- Email: [email protected]
graphite bilayers
Physica C 417 (2004) 58–62 www.elsevier.com/locate/physc
Superconducting transition temperature of niobium/graphite bilayers Toshiharu Kubo, Yoshiko F. Ohashi *, Takeshi Kinoshita Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Yokohama 223-8522, Japan Received 6 August 2004; received in revised form 7 October 2004; accepted 18 October 2004
Abstract The superconducting proximity effect in niobium/graphite bilayers was studied. Thin graphite films of various thickness ranging from around 20–160 nm were prepared by cleaving a kish graphite (KG). For making a specimen, niobium (Nb) of 40 nm in thickness was deposited on a KG film and a quartz glass substrate simultaneously using electron-beam evaporation method. Each resistance of Nb and Nb/KG films was measured at the same time, and transition temperature of Nb film (T SC ) and Nb/KG film (T C ) on the same substrate was obtained. The ratio of T C to T SC (T C =T SC ) showed a periodic characteristic with KG film thickness. Furthermore, the peak values of the ratio exceeded 1.00. This result suggests that the electron correlation at Nb/KG interface changes depending on KG film thickness because of the interference of electrons as wave in the KG film. 2004 Elsevier B.V. All rights reserved. PACS: 73.20.r; 73.50.h; 74.50.+r Keywords: Superconductor; Proximity effect; Niobium; Graphite; Transition temperature
1. Introduction Superconducting proximity effect has been studied since the early 1960s, and many studies were made to clarify the electronic properties at the interface between superconductor (S) and normal conductor (N) [1–3]. In early experiments on the *
Corresponding author. Tel.: +81 45 5661597; fax: +81 45 5628487. E-mail address: [email protected] (Y.F. Ohashi).
proximity effect, the reduction in transition temperature of S/N bilayers was paid attention, because it was considered that the electron–electron interaction in normal conductor was obtained by investigating the relation between the amount of the reduction in transition temperature and each film thickness of S and N [4–7]. In this study, we used graphite as N. Graphite is a semimetal which has the typical layer structure, and the electrical resistivity along the lamination direction called c-axis (qc) is extremely larger than
0921-4534/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.10.007
T. Kubo et al. / Physica C 417 (2004) 58–62
that in the basal plane (qa). Although the measurement of qc is more difficult than that of qa, it is investigated well experimentally and theoretically on bulk graphite [8]. As for thin graphite films, it has been reported that qa shows the size effect, while qc was fiendishly difficult to be measured [9]. However, it is expected that the electronic properties of the c-axis direction can be obtained by measuring qa through the superconducting proximity effect. Therefore, we studied experimentally the relation between the transition temperature of niobium/graphite corresponding to S/N bilayers and the thickness of graphite films.
2. Theory According to de Gennes–Werthamers theory dealing with the dirty layers, where the electron mean free path (‘) is smaller than the superconducting coherence length (n) [4–7]. The spatial dependence of the pair potential, D(r), at temperatures close to the transition temperature of S/N bilayer (T C ) is represented as Fig. 1. In this case, the electron–electron interaction is assumed to be weak attractive interaction. The value b is determined by the extrapolation from D in S region as shown in Fig. 1. Eq. (1) shows the coherence length nS,N in each layer of S and N as follows: 1=2 hDS;N nS;N ¼ ð‘ nÞ; ð1Þ 2pk B T (rr )
S
N
N
S
b
Fig. 1. Spatial dependence of the pair potential D(r) at temperatures close to the transition temperature in an N/S bilayer.
59
where T denotes the temperature, D is the diffusion coefficient corresponding to (1/3) vF‘, and vF is the Fermi velocity. In the theory by de Gennes [6], T C is approximated as 3
T C ¼ T 1 þ 2p2 n2S T SC ½b1 =ðd S þ b1 Þ e2Kd N ;
ð2Þ
nN, T SC
where K is nearly equal to the inverse of is the transition temperature of the superconductor itself, dS and dN are each film thickness of S and N, T1 and b1 are each value of T C and b when dN becomes infinite. This expression of T C implies the experimental fact that T C is lowered exponentially as dN increases. Although Eq. (2) was obtained on the assumption of dirty layers, an expansion of the theory from dirty systems to clean systems, namely ‘ > n, was made by Tanaka and Tsukada [10]. In the clean limit, nS,N are written as nS;N ¼
hvF S;N 2pk B T
ð‘ nÞ:
ð3Þ
It is considered that Eq. (2) is still valid if expressions of n and b in the clean systems are used. Therefore it is also expected that T C is lowered exponentially in the clean systems.
