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Quasiparticle injection and disappearance of superconductivity in superconducting tunneling junctions
Volume 59A, number 4
PHYSICS LETTERS
13 December 1976
QUASIPARTICLE INJECTION AND DISAPPEARANCE OF SUPERCONDUCTIVITY IN SUPERCONDUCTING TUNNELING JUNCTIONS 1. IGUCHI and K. HARA Department of Mathematical Engineering and Instrumentation Physics, University of Tokyo, Tokyo, Japan Received 28 September 1976 The destruction of superconductivity by heavy current injection in superconducting tunneling junctions is reported. The analysis based on Parker’s modified heating theory is also presented.
Recently considerable attention has been given to nonequilibrium properties of superconductors. In the study of a strongly perturbed system from thermal equilibrium, Testardi [I] observed super-normal transition in thin superconducting films by pulsed laser light. Then many experiments using optical radiation [2—6] were reported. Owen and Scalapino [7] proposed the model based an the BCS theory in which the excess quasiparticle density is maintained by an external source. Its essential features are a decrease of the gap with an increase of the excess quasiparticle density and first order transition to the normal state. The latter result, however, so far contradicts to the experimental observations. In the phonon-trapping regime, Parker [8] proposed another model which he called “modified heating theory”. He divided phonons into two groups. The phonons with energies greater than 2~are in equilibrium with the quasipartides at an effective temperature T*, while the phonons with energies less than 2~are characterized by the bath temperature T. This model provides second order transition as well as a dependence of the gap on the excess quasiparticle density. In recent papers [9, 10] we reported the appearance of a dc voltage in the superconducting films of the tunneling junctions with low resistance ~ 1 ~2 carrying high tunneling current density. The critical current densities are typically 102_103 A/cm2, depending on the sample materials and their conditions. The effect is observed in both cross- and linear-type junctions and does not depend on the superconducting materials, being qualitatively the same. Fig. 1 shows the general behavior of this effect for the samples with glass substrates. The differential peak in the lower curve of fig. 1(c) corresponds to the transition of a ,
V ____________
/s ~
7
i~-
V
I _______________
(a) ?
v
~
d l~
_________
,,/~ I~ Ib) (C)
Fig. 1. (a) Cross-type junction geometry, (b) linear-type junction geometry, (c) the general behavior of the current-voltage characteristic. ‘T is the tunneling current and V is the voltage.
superconducting film to the normal state. For the samples with sapphire substrates, the finite voltage behavior in d V/dIT versus ‘T curve becomes almost linear except near the transition region. The same phenomenon has also been observed by Gundlach using Pb-Cu junctions [11]. If the injection of quasiparticles is so large that the excess number of quasiparticles in the steady state may become of the order of N(0)z~,where N(0) is the single-spin density of states at the Fermi level and ~ is the BCS gap parameter, it may be possible that supernormal transition occurs~1.Roughly speaking, the ~ See following page.
313
Volume 59A, number 4
P1-IYSICS LETTERS
tunneling current density corresponding to this critical value is given by J~ edN(0)~/reff, where e is the electronic charge, d the thickness of a superconducting film and Teff is the effective recombination time. The estimated order of magnitude for 1~agree with that observed experimentally.
utilizing 2and were stainless prepared steel masks vacuum withevaporation their thicknesses 0.1thin 0.03mm andby immersed in liquid heliX 0.1 The mm samples with the typical dimension urn. The film thicknesses are 2000 to 3000 0.1 A. Although the local heating problem may be important, the dissipated power per unit area at the threshold is usually around I W/crn2 at the temperatures far below T~.The measurement using 5Ops pulse yields the same result as obtained by dc measurement. The finite voltage behavior in fig. I also denies the possibility of simple heating effect. We often used sapphire subalso cooled the sample below lambda ternperature. Most of our experimental results showed second order transition~2.Following Parker’s theory [8},we may obtain the relation between the tunneling current density J andwith the effective temperature T* at which the phonons energies greater than 2~are in equilibriurn with the quasiparticles. At T 0, this relation becomes simple and is given by strates and
r
J(O) = 1 (T*) ~ x2dx J~(0) 2~(3) T 2~T*)/kBT* ex 1 ~
(I)
—
where Tc is the critical temperature, ~(3) = 1 .202 ... and L~(T*)is the BCS temperature dependent energy gap. J~(0)is the critical tunneling current density at
T = 0 which is given by
13 December 1976
J~(T)
Sn
~I?i5~ i
~2 ~
(2)
0.5~—
0L~ 02
0.4
101, we speculated the phenomenon as a locally induced flux flow phenomenon due to an inhomogeneous current flow, which proved to be completely wrong by the later experiments, *2 When the samples are cooled down below lambda temperature, some of them exhibited first order transition. We believe that this phenomenon is closely related to the predictions by the Owen-Scalapino model [7J and the research along this line is under way.
