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Critical currents of strongly disordered ultra-thin superconducting films
Physica B 329–333 (2003) 1386–1388
Critical currents of strongly disordered ultra-thin superconducting films Swati S. Soman*, K. Das Gupta, N. Chandrasekhar Department of Physics, Indian Institute of Science, Bangalore 560 012, India
Abstract Quench-condensed films of various metals are well known systems for studying the superconducting state in presence of strong disorder. Critical currents of superconducting films of Bi and Sn with sheet resistance o500 O were found to vary with temperature according to the relation Ic ðTÞ ¼ Ic ð0Þð1 ðT=Tc Þ4 Þ: The result was found to be independent of the substrate used. The observed dependence implies a variation of the superconducting gap DðTÞBð1 ðT=Tc Þ4 Þ1=2 ; near Tc : This is different from the behaviour of a BCS type gap near Tc but consistent with some existing measurements on fabricated 2-D Josephson junction arrays. The I–V characteristics of these films also show hysteresis, indicating the presence of underdamped intergrain Josephson coupling. The values of the intergrain resistances and capacitances are estimated from the ratios of the observed retrapping and critical currents. r 2003 Elsevier Science B.V. All rights reserved. PACS: 73.50.h; 74.25.Sv; 74.78.w Keywords: Josephson-junction; Disorder; Quench-condensed
1. Introduction
2. Experimental set-up
The nature of the superconducting state in a disordered system has been a topic of interest for several decades now. Quench condensed ultra-thin films have been investigated as model systems to study disorder and superconductivity. The existence of an insulator to superconductor (SI) transition in many elemental as well as multi-component systems is now established [1]. We have studied quench-condensed superconducting films of Bi and Sn. These films exhibit SI transition as their thickness is increased. We show in this paper that experimentally obtained I–V characteristics of these films in their superconducting phase can be understood as arising from disordered arrays of Josephson junctions.
The experiments are done in a UHV cryostat, custom designed [2] for in situ study of ultrathin films under a hydrocarbon-free vacuum better than 108 Torr: Aquartz or crystalline sapphire, mounted with adequate thermal contact on a copper cold finger, in contact with a pumped liquid helium bath, is used as a substrate. At a time two Hall bar shaped films can be evaporated side ( Ge by side. One of the films has a pre-deposited 10 A underlayer. Electrical contacts to the sample films are ( thick, provided with platinum contact pads about 60 A pre-deposited on the substrate. Four-probe DC measurements are carried out using a high impedance current source and a nanovoltmeter.
3. Results
*Corresponding author. E-mail address: [email protected] (S.S. Soman).
A typical set of observed I–V characteristics of a film in the superconducting regime is shown in Fig. 1. The I– V curves show hysteresis similar to underdamped
0921-4526/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0921-4526(02)02262-7
S.S. Soman et al. / Physica B 329–333 (2003) 1386–1388
Sn on Ge/a-quartz
1387
1
Sn films
2
2
1
1
Tsub= 14K T=2.2K 0.4
i=IC/IC(0)
V(Volts)
# 1 2 3 4 d(A) 28.9 43.6 48.7 59.5 R (Ω) 1237 478 290 133 1.5 N Tc(K) 3.4 4.56 4.67 4.9
3
fit equation i = 1 - t4
0.3 RN ( )
dataset
0.2
#53SN_1 #59SNG_3 #60SNG_1 #60SNG_2 #60SNG_3
0.1
199 562 478 290 133
4
0.5
All films quenched on a-quartz at 14K
0.04
0
0.4
0
0.001
0.002
0.003
0.6
0.8
t = T/TC
0.004
I(Amp)
1
Bi films
Fig. 1. Typical I–V characteristics of superconducting films showing hysteretic behaviour.
Our experimental temperature range is restricted to T=Tc B0:3: The flattening of the curves at low temperature allows us to make an extrapolation of the critical current in the limit T-0: We find that near Tc for these systems [4] sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4ffi T : DðTÞB 1 Tc This is not the behaviour of a BCS gap near Tc : However, we find that a similar behaviour of DðTÞ over
fit equation i = 1 - t4
i=IC/IC(0)
Josephson-junctions. We have modelled the film as a disordered array of RC (resistance and capacitance) shunted Josephson-junctions and shown that it is possible to infer certain microscopic parameters of the junctions from the I–V characteristics of the film as a whole [3]. We study the temperature dependence of experimentally measured critical currents of the films. Fig. 2 shows a plot of normalised critical current against the reduced temperature for several Bi and Sn films. For films with sheet resistance o500 O all data points show a simple power law behaviour given by 4 ! T Ic ðTÞ ¼ Ic ð0Þ 1 : Tc
1
0.4 o dataset d(A)
0.3
#25 #35 #36 #37 #45
0.2
65 85 53 40 70
All films have o approx 10A Ge underlayer
0.1 0.4
0.6
1
0.8
t=T/TC Fig. 2. The critical current of the both films (Bi and Sn) follows the same power law behaviour as described in the text irrespective of presence/absence of underlayer, grown on different substrates.