3. Experimental In order to investigate the change of the transition temperature (TC), niobium/graphite bilayers were prepared by the following procedure. Firstly, a kish graphite (KG) was chosen as an original crystal with good crystal perfection. Thin graphite films as N were made by cleaving the KG [9], and the uniform part was selected. The thickness of KG films was determined by measuring transmitted light intensity [9], which was ranging from around 20–160 nm. The size of KG films was at most 1 mm square. They were kept on quartz glass substrates. As for the superconductor, niobium (Nb) was used because of the highest TC in the simple metals and its strong durability to the temperature change. Nb films were made by electron-beam evaporation method. The base pressure of the evaporation system was about 1 · 108 Torr. The
60
T. Kubo et al. / Physica C 417 (2004) 58–62
resistivity value and TC of Nb films are affected by a few atomic percent of the residual impurity [11], which is related to the base pressure and the deposition rate at evaporation. For making a specimen, Nb was deposited on the lamination of a KG film and a quartz glass substrate itself simultaneously, as shown in Fig. 2(a) in order to distinguish the change of TC by the proximity effect from that by the condition at evaporation. Since the contamination at the interface disturbs the proximity effect [12], the KG film surface was cleaned before evaporation by Ar+ bombardment for 10 s with the energy of 400 eV, the current density of which was about 30 mA/cm2. The quartz oscillator system controlled the thickness of Nb films about 40 nm corresponding to the coherence length of Nb. After evaporation, each electrode was attached to Nb and Nb/KG films on the same substrate as shown in Fig. 2(b), so that each resistance of Nb and Nb/KG films kept at uniform temperature could be measured at the same time by means of the conventional four-terminal method. The measurement accuracy of the TC change was 0.05. The
(a)
Nb
KG
Quartz glass substrate (b) Voltage electrodes
Nb/KG
Current electrode
Current electrode
Nb
Voltage electrodes
Fig. 2. Schematic diagram of a specimen (a) cross sectional view. Nb is deposited on the lamination of a KG film and a quartz glass substrate. (b) Electrode configuration. The length of Nb/KG film is 0.5 mm at most.
current density of each specimen was restricted within 105–106 A/m2, and it was confirmed that the current density did not have any influence on both T SC of Nb films and T C of Nb/KG films. 4. Results and discussion Three typical examples of the experimental results are shown in Fig. 3(a)–(c). The resistance (R) is normalized by R0 which is the resistance at the onset temperature T0. The resistivity of Nb films at T0 was 15–30 lX cm. The transition temperature (TC) was defined as the temperature at which R of the sample equals one-half of R0. TC of Nb films, namely T SC , was 6–7 K. Fig. 3(a) is the result of the sample whose change of TC of Nb/KG film, namely T C , was the largest. T C was lowered from T SC about 0.3. According to de Gennes–Werthamers theory [4–7], the cause of this result should be considered that the pair potential in Nb film decreases toward the interface between Nb and KG, since the Cooper pair in Nb film penetrates into KG film. On the other hand, Fig. 3(b) shows a result where T C is higher than T SC about 0.2. The conventional theory is not appropriate for this result. Fig. 3(c) shows a result where T C was lowered from T SC only 0.05, which is in-between of the two cases of Fig. 3(a) and (b). In Fig. 4, the ratio of T C to T SC (T C =T SC ) is plotted as a function of KG film thickness. The ratio shows a periodic characteristic with KG film thickness (dKG), although there is some randomness in the characteristic at large dKG. Furthermore, the peak values of the ratio exceed 1.00. The reason of this unexpected result will be explained as follows. At first, the coherence length in KG film (nNZ) is estimated under the conditions that electrons and holes are independent, and that only onedimension along the c-axis is important. The Fermi wave vector kFZ and the effective mass mZ along the c-axis are 25 · 108 m1, 14m0 for electrons, and 15 · 108 m1, 5.7m0 for holes (m0: free electron mass) [13,14]. By substituting these values for the relation vFZ ¼ hk FZ =mZ , vFZ equals 2.0 · 104 m/s for electrons and 3.0 · 104 m/s for holes, respectively. For the simplicity, ‘Z is assumed to be
T. Kubo et al. / Physica C 417 (2004) 58–62
1.5
1
1 R/R0
R/R0
1.5
61
0.5
0 5 (a)
0.5
6 7 Temperature (K)
0 5
8 (b)
6 7 Temperature (K)
8
1.5
R/R0
1
0.5
0 5
6 7 Temperature (K)
(c)
8
Fig. 3. Three typical examples of results. The open circle (s) represents the result of a Nb film, and the closed circle (d) represents that of a Nb/KG film. Nb film thickness is 40 nm and KG film thickness of Nb/KG films are (a) 87 nm, (b) 114 nm, (c) 52 nm, respectively.
