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Theoretical explanation of broad resistive transition in high temperature superconductors in magnetic field
Physica B 165&166 (1990) 1359-1360 North-Holland
THEORETICAL EXPLANATION OF BROAD RESISTIVE TRANSITION IN HIGH TEMPERATURE SUPERCONDUCTORS IN MAGNETIC FIELD Ryusuke IKEDA, Tetsuo OHMI and Toshihiko TSUNETO Department of Physics, Kyoto University, Kyoto 606, Japan
Experimental data on the broad resistive transitions in high temperature superconductors (HTSC) in strong magnetic fields, obtained with high quality samples, are compared with results of the renormalized fluctuation theory. The theory is extended to lower temperature by a partial summation method called SPH. The layer structure is kept throughout the calculation. The quantitative agreement is obtained over a wide range of temperature in both geometries IIIH and I1H. It is remarkable that the theory can explain the observed low temperature behavior of P~ suggestive of the flux flow mechanism and its absence in PI!' Anomalously broad transition is commonly observed in resistivity measurements on single crystal samples of HTSC in an applied magnetic field of several tesla. It is, in our opinion, best to look at this broadening of the superconducting transition as resulting from thermal fluctuations of the superconducting order parameter W. In the presence of the field, being quantized into Landau orbitals, the fluctuations acquire l-dimensional character. Hence their effects are enhanced by the field and become pronounced especially in HTSC because of high Tc ' the short coherence length a~d the 1ayer structures. I n a seri es of works 1 ;,2) we developed a renormalized fluctuation theory and obtained results for the resistivity in good agreement with the available data. More recently, sever~l measurements using high quality YBC03),4; and BSCC05) crystals have clearly revealed important overall features of the resistive transition. Firstly, for a given field basically the same broadening is observed in both resistivities P~ with H~I and P/I with HilI where I is measuring current, a fact that support our fluctuation theory.l) Secondly, the low temperature part of PJ. (T) and PI! (T) curves are quite different; the former has a broad tail, supposedly the flux flow region, which crosses over to behavior of the thermal activation type as T is reduced, thus giving rise to a "knee", while the latter has no such structure. In the present paper we would like to attempt quantitative comparisons of our theory with such recent data. For this purpose we have made following improvements over the previ ous work 1). Fi rst, the 1ayer structure with spacing s, particularly important for BSCCO, is kept throughout the calculation. Second, while the mass renormalization was only performed for the lowest Landau levels in ref. 1, we now consider it also for the higher 0921-4526/90/$03.50
© 1990 -
Landau levels because they become mor~ important in lower temperature. Our basic approximation is tQ use a partial resummation method called SPH2; which, being valid at high T, also leads to the mean field behaviour for quantities like < Iw/ 2> in low T region as we should expect. The dc conductivity a is calculated by Kubo formula with the help of the diffusive TDGL equation for W. The observed resistivity is assumed to be given by P=Pn/(l+C-lpno) where Pn is the extrapolated normal resistivity and C is a parameter to adjust the zero field resistivity. According to our theory, the resistivities must behave, in the low T region where the fluctuation conductivity dominates, as P..L.
'V
P/ I
'V
H
I
[H2/3
(TcwT) ,
IJ...H
(1)
I (T cH-T)]3,
IIIH
(2)
where TcH is the mean field transition temperature in the field. Note that the dependence (1) is what you expect from flux flow (or sliding flux lattice) mechanism. Whereas the scaling relation valid in the transition region, namely (3)
still persists for PII ' we have a cross-over from (3) to (1) in the case of p~.2) We have tried to fit th~ data for YBCO single crystals by Li et al. 3 ; (Fig.1) and for BSCCO by Batlogg et al. 5) (Fig.2) with our theory, the details of which will be published elsewhere. The parameters used in Fig.l for I~H and IIIH are slightly different because the repective samples have different TcO. As one can see, the agreement is satisfactory; the
Elsevier Science Publishers B.V. (North-Holland)
R. Ikeda, T. Ohmi, T. Tsuneto
1360
.P1l
--
i - - -
_.-
not well established. 6 ) we present in Fig.2 the theoretical results using two sets of the parameters. We have the good ~greement even if an extremely large value of y6) is chosen. In general. the ratio s/~Oc that expresses the dimensionality of the systems rather than y, determines the T-dependence of p~ while both ratios are important for P • II
0,5
--
JRII __ ----I
A
J,.
