a Norio T E R A D A a,c , Etsuo KAWATE d , Paul FONS a, and Yukio T A N A K A e aElectrotechnical Laboratory, 1-1-4 Umezono, Tsukuba, Ibaraki a05-8568, Japan bTsukuba University, 1-1-1 Tennoudai, Tsukuba 305-8577, Japan CKagoshima University, 1-21-40 Korimoto, Kagoshima 099-0065, Japan dNational Research Laboratory of Metrology, 1-1-4 Umezono, Tsukuba, Ibaraki 305-8568, Japan eNagoya University, Furo-cho,Chikusa-ku, Nagoya 464-8602, Japan A new method to characterize the optical constants of thin films has been applied to YBa2Cu3OT-:~ epitaxial single crystal thin films To=90 K grown on MgO substrates to determine the far-infrared optical conductivity aab(w) for w = 50 -- 250 cm-1 and T -- 34- 97 K. Analysis of the temperature dependence of the aab(w) based on the two-fluid model suggests that the symmetry of the superconducting pairing state of the specimen is d-wave.
1. I N T R O D U C T I O N Analysis of transmittance spectra T(w) and reflectance spectra R(w) of very thin films deposited on substrates sometimes encounter serious difficulties, particularly in the wavenumber w region in which both thin films and substrates are transparent. The difficulties mainly arise from multiple internal reflections within the films a n d / o r substrates. Since the number of the basic optical constants is two, as expressed by the complex re-. fractive index N = n + ik, they can be estimated in principle if two experimentally measured quantities, such as T(~) and R(w), are given. The major advantage of such a method is that it can be applied to the optical characterization of very thin films deposited on a substrate. In this paper, we report on the results of the application of such a method to the estimation of the optical conductivity al(w) of YBa2Cu3OT-z (YBCO) thin films deposited on MgO substrates in far-infrared
(FIR) region as a function of temperature T. Hereafter in this paper, al(w) is denoted as aab(W) when the unpolarized excitation is applied parallel to the a-b plane in multidomained (twinned) single crystals, while it is denoted as aa(W) and ab(~Z) when the excitation is applied parallel to the a- and b-axis in single domain (untwinned) crystals, respectively, o'a(w) is associated with only CuO2 planes, while aab(W) and ab(W) are associated with both CuO2 planes and CuO chains. 2. E X P E R I M E N T S
We refer the method of analysis used in this work as the R-T method, since both R(aJ) and T(~) are necessary. The R-T method was applied firstly by one of us (E.K.) to the study of al(w) of superconducting NbN thin films deposited on MgO and Si substrates [1]. In this method, both R(~) and T(w) are measured and the results are substituted into a set of coupled equations which
0921-4534/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. Pll S0921-4534(00)00975-8
2198
H. Shibata et aL /Physica C 341-348 (2000) 2197-2200
describe exactly the R(w) and T(w) of thin films on substrates, where the complex refractive indices n and k of the thin films are unknown parameters. The coupled equations are numerically solved by the Newton method, and the values of n and k are determined as functions of the wavenumber a;. Essentially the same idea was also proposed by Ito et a/.[2]. L. Genzel et al. also proposed the similar method[3]. YBCO thin films (thickness = 38.4 nm) were prepared by sputtering on to the (001) plane of MgO substrates (thickness = 0.5 mm). The films were epitaxial (Tc "~ 90K) with the c-axis perpendicular to the MgO substrate, but were highly twinned within the a-b plane. The measurements of R(w) and T(w) were performed using a Fouriertransform interferometer with an unpolarized Hg arc lamp source and a Si:B bolometer. The electric field of the incident FIR radiation was predominantly parallel to the a-b plane. The spectral resolution was 0.1 c m - :.