TC*/TCS
1.05
Nb=40nm
1.00
0.95 0
50
100
150
KG film thickness (nm)
Fig. 4. Periodic characteristics of the ratio of T C to T SC vs. KG film thickness. The period shown in this figure is about 30 nm.
50 nm for both electrons and holes, because the transport properties show the size effect when KG film thickness is thinner than about 50 nm [9]. By using Eq. (1) and the relation DZ = vFZ Æ ‘Z, nNZ in the dirty limit at liquid helium temperature
(4.2 K) is estimated at 17 nm for electrons and at 21 nm for holes. According to these estimations, nNZ is smaller than ‘Z, therefore, KG film should not be dirty. On the other hand, by using Eq. (3), nNZ in the clean limit at 4.2 K is estimated at 5.9 nm for electrons and at 8.7 nm for holes. Consequently, in Eq. (2), it is expected that the reduction of T C is saturated when KG film thickness exceeds 10 nm at most and that the amount is negligibly small because of the large difference of the density of states between Nb and KG at the Fermi level. This estimation does not support the experimental result. On the other hand, the periodic characteristic of TC is revealed in Nb/KG bilayers. As for the oscillatory behavior of TC, Tanaka and Tsukada essentially discussed in the superconducting superlattice [15,16]. According to their theory, the cause is that the density of states at the Fermi level of the superlattice in the normal state oscillates as a function of
62
T. Kubo et al. / Physica C 417 (2004) 58–62
the length of the unit period because of the change of the energy band structure. However, the periodic characteristic of TC in Nb/KG bilayers seems to be related to the interference of electrons as wave in the KG film, that is to say, the electron correlation leading to the superconductivity at Nb/KG interface should be affected by the change of the quasiparticles local density of states, which is a function of the distance from the Nb/KG boundary along the c-axis of KG films. As for the electron interference in the clean N film, Rowell and McMillan reported at first [17]. According to them, the dependence of the local density of states on the thickness of N shows a periodic characteristic. This period is given by p⁄vF/2x for the energy x. Therefore, by substituting the period, 30 nm in Fig. 4, and vFZ of KG, the energy x is estimated at 0.7 meV for electrons (1.1 meV for holes), which is the same order of the pair potential of Nb at 0 K: 1.5 meV. This result seems to show the occurrence of the electron interference in KG. Although the theory of clean systems has been extended to some theories including the reflection at the S/N interface and the spatial dependence of the pair potential [18–20], the experimental result T C =T SC > 1 has not been suggested since the electron correlation relating to the superconductivity is regarded as weak in the N region. The fact implies that the electron correlation in KG is helpful to the superconductivity under certain condition of the electron/ hole interference. Therefore, some additional theory should be made by taking into account the peculiarity of graphite.
5. Conclusions The superconducting transition temperature of Nb/KG bilayers (T C ) was measured for various KG film thickness (dKG). The thickness of Nb films was controlled about 40 nm corresponding to the coherence length of Nb. As the result, it was found that the ratio T C =T SC showed a periodic characteristic with dKG. Furthermore, the peak values of the ratio exceeded 1.00 although T C was merely lowered in other materials on the proximity effect. In order to explain this result, the
peculiarity of the electronic properties in graphite should be taken into account.
Acknowledgments We are grateful to Professor Y. Hishiyama of Musashi Institute of Technology for kindly supplying a precious KG crystal. We would thank K. Kitamura for his help in evaporation of Nb films and also thank Professor S. Anzai for valuable discussions. A part of this work was supported by Keio Gijuku Academic Development Funds.
