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Superconductivity near the metal-insulator transition
Physica 148B (1987) 510-512 North-Holland, Amsterdam
S U P E R C O N D U C T I V I T Y N E A R THE M E T A L - I N S U L A T O R T R A N S I T I O N
T.A. M I L L E R , M. K U N C H U R , Y.Z. Z H A N G , P. L I N D E N F E L D and W.L. M c L E A N Serin Physics Laboratory, Rutgers University, P. O. Box 849, Piscataway, NJ 08855-0849, USA Received 3 August 1987
Spin-orbit scattering is enhanced in granular aluminum by the addition of small amounts of bismuth. The metalinsulator transition is displaced to larger values of room-temperature resistivity. The superconducting-normal threshold is displaced by an approximately equal amount.
The relationship of superconductivity to the metal-insulator transition is a subject of considerable current investigation and speculation [1, 2]. In particular it has been suggested that spin-orbit scattering plays a major role in determining whether superconductivity persists to the m - i transition [3, 4]. We have investigated the effect of enhanced spin-orbit scattering resulting from the addition of small amounts of bismuth to granular aluminum. The results demonstrate a substantial shift in the m - i transition, accompanied by an at least approximately equal shift in the concentration of metallic aluminum to which superconductivity persists. The experiments were made on a series of samples of granular aluminum, evaporated from an electron-beam source onto water-cooled glass substrates in the presence of a small amount of oxygen. Bismuth was evaporated simultaneously from a second neighboring source. The deposition rates were measured and kept constant by independent crystal monitors. The amount of Bi as a fraction of metallic A1 was about 2% (at). We do not expect this amount of Bi to lead to any changes in structure or grain size. The solubility of Bi in AI is given by Hansen [5] as 0.02% (at), so that the Bi is presumably primarily outside the grains. Its effectiveness in changing the spin-orbit scattering is apparent from the critical field which shows a value of Hc2(0 ) of 6.5 T for a specimen with PRX equal to 7.4 X 103 p~l-Icm, or about twice as much as the value of 3.6 T [6] in 0378-4363/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) and Yamada Science Foundation
the absence of Bi. The analysis of the magnetoresistance leads to a value of 7so of 6 × 10 13 s for the same specimen, compared with a value of about 2 x 10 -11 s for a specimen with a similar resistivity without Bi [7]. Fig. 1 shows T~ (the midpoint of the resistive transition) as a function of the room-temperature resistivity PRT for superconducting specimens with and without Bi. We use the value of PRT as a sensitive measure of the relative amounts of A1 and A1203, essentially unaffected by supercon-
1.2 1.1 1.0
T T
0.9
o
+
o
C
0.8 CO
0.7 0.6 0.5
o
.
10 ~
.
.
.
.
.
.
.
.
10 a
.
.
.
.
.
.
.
.
.
104
.
.
,
, , , , ,
10 s
~.r ( j~i')-c m ) Fig. 1. To~To as a function of flRT for specimens with Bi (circles) and without Bi (crosses). T~o is 2.43 K for the specimens without Bi, and 2.28 K for the specimens with Bi.
T.A. Miller et al. / Superconductivity near the m - i transition
ductivity, localization, or the presence of small amounts of Bi. It m a y be seen that T c decreases as PRT increases in both kinds of specimens, but that superconductivity remains to values of PRT about 3 times as high in the specimens which contain Bi. For an unambiguous determination whether a specimen is metallic normal-state m e a s u r e m e n t s at very low t e m p e r a t u r e s must be used. Since we have only preliminary m e a s u r e m e n t s of that kind we present on fig. 2 the ratio r R 4 . 2 / R R T as a function of PRT" The value of r increases steeply as the m - i transition is approached. The choice of 4.2 K for the resistance in the n u m e r a t o r of this ratio is not completely arbitrary. It represents a t e m p e r a t u r e which is low but with only very minor indications of superconducting fluctuations. The figure shows a shift in the m - i transition in the specimens containing Bi which is close to or the same as the shift in the superconducting threshold shown in fig. 1. The observation that the two variations are similar is confirmed by fig. 3, which shows T c as a function of r. We do not rule out the possibility of small differences in the shifts of the m - i transition and the S - N threshold or in the shapes of the curves, but wish to concentrate in this report on their striking similarity. It is clear, first of all, that the increase in the spin-orbit scattering shifts the m - i transition. Since s p i n - o r b i t scattering cannot affect the percolation threshold we conclude that the m - i transition is determined ( " d r i v e n " ) by localization rather than by percolation. This conclusion is supported by the continuous decrease in To, which is expected when localization and the associated e l e c t r o n - e l e c t r o n interactions come into play [8]. Finally, if the S - N threshold is shifted by the same amount, it follows that the position of this threshold as a function of PRT is determined by the position of the m - i transition. It has been conjectured [3] that the enhancement of s p i n - o r b i t scattering separates the S - N threshold from the m - i transition. Our results do not support this conclusion. The existence of a non-superconducting metallic region in 3D systems with strong s p i n - o r b i t scattering is also
511
? o
6
o o
5
+
o
4
r 3 2
=
o
102
103
10 s
104
pRZ( p ~ - - C m ) Fig. 2. The ratio r R42/RRT as a function of PRT for specimens with Bi (circles) and without Bi (crosses). =
1 2 1
1
1 0
T
0
9
c
- - 0 8
T
co 0
7
0
6
+
o O
0.5
O
I
I
I
I
I
I
1
2
3
4
5
6
r Fig. 3.