"'!l
01
I
0t-~_l."-'_-A-_-"_~_-"--_ _---j
g .s
c.l ~
10
- - - - t ----
(b)
1/1 BII c. Pn
0-
c A-
---~
-----
•
I
I I
D
v- b
70
•- 8
., 80
90
T tIC)
FIGURE 1 Comparisons with the YBCO data of ref.3. (a) The resistivity p~(T) with I~B//c-axis. and (b) PI! (T) with II /B/ /c. The parameters used for theoretical calculations (solid curves) are ~0=9(A). ~C=52.5(mJ/K·cm3). TcO=94.1(K) and C=3.7 for (a). and 10. 50.2. 92.8 and 4.3 for (b) respectively. In both cases s=ll(A) and ~Oc=1.8(A). theory captures the overall features of the data. especially the lower T behaviour which reflects the relation (1) and (2). except for the cross-over to the activation type region. To account for this we perhaps need to put in additional ingredient like pinnings. There is a discrepancy in the high T side for the case H~I in the sense that the expected positive magneto-resistance is absent in the data. More careful measurements are desirable in this region. Since the parameters for BSCCO, especially the anisotropy ratio Y=~O/~Oc' are
90 T(K)
FIGURE 2 Comparisons with the BSCCO data of ref.5. Two sets of the parameters are used for theoretical calculations; (1) ~0=8(A). ~Oc=0.9(A). ~C= 38.5 (mJ/Kcm 3 ). and C=0.82 (solid curves). and (2) 10. 0.2. 37.9 and 0.9 (dotted curves) respectively. with the same s=12(A) and TcO=90(K). REFERENCES (1) R. Ikeda. T. Ohmi and T. Tsuneto. J. Phys. Soc. Jpn. 58. 1377 (1989); R. Ikeda. ibid 58. 1906 (1989). (2) R. Ikeda. T. Ohmi and T. Tsuneto. to be published in J. Phys. Soc. Jpn. (3) J.N. Li. K. Kadowaki. M.J.V. Menken. A.A. Menovsky and J.J.M. Franse. Physica C161. 313 (1989). (4) W.K. Kwok. U. We1p. G.W. Crabtree. K.G. Vandervoort. R. Hulscher and J.Z. Liu. Phys. Rev. Lett. 64. 966 (1990). (5) B. Batlogg. T.T.M. Palstra. L.F. Schneemeyer. R.B. Van Dover, and R.J. Cava. Physica C153-155, 1062 (1988); T. T.M. Palstra. B. Bat1ogg. L.F. Schneemeyer and J.V. Waszczak. Phys. Rev. Lett. 61. 1662 (1988). (6) P.H. Kes. J. Aarts. V.M. Vinokur and C.J. van der Beek. Phys. Rev. Lett. 64. 1063 (1990).
THEORETICAL EXPLANATION OF BROAD RESISTIVE TRANSITION IN HIGH TEMPERATURE SUPERCONDUCTORS IN MAGNETIC FIELD Ryusuke IKEDA, Tetsuo OHMI and Toshihiko TSUNETO Department of Physics, Kyoto University, Kyoto 606, Japan
Experimental data on the broad resistive transitions in high temperature superconductors (HTSC) in strong magnetic fields, obtained with high quality samples, are compared with results of the renormalized fluctuation theory. The theory is extended to lower temperature by a partial summation method called SPH. The layer structure is kept throughout the calculation. The quantitative agreement is obtained over a wide range of temperature in both geometries IIIH and I1H. It is remarkable that the theory can explain the observed low temperature behavior of P~ suggestive of the flux flow mechanism and its absence in PI!' Anomalously broad transition is commonly observed in resistivity measurements on single crystal samples of HTSC in an applied magnetic field of several tesla. It is, in our opinion, best to look at this broadening of the superconducting transition as resulting from thermal fluctuations of the superconducting order parameter W. In the presence of the field, being quantized into Landau orbitals, the fluctuations acquire l-dimensional character. Hence their effects are enhanced by the field and become pronounced especially in HTSC because of high Tc ' the short coherence length a~d the 1ayer structures. I n a seri es of works 1 ;,2) we developed a renormalized fluctuation theory and obtained results for the resistivity in good agreement with the available data. More recently, sever~l measurements using high quality YBC03),4; and BSCC05) crystals have clearly revealed important overall features of the resistive transition. Firstly, for a given field basically the same broadening is observed in both resistivities P~ with H~I and P/I with HilI where I is measuring current, a fact that support our fluctuation theory.l) Secondly, the low temperature part of PJ. (T) and PI! (T) curves are quite different; the former has a broad tail, supposedly the flux flow region, which crosses over to behavior of the thermal activation type as T is reduced, thus giving rise to a "knee", while the latter has no such structure. In the present paper we would like to attempt quantitative comparisons of our theory with such recent data. For this purpose we have made following improvements over the previ ous work 1). Fi rst, the 1ayer structure with spacing s, particularly important for BSCCO, is kept throughout the calculation. Second, while the mass renormalization was only performed for the lowest Landau levels in ref. 1, we now consider it also for the higher 0921-4526/90/$03.50
© 1990 -
Landau levels because they become mor~ important in lower temperature. Our basic approximation is tQ use a partial resummation method called SPH2; which, being valid at high T, also leads to the mean field behaviour for quantities like < Iw/ 2> in low T region as we should expect. The dc conductivity a is calculated by Kubo formula with the help of the diffusive TDGL equation for W. The observed resistivity is assumed to be given by P=Pn/(l+C-lpno) where Pn is the extrapolated normal resistivity and C is a parameter to adjust the zero field resistivity. According to our theory, the resistivities must behave, in the low T region where the fluctuation conductivity dominates, as P..L.