References [1] G. Deutscher, P.G. de Gennes, in: R.D. Parks (Ed.), Superconductivity, Marcel Dekker, New York, 1969, p. 1005. [2] P.G. de Gennes, Superconductivity of Metals and Alloys, Benjamin, New York, 1969. [3] B. van Wees, H. Takayanagi, Mesoscopic Electron Transport, Kluwer Academic Publishers, Dordrecht, 1997, p. 469. [4] P.G. deGennes, Rev. Mod. Phys. 36 (1964) 225. [5] J.J. Hauser, H.C. Theuerer, N.R. Werthamer, Phys. Rev. 136 (1964) A637. [6] J.J. Hauser, H.C. Theuerer, Phys. Lett. 14 (1965) 270. [7] W.M. vanHuffelen, T.M. Klapwijk, E.P.Th.M. Suurmeijer, Phys. Rev. B 47 (1993) 5151. [8] K. Matsubara, K. Sugihara, T. Tsuzuku, Phys. Rev. B 41 (1990) 969. [9] Y. Ohashi, T. Koizumi, T. Yoshikawa, T. Hironaka, K. Shiiki, TANSO (180) (1997) 235. [10] Y. Tanaka, M. Tsukada, Phys. Rev. B 42 (1990) 2066. [11] W. De Sorbo, Phys. Rev. 132 (1963) 107. [12] T. Kawakami, H. Takayanagi, Appl. Phys. Lett. 46 (1985) 92. [13] D.E. Soule, J.W. McClure, L.B. Smith, Phys. Rev. 134A (1964) 453. [14] P.R. Shroeder, M.S. Dresselhaus, A. Javan, Phys. Rev. Lett. 20 (1968) 1292. [15] Y. Tanaka, M. Tsukada, Phys. Rev. B 40 (1989) 4482. [16] Y. Tanaka, M. Tsukada, J. Phys. Soc. Jpn. 60 (1991) 1327. [17] J.M. Rowell, W.L. McMillan, Phys. Rev. Lett. 16 (1966) 453. [18] M. Ashida, J. Hara, K. Nagai, Phys. Rev. B 45 (1992) 828. [19] J. Hara, M. Ashida, K. Nagai, Phys. Rev. B 47 (1993) 11263. [20] Y. Nagato, K. Nagai, J. Hara, J. Low Temp. Phys. 93 (1993) 33.
Superconducting transition temperature of niobium/graphite bilayers Toshiharu Kubo, Yoshiko F. Ohashi *, Takeshi Kinoshita Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Yokohama 223-8522, Japan Received 6 August 2004; received in revised form 7 October 2004; accepted 18 October 2004
Abstract The superconducting proximity effect in niobium/graphite bilayers was studied. Thin graphite films of various thickness ranging from around 20–160 nm were prepared by cleaving a kish graphite (KG). For making a specimen, niobium (Nb) of 40 nm in thickness was deposited on a KG film and a quartz glass substrate simultaneously using electron-beam evaporation method. Each resistance of Nb and Nb/KG films was measured at the same time, and transition temperature of Nb film (T SC ) and Nb/KG film (T C ) on the same substrate was obtained. The ratio of T C to T SC (T C =T SC ) showed a periodic characteristic with KG film thickness. Furthermore, the peak values of the ratio exceeded 1.00. This result suggests that the electron correlation at Nb/KG interface changes depending on KG film thickness because of the interference of electrons as wave in the KG film. 2004 Elsevier B.V. All rights reserved. PACS: 73.20.r; 73.50.h; 74.50.+r Keywords: Superconductor; Proximity effect; Niobium; Graphite; Transition temperature
1. Introduction Superconducting proximity effect has been studied since the early 1960s, and many studies were made to clarify the electronic properties at the interface between superconductor (S) and normal conductor (N) [1–3]. In early experiments on the *
Corresponding author. Tel.: +81 45 5661597; fax: +81 45 5628487. E-mail address: [email protected] (Y.F. Ohashi).
proximity effect, the reduction in transition temperature of S/N bilayers was paid attention, because it was considered that the electron–electron interaction in normal conductor was obtained by investigating the relation between the amount of the reduction in transition temperature and each film thickness of S and N [4–7]. In this study, we used graphite as N. Graphite is a semimetal which has the typical layer structure, and the electrical resistivity along the lamination direction called c-axis (qc) is extremely larger than
0921-4534/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.10.007
T. Kubo et al. / Physica C 417 (2004) 58–62
that in the basal plane (qa). Although the measurement of qc is more difficult than that of qa, it is investigated well experimentally and theoretically on bulk graphite [8]. As for thin graphite films, it has been reported that qa shows the size effect, while qc was fiendishly difficult to be measured [9]. However, it is expected that the electronic properties of the c-axis direction can be obtained by measuring qa through the superconducting proximity effect. Therefore, we studied experimentally the relation between the transition temperature of niobium/graphite corresponding to S/N bilayers and the thickness of graphite films.