the entire range of temperature has been seen in fabricated regular Josephson junction arrays [5]. At low temperature Ic as well as Ir tend to constant values. Hence the ratio ðIr =Ic Þ varies very little. We estimate values of intergrain resistance and capacitance from the ratio of observed retrapping and critical current [3]. Table 1 shows the estimated values for a superconducting Sn film.
Table 1 ( Sn film in the limit T-0 Estimate of the bond parameters and energy scales for the 48:7 A Ir =Ic
b
Rbond
Ic =bond
Cbond
EJ
Ec
0.44
8.4
290 O
3:8mA
8:6 1015 F
7:92 meV
9:4 103 meV
1388
S.S. Soman et al. / Physica B 329–333 (2003) 1386–1388
Acknowledgements The authors acknowledge G. Sambandamurthy for his help with several measurements. This work was supported by DST, Government of India. KDG thanks CSIR, Govt. of India for a research fellowship.
[2] [3]
References
[4]
[1] D.B. Haviland, Y. Liu, A.M. Goldman, Phys. Rev. Lett. 62 (1989) 2180;
[5]
E. Bielejec, J. Ruan, Wenhao Yu, Phys. Rev. Lett. 87 (2001) 036801; S.J. Lee, J.B. Ketterson, Phys. Rev. Lett. 64 (1990) 3078; B.G. Orr, H.M. Jaeger, A.M. Goldman, Phys. Rev. B 32 (1985) 7586. G. Sambandmurthy, K. Das Gupta, N. Chandrasekhar, Phys. Rev. B 64 (2001) 014506. K. Das Gupta, Swati S. Soman, N. Chandrasekhar, Phys. Rev. B (communicated). V. Ambegaokar, A. Baratoff, Phys. Rev. Lett. 10 (1963) 486 (erratum, 11 (1963) 104). P. Delsing, C.D. Chen, D.B. Haviland, Y. Harada, T. Cleason, Phys. Rev. B 50 (1994) 3959.
Critical currents of strongly disordered ultra-thin superconducting films Swati S. Soman*, K. Das Gupta, N. Chandrasekhar Department of Physics, Indian Institute of Science, Bangalore 560 012, India
Abstract Quench-condensed films of various metals are well known systems for studying the superconducting state in presence of strong disorder. Critical currents of superconducting films of Bi and Sn with sheet resistance o500 O were found to vary with temperature according to the relation Ic ðTÞ ¼ Ic ð0Þð1 ðT=Tc Þ4 Þ: The result was found to be independent of the substrate used. The observed dependence implies a variation of the superconducting gap DðTÞBð1 ðT=Tc Þ4 Þ1=2 ; near Tc : This is different from the behaviour of a BCS type gap near Tc but consistent with some existing measurements on fabricated 2-D Josephson junction arrays. The I–V characteristics of these films also show hysteresis, indicating the presence of underdamped intergrain Josephson coupling. The values of the intergrain resistances and capacitances are estimated from the ratios of the observed retrapping and critical currents. r 2003 Elsevier Science B.V. All rights reserved. PACS: 73.50.h; 74.25.Sv; 74.78.w Keywords: Josephson-junction; Disorder; Quench-condensed
1. Introduction
2. Experimental set-up
The nature of the superconducting state in a disordered system has been a topic of interest for several decades now. Quench condensed ultra-thin films have been investigated as model systems to study disorder and superconductivity. The existence of an insulator to superconductor (SI) transition in many elemental as well as multi-component systems is now established [1]. We have studied quench-condensed superconducting films of Bi and Sn. These films exhibit SI transition as their thickness is increased. We show in this paper that experimentally obtained I–V characteristics of these films in their superconducting phase can be understood as arising from disordered arrays of Josephson junctions.
The experiments are done in a UHV cryostat, custom designed [2] for in situ study of ultrathin films under a hydrocarbon-free vacuum better than 108 Torr: Aquartz or crystalline sapphire, mounted with adequate thermal contact on a copper cold finger, in contact with a pumped liquid helium bath, is used as a substrate. At a time two Hall bar shaped films can be evaporated side ( Ge by side. One of the films has a pre-deposited 10 A underlayer. Electrical contacts to the sample films are ( thick, provided with platinum contact pads about 60 A pre-deposited on the substrate. Four-probe DC measurements are carried out using a high impedance current source and a nanovoltmeter.