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i
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t~ ,g
i
0.2 0.0 50
I
I
100
150
Transm,ttance ,
200
-:
250
Wavenumber ( cm "L)
Figure 1. Reflectance and Transmittance spectra at T = 34 K of YBCO thin films deposited on MgO substrates.
conventional two-fluid model; 3. R E S U L T S As a typical example of R(w) and T(w) for YBCO thin films deposited on MgO substrates, the results obtained at T = 34 K are shown in Fig. 1. The interference fringes due to multiple internal reflections within the MgO substrate are clearly observed. crl (w) of YBCO has been calculated by the R-T method using tile experimental results for R(w) and T(w) at T = 34, 57, 75 and 97K. These resuits are shown in Fig. 2. al(w) shown in Fig. 2 is CYab(W). The spectral shape of cq(w) in Fig. 2 at T = 34, 57 and 75 K can be considered as a simple Drude-like structure, although weak wiggles can be observed in the spectra. The origin of the wiggles is currently unclear, but is thought to be a consequence of experimental error in R(w) and/or T(w). Therefore, they will not be discussed further in this work. The spectral shape o f o"1 (02) at T --- 97 K is unclear because of the lack of data in the large w region. The origin of the Drude-like component in al(w) at T below Tc is expected to be a consequence of quasiparticle excitation at finite T, since cq(,;) below Tc is given as follows in the
_•
, 2 Fn 47r w2 + r2~ '
(1)
where the first term is the contribution of the superfluid whose density is proportional to w2, and the second term is that of the normal fluid formed by thermally excited quasipartictes having a scattering rate Fn and a density proportional to 2 02 n •
The spectral weight of the Drude-like component increases with increasing T in Fig. 2, which is qualitatively consistent with the increase of w~ with the increase of T. However, the spectral weight seems to be very large at T = 34 K, where T/Tc ~ 0.4 and the excitation of quasiparticles is expected to be very low. Collins et al. reported that a l ( W ) '~ 0 ~ - l c m - 1 for w below ,,, 400cm -1 at T/Tc "~ 0.3[4]. This difference arises simply because the al(W) shown in Fig. 2 is aab(W), whereas that reported by Collins et al. is aa(a;), i. e. the contribution from CuO chains is included in our results. Therefore, most of the spectral weight of al(W) at T = 34K in Fig. 2 can be considered to arise from conductivity of CuO chains.
H. Shibata et aL / Physica C 341-348 (2000) 2197-2200
2000 "7 E "7
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.T=34K
~-
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%s ,
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Figure 2. al (w) of Y B C O at T = 34 K (closed circles), 57 K (open circles), 75 K (closed squares) and 97 K (open squares).
4. D I S C U S S I O N S Annett et al. emphasized theoretically the behavior of ) ~ ( 0 ) 2 / ~ ( T ) 2 = 1 - (T/Tc) in d-wave superconductors, where A(T) is the London penetration depth [5]. They also suggested that ~ ( 0 ) 2 / ) ~ ( T ) 2 -- 1 - (T/T¢) 2 for d-wave superconductors with weak disorder. The T dependence of A(T) is related to the superfluid fraction xs(T) and the normal fluid fraction xn(T) = 1 - xs(T) in the two-fluid model of superconductivity in the form xs(T) = )~(0)2/)~(T) 2 and x~(T) = 1 - ) ~ ( 0 ) 2 / A ( T ) 2. Therefore, one can also expect xn(T) = (T/Tc) ~ with ~ = 1 ~" 2 in d-wave superconductors. In order to discuss the T dependence of xn(T) from the results in Fig 2, we must eliminate the contribution of the CuO chains from the data in an appropriate manner. As was discussed by van der Marel et al., the most simple way to do so is to assume that aab(~) can be regarded as an additive superposition of aplane(W) and achain(W) such a s O'ab(0)) = drplane(O)) Jr (Tchain(W), where apZ~e(w) and aehai~(w) are the contributions of the CuO2 planes and CuO chains, respectively [6]. Thus, (Yplane(W) is given a s aplane(td ) = O'ab(W) --O'chain(td ). In addition, they assumed
J
• o
0
~
~
1
J ,"1,
40
80
120
160
200
Wavenumber ( cm -] )
Figure 3. aptane(W) of Y B C O at T = 34 K (closed circles), 57 K (open circles), 75 K (closed squares) and 97 K (open squares).