2. Theory According to de Gennes–Werthamers theory dealing with the dirty layers, where the electron mean free path (‘) is smaller than the superconducting coherence length (n) [4–7]. The spatial dependence of the pair potential, D(r), at temperatures close to the transition temperature of S/N bilayer (T C ) is represented as Fig. 1. In this case, the electron–electron interaction is assumed to be weak attractive interaction. The value b is determined by the extrapolation from D in S region as shown in Fig. 1. Eq. (1) shows the coherence length nS,N in each layer of S and N as follows: 1=2 hDS;N nS;N ¼ ð‘ nÞ; ð1Þ 2pk B T (rr )
S
N
N
S
b
Fig. 1. Spatial dependence of the pair potential D(r) at temperatures close to the transition temperature in an N/S bilayer.
59
where T denotes the temperature, D is the diffusion coefficient corresponding to (1/3) vF‘, and vF is the Fermi velocity. In the theory by de Gennes [6], T C is approximated as 3
T C ¼ T 1 þ 2p2 n2S T SC ½b1 =ðd S þ b1 Þ e2Kd N ;
ð2Þ
nN, T SC
where K is nearly equal to the inverse of is the transition temperature of the superconductor itself, dS and dN are each film thickness of S and N, T1 and b1 are each value of T C and b when dN becomes infinite. This expression of T C implies the experimental fact that T C is lowered exponentially as dN increases. Although Eq. (2) was obtained on the assumption of dirty layers, an expansion of the theory from dirty systems to clean systems, namely ‘ > n, was made by Tanaka and Tsukada [10]. In the clean limit, nS,N are written as nS;N ¼
hvF S;N 2pk B T
ð‘ nÞ:
ð3Þ
It is considered that Eq. (2) is still valid if expressions of n and b in the clean systems are used. Therefore it is also expected that T C is lowered exponentially in the clean systems.
3. Experimental In order to investigate the change of the transition temperature (TC), niobium/graphite bilayers were prepared by the following procedure. Firstly, a kish graphite (KG) was chosen as an original crystal with good crystal perfection. Thin graphite films as N were made by cleaving the KG [9], and the uniform part was selected. The thickness of KG films was determined by measuring transmitted light intensity [9], which was ranging from around 20–160 nm. The size of KG films was at most 1 mm square. They were kept on quartz glass substrates. As for the superconductor, niobium (Nb) was used because of the highest TC in the simple metals and its strong durability to the temperature change. Nb films were made by electron-beam evaporation method. The base pressure of the evaporation system was about 1 · 108 Torr. The
60
T. Kubo et al. / Physica C 417 (2004) 58–62
resistivity value and TC of Nb films are affected by a few atomic percent of the residual impurity [11], which is related to the base pressure and the deposition rate at evaporation. For making a specimen, Nb was deposited on the lamination of a KG film and a quartz glass substrate itself simultaneously, as shown in Fig. 2(a) in order to distinguish the change of TC by the proximity effect from that by the condition at evaporation. Since the contamination at the interface disturbs the proximity effect [12], the KG film surface was cleaned before evaporation by Ar+ bombardment for 10 s with the energy of 400 eV, the current density of which was about 30 mA/cm2. The quartz oscillator system controlled the thickness of Nb films about 40 nm corresponding to the coherence length of Nb. After evaporation, each electrode was attached to Nb and Nb/KG films on the same substrate as shown in Fig. 2(b), so that each resistance of Nb and Nb/KG films kept at uniform temperature could be measured at the same time by means of the conventional four-terminal method. The measurement accuracy of the TC change was 0.05. The
(a)
Nb
KG
Quartz glass substrate (b) Voltage electrodes
Nb/KG
Current electrode
Current electrode
Nb
Voltage electrodes
Fig. 2. Schematic diagram of a specimen (a) cross sectional view. Nb is deposited on the lamination of a KG film and a quartz glass substrate. (b) Electrode configuration. The length of Nb/KG film is 0.5 mm at most.