'V
P/ I
'V
H
I
[H2/3
(TcwT) ,
IJ...H
(1)
I (T cH-T)]3,
IIIH
(2)
where TcH is the mean field transition temperature in the field. Note that the dependence (1) is what you expect from flux flow (or sliding flux lattice) mechanism. Whereas the scaling relation valid in the transition region, namely (3)
still persists for PII ' we have a cross-over from (3) to (1) in the case of p~.2) We have tried to fit th~ data for YBCO single crystals by Li et al. 3 ; (Fig.1) and for BSCCO by Batlogg et al. 5) (Fig.2) with our theory, the details of which will be published elsewhere. The parameters used in Fig.l for I~H and IIIH are slightly different because the repective samples have different TcO. As one can see, the agreement is satisfactory; the
Elsevier Science Publishers B.V. (North-Holland)
R. Ikeda, T. Ohmi, T. Tsuneto
1360
.P1l
--
i - - -
_.-
not well established. 6 ) we present in Fig.2 the theoretical results using two sets of the parameters. We have the good ~greement even if an extremely large value of y6) is chosen. In general. the ratio s/~Oc that expresses the dimensionality of the systems rather than y, determines the T-dependence of p~ while both ratios are important for P • II
0,5
--
JRII __ ----I
A
J,.
"'!l
01
I
0t-~_l."-'_-A-_-"_~_-"--_ _---j
g .s
c.l ~
10
- - - - t ----
(b)
1/1 BII c. Pn
0-
c A-
---~
-----
•
I
I I
D
v- b
70
•- 8
., 80
90
T tIC)
FIGURE 1 Comparisons with the YBCO data of ref.3. (a) The resistivity p~(T) with I~B//c-axis. and (b) PI! (T) with II /B/ /c. The parameters used for theoretical calculations (solid curves) are ~0=9(A). ~C=52.5(mJ/K·cm3). TcO=94.1(K) and C=3.7 for (a). and 10. 50.2. 92.8 and 4.3 for (b) respectively. In both cases s=ll(A) and ~Oc=1.8(A). theory captures the overall features of the data. especially the lower T behaviour which reflects the relation (1) and (2). except for the cross-over to the activation type region. To account for this we perhaps need to put in additional ingredient like pinnings. There is a discrepancy in the high T side for the case H~I in the sense that the expected positive magneto-resistance is absent in the data. More careful measurements are desirable in this region. Since the parameters for BSCCO, especially the anisotropy ratio Y=~O/~Oc' are
90 T(K)
FIGURE 2 Comparisons with the BSCCO data of ref.5. Two sets of the parameters are used for theoretical calculations; (1) ~0=8(A). ~Oc=0.9(A). ~C= 38.5 (mJ/Kcm 3 ). and C=0.82 (solid curves). and (2) 10. 0.2. 37.9 and 0.9 (dotted curves) respectively. with the same s=12(A) and TcO=90(K). REFERENCES (1) R. Ikeda. T. Ohmi and T. Tsuneto. J. Phys. Soc. Jpn. 58. 1377 (1989); R. Ikeda. ibid 58. 1906 (1989). (2) R. Ikeda. T. Ohmi and T. Tsuneto. to be published in J. Phys. Soc. Jpn. (3) J.N. Li. K. Kadowaki. M.J.V. Menken. A.A. Menovsky and J.J.M. Franse. Physica C161. 313 (1989). (4) W.K. Kwok. U. We1p. G.W. Crabtree. K.G. Vandervoort. R. Hulscher and J.Z. Liu. Phys. Rev. Lett. 64. 966 (1990). (5) B. Batlogg. T.T.M. Palstra. L.F. Schneemeyer. R.B. Van Dover, and R.J. Cava. Physica C153-155, 1062 (1988); T. T.M. Palstra. B. Bat1ogg. L.F. Schneemeyer and J.V. Waszczak. Phys. Rev. Lett. 61. 1662 (1988). (6) P.H. Kes. J. Aarts. V.M. Vinokur and C.J. van der Beek. Phys. Rev. Lett. 64. 1063 (1990).