3. Results
*Corresponding author. E-mail address: [email protected] (S.S. Soman).
A typical set of observed I–V characteristics of a film in the superconducting regime is shown in Fig. 1. The I– V curves show hysteresis similar to underdamped
0921-4526/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0921-4526(02)02262-7
S.S. Soman et al. / Physica B 329–333 (2003) 1386–1388
Sn on Ge/a-quartz
1387
1
Sn films
2
2
1
1
Tsub= 14K T=2.2K 0.4
i=IC/IC(0)
V(Volts)
# 1 2 3 4 d(A) 28.9 43.6 48.7 59.5 R (Ω) 1237 478 290 133 1.5 N Tc(K) 3.4 4.56 4.67 4.9
3
fit equation i = 1 - t4
0.3 RN ( )
dataset
0.2
#53SN_1 #59SNG_3 #60SNG_1 #60SNG_2 #60SNG_3
0.1
199 562 478 290 133
4
0.5
All films quenched on a-quartz at 14K
0.04
0
0.4
0
0.001
0.002
0.003
0.6
0.8
t = T/TC
0.004
I(Amp)
1
Bi films
Fig. 1. Typical I–V characteristics of superconducting films showing hysteretic behaviour.
Our experimental temperature range is restricted to T=Tc B0:3: The flattening of the curves at low temperature allows us to make an extrapolation of the critical current in the limit T-0: We find that near Tc for these systems [4] sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4ffi T : DðTÞB 1 Tc This is not the behaviour of a BCS gap near Tc : However, we find that a similar behaviour of DðTÞ over
fit equation i = 1 - t4
i=IC/IC(0)
Josephson-junctions. We have modelled the film as a disordered array of RC (resistance and capacitance) shunted Josephson-junctions and shown that it is possible to infer certain microscopic parameters of the junctions from the I–V characteristics of the film as a whole [3]. We study the temperature dependence of experimentally measured critical currents of the films. Fig. 2 shows a plot of normalised critical current against the reduced temperature for several Bi and Sn films. For films with sheet resistance o500 O all data points show a simple power law behaviour given by 4 ! T Ic ðTÞ ¼ Ic ð0Þ 1 : Tc
1
0.4 o dataset d(A)
0.3
#25 #35 #36 #37 #45
0.2
65 85 53 40 70
All films have o approx 10A Ge underlayer
0.1 0.4
0.6
1
0.8
t=T/TC Fig. 2. The critical current of the both films (Bi and Sn) follows the same power law behaviour as described in the text irrespective of presence/absence of underlayer, grown on different substrates.
the entire range of temperature has been seen in fabricated regular Josephson junction arrays [5]. At low temperature Ic as well as Ir tend to constant values. Hence the ratio ðIr =Ic Þ varies very little. We estimate values of intergrain resistance and capacitance from the ratio of observed retrapping and critical current [3]. Table 1 shows the estimated values for a superconducting Sn film.
Table 1 ( Sn film in the limit T-0 Estimate of the bond parameters and energy scales for the 48:7 A Ir =Ic
b
Rbond
Ic =bond
Cbond
EJ
Ec
0.44
8.4
290 O
3:8mA
8:6 1015 F
7:92 meV
9:4 103 meV
1388
S.S. Soman et al. / Physica B 329–333 (2003) 1386–1388
Acknowledgements The authors acknowledge G. Sambandamurthy for his help with several measurements. This work was supported by DST, Government of India. KDG thanks CSIR, Govt. of India for a research fellowship.
[2] [3]
References
[4]
[1] D.B. Haviland, Y. Liu, A.M. Goldman, Phys. Rev. Lett. 62 (1989) 2180;
[5]
E. Bielejec, J. Ruan, Wenhao Yu, Phys. Rev. Lett. 87 (2001) 036801; S.J. Lee, J.B. Ketterson, Phys. Rev. Lett. 64 (1990) 3078; B.G. Orr, H.M. Jaeger, A.M. Goldman, Phys. Rev. B 32 (1985) 7586. G. Sambandmurthy, K. Das Gupta, N. Chandrasekhar, Phys. Rev. B 64 (2001) 014506. K. Das Gupta, Swati S. Soman, N. Chandrasekhar, Phys. Rev. B (communicated). V. Ambegaokar, A. Baratoff, Phys. Rev. Lett. 10 (1963) 486 (erratum, 11 (1963) 104). P. Delsing, C.D. Chen, D.B. Haviland, Y. Harada, T. Cleason, Phys. Rev. B 50 (1994) 3959.