T,]T,.o as a function of r for specimens with Bi
(circles) without Bi (crosses). suggested in ref. [4]. T h e r e is, however, no prediction about a possible change as the s p i n orbit scattering rate is altered. We may summarize our main conclusion by saying that an increase in the s p i n - o r b i t scattering rate shifts the m e t a l - i n s u l a t o r transition, and with it the s u p e r c o n d u c t i n g - n o r m a l threshold.
512
T . A . Miller et al. / Superconductivity near the m - i transition
We w o u l d like to t h a n k G . D e u t s c h e r for v a l u a b l e a n d s t i m u l a t i n g discussions a n d comm e n t s . This w o r k was s u p p o r t e d by the N a t i o n a l Science F o u n d a t i o n u n d e r g r a n t D M R - 8 5 - 1 1 9 8 2 .
References [1] M. Ma and P.A. Lee, Phys. Rev. B 32 (1985) 5658. [2] G. Kotliar and A. Kapitulnik, Phys. Rev. B 33 (1986) 3146.
[3] D.J. Bishop, E.G. Spencer, J.P. Garno and R.C. Dynes, Bull. Am. Phys. Soc. 29 (1984) 343. [4] M. Ma and E. Fradkin, Phys. Rev. Lett. 56 (1986) 1416. [5] M. Hansen, Constitution of Binary Alloys (McGraw-Hill, New York, 1958). [6] T. Chui, P. Lindenfeld, W.L. McLean and K. Mui, Phys. Rev. B 24 (1981) 6728. [7] K.C, Mui, P. Lindenfeld and W.L. McLean, Phys. Rev. B 30 (1984) 2951. [8] H. Fukuyama, H. Ebisawa and S. Maekawa, J. Phys. Soc. Jap. 53 (1984) 3560.
S U P E R C O N D U C T I V I T Y N E A R THE M E T A L - I N S U L A T O R T R A N S I T I O N
T.A. M I L L E R , M. K U N C H U R , Y.Z. Z H A N G , P. L I N D E N F E L D and W.L. M c L E A N Serin Physics Laboratory, Rutgers University, P. O. Box 849, Piscataway, NJ 08855-0849, USA Received 3 August 1987
Spin-orbit scattering is enhanced in granular aluminum by the addition of small amounts of bismuth. The metalinsulator transition is displaced to larger values of room-temperature resistivity. The superconducting-normal threshold is displaced by an approximately equal amount.
The relationship of superconductivity to the metal-insulator transition is a subject of considerable current investigation and speculation [1, 2]. In particular it has been suggested that spin-orbit scattering plays a major role in determining whether superconductivity persists to the m - i transition [3, 4]. We have investigated the effect of enhanced spin-orbit scattering resulting from the addition of small amounts of bismuth to granular aluminum. The results demonstrate a substantial shift in the m - i transition, accompanied by an at least approximately equal shift in the concentration of metallic aluminum to which superconductivity persists. The experiments were made on a series of samples of granular aluminum, evaporated from an electron-beam source onto water-cooled glass substrates in the presence of a small amount of oxygen. Bismuth was evaporated simultaneously from a second neighboring source. The deposition rates were measured and kept constant by independent crystal monitors. The amount of Bi as a fraction of metallic A1 was about 2% (at). We do not expect this amount of Bi to lead to any changes in structure or grain size. The solubility of Bi in AI is given by Hansen [5] as 0.02% (at), so that the Bi is presumably primarily outside the grains. Its effectiveness in changing the spin-orbit scattering is apparent from the critical field which shows a value of Hc2(0 ) of 6.5 T for a specimen with PRX equal to 7.4 X 103 p~l-Icm, or about twice as much as the value of 3.6 T [6] in 0378-4363/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) and Yamada Science Foundation
the absence of Bi. The analysis of the magnetoresistance leads to a value of 7so of 6 × 10 13 s for the same specimen, compared with a value of about 2 x 10 -11 s for a specimen with a similar resistivity without Bi [7]. Fig. 1 shows T~ (the midpoint of the resistive transition) as a function of the room-temperature resistivity PRT for superconducting specimens with and without Bi. We use the value of PRT as a sensitive measure of the relative amounts of A1 and A1203, essentially unaffected by supercon-
1.2 1.1 1.0
T T
0.9
o
+
o
C
0.8 CO
0.7 0.6 0.5
o
.