that achain(W) "~ 6 4 0 ~ - 1 c m -1, which is independent of both T and w for w = 0 - 2000 c m - 1 and T ---- 3 0 - 150 K [6]. We also adopted these, assumptions and values in this work. Therefore, in conclusion, we assumed in this work that aptane(W) can be estimated simply by O'plane(W) = aab(W) -- 6 4 0 ~ - 1 c m -1. The results of the estimation of ap~ane(W) are shown in Fig. 3. It is obvious from Fig. 3 that the spectral weight of the aptane(W) at T = 34K is strongly suppressed to ,., 10012-1cm -1, which is consistent with the results reported by Collins et al. [4]. Hereafter, we denote the T dependence of ffplane(W) in Fig. 3 a s ffplane(w,T). Once aptane (W, T) is estimated, discussion of the T dependence of the xn(T) is possible, as was performed by Collins et al. [4]. Their method to calculate xn(T) is based on the simple two-fluid model given by Eq. (1), and is equivalent to assume that xn(T) = ffplane(~d, T) /apt~e(w, Tc). We assumed in this work that aplane(w, Tc) is approximately given by aptane(W, 97), and hence xn(T) is approximately given by xn(T) = aptane(W, T)/apl~e(W, 97). In this work, such calculation is possible only in the region of w in which data of apt~ne(W, 97) exist, which is in the range 60 - 140cm -1. The calculated results for
I-£ Shibata et aL /Physica C 341-348 (2000) 2197-2200
2200
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Wavenumber ( cm 4 )
Figure 4. aptane(W, T)/aplane(W, 97) at T = 34 K (closed circles), 57K (open circles) and 75K (closed squares). The values averaged over the region are indicated by dashed lines.
40
Figure 5. xn(T) as a function of T. The dashed curve shows a least squares fit to the power law xn(T) = (T/97) a, w h e r e t h e most probable value for a is 1.63.
5. C O N C L U S I O N S
apZan~(W, T)/aplane(w, 97) are shown in Fig. 4 for T = 34, 57 and 75K for w = 60 - 140cm -1. Although strong wiggles can be observed in the results, the results seem to be almost independent of w. The values of •plane (W, T)/ffplane (W, 97) averaged over the w region are 0.135, 0.394 and 0.742 for T = 34, 57 and 75K, which are indicated by the dashed lines in Fig. 4. We have regarded these values as xn(T) at a given T. The trivial result of Xn(97) = 1.0 can also be concluded. The results for xn(T) are shown in Fig. 5 for T = 34, 57, 75 and 97 K by closed circles. We have analyzed the results shown in Fig. 5 by a least squares fit to a simple power law xn(T) = (T/97) a, where a is a fitting parameter. The result of the fit is shown in Fig. 5 as a dashed curve. This revealed that the most probable value for a is 1.63, which suggests the power law is x,~(T) = (T/Tc) 163. This result is in strong disagreement with the results obtained by Collins et al. [4], where x~(T) = (T/Tc) 4 is claimed. However, it must be also noted that the value of a = 1.63 is in good agreement with the claim of Annett et al. for d-wave superconductors [5].
A new method to characterize the optical constants of thin films deposited on the substrates has been applied to Y B C O epitaxial single crystal thin films grown on MgO substrates to determine aab(W) for w = 50-- 250cm -1 at T = 34 - 97K. Analysis of the temperature dependence of the aab(W) based on the two-fluid model suggests that the T dependence of the normal fluid fraction is given by x n ( T ) = ( T / T c ) 1"63, which suggests that the symmetry of the superconducting pairing state of the specimen is d-wave.
REFERENCES 1.
2. 3. 4. 5. 6.
M. Koguchi et al., Meeting Abstracts of the 53rd Annual Meeting of the Physical Society of Japan 53 (1998) 614. T. Itoet aL, Physica C302 (1998) 229. T. Ito et aL , J. Phys. Chem. Solids 60 (1999) 41. L. Genzel et al., Z. Phys. B90 (1992) 3. R. T. Collins et al., Phys. Rev. B43 (1991) 8701. J. Annett et aL, Phys. Rev. B43 (1991) 2778. D. van der Marel et al., Physica C176 (1991) 1.