current density of each specimen was restricted within 105–106 A/m2, and it was confirmed that the current density did not have any influence on both T SC of Nb films and T C of Nb/KG films. 4. Results and discussion Three typical examples of the experimental results are shown in Fig. 3(a)–(c). The resistance (R) is normalized by R0 which is the resistance at the onset temperature T0. The resistivity of Nb films at T0 was 15–30 lX cm. The transition temperature (TC) was defined as the temperature at which R of the sample equals one-half of R0. TC of Nb films, namely T SC , was 6–7 K. Fig. 3(a) is the result of the sample whose change of TC of Nb/KG film, namely T C , was the largest. T C was lowered from T SC about 0.3. According to de Gennes–Werthamers theory [4–7], the cause of this result should be considered that the pair potential in Nb film decreases toward the interface between Nb and KG, since the Cooper pair in Nb film penetrates into KG film. On the other hand, Fig. 3(b) shows a result where T C is higher than T SC about 0.2. The conventional theory is not appropriate for this result. Fig. 3(c) shows a result where T C was lowered from T SC only 0.05, which is in-between of the two cases of Fig. 3(a) and (b). In Fig. 4, the ratio of T C to T SC (T C =T SC ) is plotted as a function of KG film thickness. The ratio shows a periodic characteristic with KG film thickness (dKG), although there is some randomness in the characteristic at large dKG. Furthermore, the peak values of the ratio exceed 1.00. The reason of this unexpected result will be explained as follows. At first, the coherence length in KG film (nNZ) is estimated under the conditions that electrons and holes are independent, and that only onedimension along the c-axis is important. The Fermi wave vector kFZ and the effective mass mZ along the c-axis are 25 · 108 m1, 14m0 for electrons, and 15 · 108 m1, 5.7m0 for holes (m0: free electron mass) [13,14]. By substituting these values for the relation vFZ ¼ hk FZ =mZ , vFZ equals 2.0 · 104 m/s for electrons and 3.0 · 104 m/s for holes, respectively. For the simplicity, ‘Z is assumed to be
T. Kubo et al. / Physica C 417 (2004) 58–62
1.5
1
1 R/R0
R/R0
1.5
61
0.5
0 5 (a)
0.5
6 7 Temperature (K)
0 5
8 (b)
6 7 Temperature (K)
8
1.5
R/R0
1
0.5
0 5
6 7 Temperature (K)
(c)
8
Fig. 3. Three typical examples of results. The open circle (s) represents the result of a Nb film, and the closed circle (d) represents that of a Nb/KG film. Nb film thickness is 40 nm and KG film thickness of Nb/KG films are (a) 87 nm, (b) 114 nm, (c) 52 nm, respectively.
TC*/TCS
1.05
Nb=40nm
1.00
0.95 0
50
100
150
KG film thickness (nm)
Fig. 4. Periodic characteristics of the ratio of T C to T SC vs. KG film thickness. The period shown in this figure is about 30 nm.
50 nm for both electrons and holes, because the transport properties show the size effect when KG film thickness is thinner than about 50 nm [9]. By using Eq. (1) and the relation DZ = vFZ Æ ‘Z, nNZ in the dirty limit at liquid helium temperature
(4.2 K) is estimated at 17 nm for electrons and at 21 nm for holes. According to these estimations, nNZ is smaller than ‘Z, therefore, KG film should not be dirty. On the other hand, by using Eq. (3), nNZ in the clean limit at 4.2 K is estimated at 5.9 nm for electrons and at 8.7 nm for holes. Consequently, in Eq. (2), it is expected that the reduction of T C is saturated when KG film thickness exceeds 10 nm at most and that the amount is negligibly small because of the large difference of the density of states between Nb and KG at the Fermi level. This estimation does not support the experimental result. On the other hand, the periodic characteristic of TC is revealed in Nb/KG bilayers. As for the oscillatory behavior of TC, Tanaka and Tsukada essentially discussed in the superconducting superlattice [15,16]. According to their theory, the cause is that the density of states at the Fermi level of the superlattice in the normal state oscillates as a function of
62
T. Kubo et al. / Physica C 417 (2004) 58–62
the length of the unit period because of the change of the energy band structure. However, the periodic characteristic of TC in Nb/KG bilayers seems to be related to the interference of electrons as wave in the KG film, that is to say, the electron correlation leading to the superconductivity at Nb/KG interface should be affected by the change of the quasiparticles local density of states, which is a function of the distance from the Nb/KG boundary along the c-axis of KG films. As for the electron interference in the clean N film, Rowell and McMillan reported at first [17]. According to them, the dependence of the local density of states on the thickness of N shows a periodic characteristic. This period is given by p⁄vF/2x for the energy x. Therefore, by substituting the period, 30 nm in Fig. 4, and vFZ of KG, the energy x is estimated at 0.7 meV for electrons (1.1 meV for holes), which is the same order of the pair potential of Nb at 0 K: 1.5 meV. This result seems to show the occurrence of the electron interference in KG. Although the theory of clean systems has been extended to some theories including the reflection at the S/N interface and the spatial dependence of the pair potential [18–20], the experimental result T C =T SC > 1 has not been suggested since the electron correlation relating to the superconductivity is regarded as weak in the N region. The fact implies that the electron correlation in KG is helpful to the superconductivity under certain condition of the electron/ hole interference. Therefore, some additional theory should be made by taking into account the peculiarity of graphite.