10 ~
.
.
.
.
.
.
.
.
10 a
.
.
.
.
.
.
.
.
.
104
.
.
,
, , , , ,
10 s
~.r ( j~i')-c m ) Fig. 1. To~To as a function of flRT for specimens with Bi (circles) and without Bi (crosses). T~o is 2.43 K for the specimens without Bi, and 2.28 K for the specimens with Bi.
T.A. Miller et al. / Superconductivity near the m - i transition
ductivity, localization, or the presence of small amounts of Bi. It m a y be seen that T c decreases as PRT increases in both kinds of specimens, but that superconductivity remains to values of PRT about 3 times as high in the specimens which contain Bi. For an unambiguous determination whether a specimen is metallic normal-state m e a s u r e m e n t s at very low t e m p e r a t u r e s must be used. Since we have only preliminary m e a s u r e m e n t s of that kind we present on fig. 2 the ratio r R 4 . 2 / R R T as a function of PRT" The value of r increases steeply as the m - i transition is approached. The choice of 4.2 K for the resistance in the n u m e r a t o r of this ratio is not completely arbitrary. It represents a t e m p e r a t u r e which is low but with only very minor indications of superconducting fluctuations. The figure shows a shift in the m - i transition in the specimens containing Bi which is close to or the same as the shift in the superconducting threshold shown in fig. 1. The observation that the two variations are similar is confirmed by fig. 3, which shows T c as a function of r. We do not rule out the possibility of small differences in the shifts of the m - i transition and the S - N threshold or in the shapes of the curves, but wish to concentrate in this report on their striking similarity. It is clear, first of all, that the increase in the spin-orbit scattering shifts the m - i transition. Since s p i n - o r b i t scattering cannot affect the percolation threshold we conclude that the m - i transition is determined ( " d r i v e n " ) by localization rather than by percolation. This conclusion is supported by the continuous decrease in To, which is expected when localization and the associated e l e c t r o n - e l e c t r o n interactions come into play [8]. Finally, if the S - N threshold is shifted by the same amount, it follows that the position of this threshold as a function of PRT is determined by the position of the m - i transition. It has been conjectured [3] that the enhancement of s p i n - o r b i t scattering separates the S - N threshold from the m - i transition. Our results do not support this conclusion. The existence of a non-superconducting metallic region in 3D systems with strong s p i n - o r b i t scattering is also
511
? o
6
o o
5
+
o
4
r 3 2
=
o
102
103
10 s
104
pRZ( p ~ - - C m ) Fig. 2. The ratio r R42/RRT as a function of PRT for specimens with Bi (circles) and without Bi (crosses). =
1 2 1
1
1 0
T
0
9
c
- - 0 8
T
co 0
7
0
6
+
o O
0.5
O
I
I
I
I
I
I
1
2
3
4
5
6
r Fig. 3.
T,]T,.o as a function of r for specimens with Bi
(circles) without Bi (crosses). suggested in ref. [4]. T h e r e is, however, no prediction about a possible change as the s p i n orbit scattering rate is altered. We may summarize our main conclusion by saying that an increase in the s p i n - o r b i t scattering rate shifts the m e t a l - i n s u l a t o r transition, and with it the s u p e r c o n d u c t i n g - n o r m a l threshold.
512
T . A . Miller et al. / Superconductivity near the m - i transition
We w o u l d like to t h a n k G . D e u t s c h e r for v a l u a b l e a n d s t i m u l a t i n g discussions a n d comm e n t s . This w o r k was s u p p o r t e d by the N a t i o n a l Science F o u n d a t i o n u n d e r g r a n t D M R - 8 5 - 1 1 9 8 2 .
References [1] M. Ma and P.A. Lee, Phys. Rev. B 32 (1985) 5658. [2] G. Kotliar and A. Kapitulnik, Phys. Rev. B 33 (1986) 3146.
[3] D.J. Bishop, E.G. Spencer, J.P. Garno and R.C. Dynes, Bull. Am. Phys. Soc. 29 (1984) 343. [4] M. Ma and E. Fradkin, Phys. Rev. Lett. 56 (1986) 1416. [5] M. Hansen, Constitution of Binary Alloys (McGraw-Hill, New York, 1958). [6] T. Chui, P. Lindenfeld, W.L. McLean and K. Mui, Phys. Rev. B 24 (1981) 6728. [7] K.C, Mui, P. Lindenfeld and W.L. McLean, Phys. Rev. B 30 (1984) 2951. [8] H. Fukuyama, H. Ebisawa and S. Maekawa, J. Phys. Soc. Jap. 53 (1984) 3560.