Physica C 341-348 (2000) 2197-2200
www.elsevier.nl/Iocate/physc
Far-infrared optical conductivity of YBa2CuaOT-x thin films Hajime SHIBATA a, Shinji K I M U R A ~, Satoshi KASHIWAYA~, Shigehiro UENO a'b, Masao KOYANAGI a Norio T E R A D A a,c , Etsuo KAWATE d , Paul FONS a, and Yukio T A N A K A e aElectrotechnical Laboratory, 1-1-4 Umezono, Tsukuba, Ibaraki a05-8568, Japan bTsukuba University, 1-1-1 Tennoudai, Tsukuba 305-8577, Japan CKagoshima University, 1-21-40 Korimoto, Kagoshima 099-0065, Japan dNational Research Laboratory of Metrology, 1-1-4 Umezono, Tsukuba, Ibaraki 305-8568, Japan eNagoya University, Furo-cho,Chikusa-ku, Nagoya 464-8602, Japan A new method to characterize the optical constants of thin films has been applied to YBa2Cu3OT-:~ epitaxial single crystal thin films To=90 K grown on MgO substrates to determine the far-infrared optical conductivity aab(w) for w = 50 -- 250 cm-1 and T -- 34- 97 K. Analysis of the temperature dependence of the aab(w) based on the two-fluid model suggests that the symmetry of the superconducting pairing state of the specimen is d-wave.
1. I N T R O D U C T I O N Analysis of transmittance spectra T(w) and reflectance spectra R(w) of very thin films deposited on substrates sometimes encounter serious difficulties, particularly in the wavenumber w region in which both thin films and substrates are transparent. The difficulties mainly arise from multiple internal reflections within the films a n d / o r substrates. Since the number of the basic optical constants is two, as expressed by the complex re-. fractive index N = n + ik, they can be estimated in principle if two experimentally measured quantities, such as T(~) and R(w), are given. The major advantage of such a method is that it can be applied to the optical characterization of very thin films deposited on a substrate. In this paper, we report on the results of the application of such a method to the estimation of the optical conductivity al(w) of YBa2Cu3OT-z (YBCO) thin films deposited on MgO substrates in far-infrared
(FIR) region as a function of temperature T. Hereafter in this paper, al(w) is denoted as aab(W) when the unpolarized excitation is applied parallel to the a-b plane in multidomained (twinned) single crystals, while it is denoted as aa(W) and ab(~Z) when the excitation is applied parallel to the a- and b-axis in single domain (untwinned) crystals, respectively, o'a(w) is associated with only CuO2 planes, while aab(W) and ab(W) are associated with both CuO2 planes and CuO chains. 2. E X P E R I M E N T S
We refer the method of analysis used in this work as the R-T method, since both R(aJ) and T(~) are necessary. The R-T method was applied firstly by one of us (E.K.) to the study of al(w) of superconducting NbN thin films deposited on MgO and Si substrates [1]. In this method, both R(~) and T(w) are measured and the results are substituted into a set of coupled equations which
0921-4534/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. Pll S0921-4534(00)00975-8
2198
H. Shibata et aL /Physica C 341-348 (2000) 2197-2200
describe exactly the R(w) and T(w) of thin films on substrates, where the complex refractive indices n and k of the thin films are unknown parameters. The coupled equations are numerically solved by the Newton method, and the values of n and k are determined as functions of the wavenumber a;. Essentially the same idea was also proposed by Ito et a/.[2]. L. Genzel et al. also proposed the similar method[3]. YBCO thin films (thickness = 38.4 nm) were prepared by sputtering on to the (001) plane of MgO substrates (thickness = 0.5 mm). The films were epitaxial (Tc "~ 90K) with the c-axis perpendicular to the MgO substrate, but were highly twinned within the a-b plane. The measurements of R(w) and T(w) were performed using a Fouriertransform interferometer with an unpolarized Hg arc lamp source and a Si:B bolometer. The electric field of the incident FIR radiation was predominantly parallel to the a-b plane. The spectral resolution was 0.1 c m - :.
e~ e-
.:2_
1.0
-
I
i
i
0.8 0.6 0.4 '
t~ ,g
i
0.2 0.0 50
I
I
100
150
Transm,ttance ,
200
-:
250
Wavenumber ( cm "L)
Figure 1. Reflectance and Transmittance spectra at T = 34 K of YBCO thin films deposited on MgO substrates.