5. Conclusions The superconducting transition temperature of Nb/KG bilayers (T C ) was measured for various KG film thickness (dKG). The thickness of Nb films was controlled about 40 nm corresponding to the coherence length of Nb. As the result, it was found that the ratio T C =T SC showed a periodic characteristic with dKG. Furthermore, the peak values of the ratio exceeded 1.00 although T C was merely lowered in other materials on the proximity effect. In order to explain this result, the
peculiarity of the electronic properties in graphite should be taken into account.
Acknowledgments We are grateful to Professor Y. Hishiyama of Musashi Institute of Technology for kindly supplying a precious KG crystal. We would thank K. Kitamura for his help in evaporation of Nb films and also thank Professor S. Anzai for valuable discussions. A part of this work was supported by Keio Gijuku Academic Development Funds.
References [1] G. Deutscher, P.G. de Gennes, in: R.D. Parks (Ed.), Superconductivity, Marcel Dekker, New York, 1969, p. 1005. [2] P.G. de Gennes, Superconductivity of Metals and Alloys, Benjamin, New York, 1969. [3] B. van Wees, H. Takayanagi, Mesoscopic Electron Transport, Kluwer Academic Publishers, Dordrecht, 1997, p. 469. [4] P.G. deGennes, Rev. Mod. Phys. 36 (1964) 225. [5] J.J. Hauser, H.C. Theuerer, N.R. Werthamer, Phys. Rev. 136 (1964) A637. [6] J.J. Hauser, H.C. Theuerer, Phys. Lett. 14 (1965) 270. [7] W.M. vanHuffelen, T.M. Klapwijk, E.P.Th.M. Suurmeijer, Phys. Rev. B 47 (1993) 5151. [8] K. Matsubara, K. Sugihara, T. Tsuzuku, Phys. Rev. B 41 (1990) 969. [9] Y. Ohashi, T. Koizumi, T. Yoshikawa, T. Hironaka, K. Shiiki, TANSO (180) (1997) 235. [10] Y. Tanaka, M. Tsukada, Phys. Rev. B 42 (1990) 2066. [11] W. De Sorbo, Phys. Rev. 132 (1963) 107. [12] T. Kawakami, H. Takayanagi, Appl. Phys. Lett. 46 (1985) 92. [13] D.E. Soule, J.W. McClure, L.B. Smith, Phys. Rev. 134A (1964) 453. [14] P.R. Shroeder, M.S. Dresselhaus, A. Javan, Phys. Rev. Lett. 20 (1968) 1292. [15] Y. Tanaka, M. Tsukada, Phys. Rev. B 40 (1989) 4482. [16] Y. Tanaka, M. Tsukada, J. Phys. Soc. Jpn. 60 (1991) 1327. [17] J.M. Rowell, W.L. McMillan, Phys. Rev. Lett. 16 (1966) 453. [18] M. Ashida, J. Hara, K. Nagai, Phys. Rev. B 45 (1992) 828. [19] J. Hara, M. Ashida, K. Nagai, Phys. Rev. B 47 (1993) 11263. [20] Y. Nagato, K. Nagai, J. Hara, J. Low Temp. Phys. 93 (1993) 33.