conventional two-fluid model; 3. R E S U L T S As a typical example of R(w) and T(w) for YBCO thin films deposited on MgO substrates, the results obtained at T = 34 K are shown in Fig. 1. The interference fringes due to multiple internal reflections within the MgO substrate are clearly observed. crl (w) of YBCO has been calculated by the R-T method using tile experimental results for R(w) and T(w) at T = 34, 57, 75 and 97K. These resuits are shown in Fig. 2. al(w) shown in Fig. 2 is CYab(W). The spectral shape of cq(w) in Fig. 2 at T = 34, 57 and 75 K can be considered as a simple Drude-like structure, although weak wiggles can be observed in the spectra. The origin of the wiggles is currently unclear, but is thought to be a consequence of experimental error in R(w) and/or T(w). Therefore, they will not be discussed further in this work. The spectral shape o f o"1 (02) at T --- 97 K is unclear because of the lack of data in the large w region. The origin of the Drude-like component in al(w) at T below Tc is expected to be a consequence of quasiparticle excitation at finite T, since cq(,;) below Tc is given as follows in the
_•
, 2 Fn 47r w2 + r2~ '
(1)
where the first term is the contribution of the superfluid whose density is proportional to w2, and the second term is that of the normal fluid formed by thermally excited quasipartictes having a scattering rate Fn and a density proportional to 2 02 n •
The spectral weight of the Drude-like component increases with increasing T in Fig. 2, which is qualitatively consistent with the increase of w~ with the increase of T. However, the spectral weight seems to be very large at T = 34 K, where T/Tc ~ 0.4 and the excitation of quasiparticles is expected to be very low. Collins et al. reported that a l ( W ) '~ 0 ~ - l c m - 1 for w below ,,, 400cm -1 at T/Tc "~ 0.3[4]. This difference arises simply because the al(W) shown in Fig. 2 is aab(W), whereas that reported by Collins et al. is aa(a;), i. e. the contribution from CuO chains is included in our results. Therefore, most of the spectral weight of al(W) at T = 34K in Fig. 2 can be considered to arise from conductivity of CuO chains.
H. Shibata et aL / Physica C 341-348 (2000) 2197-2200
2000 "7 E "7
~"
'
I
'
1200F
I
I
'
I
'
I
'
I
'
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]
aP
1600 =
800 ~
1200 800
T=57K
**
~°,,m"*~ "~ a
400 40
,
I ! 00
• i ~ . . -:~
600/1 "-T=75K
.T=34K
~-
'
2199
,
I 200
400
T=57K
%s ,
i t00
Wavenumber ( cm -I )
Figure 2. al (w) of Y B C O at T = 34 K (closed circles), 57 K (open circles), 75 K (closed squares) and 97 K (open squares).
4. D I S C U S S I O N S Annett et al. emphasized theoretically the behavior of ) ~ ( 0 ) 2 / ~ ( T ) 2 = 1 - (T/Tc) in d-wave superconductors, where A(T) is the London penetration depth [5]. They also suggested that ~ ( 0 ) 2 / ) ~ ( T ) 2 -- 1 - (T/T¢) 2 for d-wave superconductors with weak disorder. The T dependence of A(T) is related to the superfluid fraction xs(T) and the normal fluid fraction xn(T) = 1 - xs(T) in the two-fluid model of superconductivity in the form xs(T) = )~(0)2/)~(T) 2 and x~(T) = 1 - ) ~ ( 0 ) 2 / A ( T ) 2. Therefore, one can also expect xn(T) = (T/Tc) ~ with ~ = 1 ~" 2 in d-wave superconductors. In order to discuss the T dependence of xn(T) from the results in Fig 2, we must eliminate the contribution of the CuO chains from the data in an appropriate manner. As was discussed by van der Marel et al., the most simple way to do so is to assume that aab(~) can be regarded as an additive superposition of aplane(W) and achain(W) such a s O'ab(0)) = drplane(O)) Jr (Tchain(W), where apZ~e(w) and aehai~(w) are the contributions of the CuO2 planes and CuO chains, respectively [6]. Thus, (Yplane(W) is given a s aplane(td ) = O'ab(W) --O'chain(td ). In addition, they assumed
J
• o
0
~
~
1
J ,"1,
40
80
120
160
200
Wavenumber ( cm -] )
Figure 3. aptane(W) of Y B C O at T = 34 K (closed circles), 57 K (open circles), 75 K (closed squares) and 97 K (open squares).
that achain(W) "~ 6 4 0 ~ - 1 c m -1, which is independent of both T and w for w = 0 - 2000 c m - 1 and T ---- 3 0 - 150 K [6]. We also adopted these, assumptions and values in this work. Therefore, in conclusion, we assumed in this work that aptane(W) can be estimated simply by O'plane(W) = aab(W) -- 6 4 0 ~ - 1 c m -1. The results of the estimation of ap~ane(W) are shown in Fig. 3. It is obvious from Fig. 3 that the spectral weight of the aptane(W) at T = 34K is strongly suppressed to ,., 10012-1cm -1, which is consistent with the results reported by Collins et al. [4]. Hereafter, we denote the T dependence of ffplane(W) in Fig. 3 a s ffplane(w,T). Once aptane (W, T) is estimated, discussion of the T dependence of the xn(T) is possible, as was performed by Collins et al. [4]. Their method to calculate xn(T) is based on the simple two-fluid model given by Eq. (1), and is equivalent to assume that xn(T) = ffplane(~d, T) /apt~e(w, Tc). We assumed in this work that aplane(w, Tc) is approximately given by aptane(W, 97), and hence xn(T) is approximately given by xn(T) = aptane(W, T)/apl~e(W, 97). In this work, such calculation is possible only in the region of w in which data of apt~ne(W, 97) exist, which is in the range 60 - 140cm -1. The calculated results for
I-£ Shibata et aL /Physica C 341-348 (2000) 2197-2200
2200
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- :75K
0.6
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-T=57K
-
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T=34K
.
.
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80
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I
120
,
0
160
80
120
Temperature ( K )
Wavenumber ( cm 4 )
Figure 4. aptane(W, T)/aplane(W, 97) at T = 34 K (closed circles), 57K (open circles) and 75K (closed squares). The values averaged over the region are indicated by dashed lines.
40
Figure 5. xn(T) as a function of T. The dashed curve shows a least squares fit to the power law xn(T) = (T/97) a, w h e r e t h e most probable value for a is 1.63.
5. C O N C L U S I O N S
apZan~(W, T)/aplane(w, 97) are shown in Fig. 4 for T = 34, 57 and 75K for w = 60 - 140cm -1. Although strong wiggles can be observed in the results, the results seem to be almost independent of w. The values of •plane (W, T)/ffplane (W, 97) averaged over the w region are 0.135, 0.394 and 0.742 for T = 34, 57 and 75K, which are indicated by the dashed lines in Fig. 4. We have regarded these values as xn(T) at a given T. The trivial result of Xn(97) = 1.0 can also be concluded. The results for xn(T) are shown in Fig. 5 for T = 34, 57, 75 and 97 K by closed circles. We have analyzed the results shown in Fig. 5 by a least squares fit to a simple power law xn(T) = (T/97) a, where a is a fitting parameter. The result of the fit is shown in Fig. 5 as a dashed curve. This revealed that the most probable value for a is 1.63, which suggests the power law is x,~(T) = (T/Tc) 163. This result is in strong disagreement with the results obtained by Collins et al. [4], where x~(T) = (T/Tc) 4 is claimed. However, it must be also noted that the value of a = 1.63 is in good agreement with the claim of Annett et al. for d-wave superconductors [5].
A new method to characterize the optical constants of thin films deposited on the substrates has been applied to Y B C O epitaxial single crystal thin films grown on MgO substrates to determine aab(W) for w = 50-- 250cm -1 at T = 34 - 97K. Analysis of the temperature dependence of the aab(W) based on the two-fluid model suggests that the T dependence of the normal fluid fraction is given by x n ( T ) = ( T / T c ) 1"63, which suggests that the symmetry of the superconducting pairing state of the specimen is d-wave.
REFERENCES 1.
2. 3. 4. 5. 6.
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