0.6
0.8
1.0
T/T~ Fig. 2. Temperature dependence of the critical tunneling current density Jc(T) normalized by Jc(0). The theoretical curve
corresponds to eq. (3).
where is the net transition probability for phonons to be lost out of the energy range >2~by processes other than pair excitation and c 5 is the average sound velocity. In a good approximation, ~ is well represented by 4d/r~c5where i~is the average phonon transmission probability at the interface [12] With this approximation,J~(0)depends on only one parameter i~in the phonon-trapping regime. For tin 2. at Most T = 0,ofassuming 17 0.1 J~(0)are1 .4coated X I 0~A/cm our samples, however, by photoresist in order to prevent the film surface from chemical reaction. This reduces 17 considerably and the estimated i~are 0.03—0.08. At finite temperatures, T increases with an increase ofJ in a similar manner as in T = 0, whose behavior with the experimental observationsqualitatively obtained byagrees the method using two indepen-
,
‘—j
dent currents. The temperature dependence of the critical current density ~C(fl is easily calculated and the result becomes
~~(°) =
—
I /T 2~(3) C
*1 In the preliminary works of the cross-type junctions [9,
Cu
sample P~.72
kBT~3 =
-
sample No.104
0.
‘~
j
x2 dx
2~s(fl/kBT ex
—
.
1
(3)
2 shows the expermiental data for Sn-Cu junctions curve given by eq. (3). The data are normalized at the lowest experimental Fig.
together with the theoretical
temperature to fit the theory. The agreement between the experiments and the theory is good. Below lambda temperature (T/Tc ~ 0.58), i~is greatly enhanced owing to superfluid helium and ~c increases to higher values. Fig. 3 shows the second derivative d2 VT/dir2 of a
314
Volume 59A, number 4
PHYSICS LETTERS
13 December 1976
the scattering due to excess phonons. To analyze the
f~Yi
Pb1-NICrCLJ 2 1~=4 2K Area 0.1 xO.1mm
d I.~?
(arb.units)
four terminallayer method, inelastic phonon experimental data correctly, the corrections fortaken thein an insulating and the other effects should effect be into account. In the preliminary papers [9, 10] lots of strange current-voltage characteristics were reported, all of which can be interpreted by the four terminal calculations. It is noted that the phenomenon calls attention to measurements of superconducting properties using tunneling junctions carrying relatively high current density. A detailed paper will be published elsewhere. ,
We wish to thank Prof. Y. Wada and Dr. T. Fujita for helpful discussions and Dr. K.H. Gundlach for sending us his experimental data.
References Pb positive
*—
I
I
-30
-20
-10
0
.10
I
‘20 .30 VT IN mV
Fig. 3. The second derivative d2 V’r/dI~rversus VT of a tunneling characteristic. VT is the voltage across the junction.
[11 L.R. Testardi, Phys. Rev. B4 (1971) 2189. [2] W.H. Parker and W.D. Wffliams, Phys. Rev. Lett. 29 (1972) 924. [31 G.A. Sai-Flalasz, C.C. Chin, A. Denenstein and D.N. Langenberg, Phys. Rev. Left. 33(1974) 215. [41 P. Hu, R.C. Dynes and V. Narayanamurti, Phys. Rev. BlO (1974) 2786.
tunneling characteristic versus the tunneling voltage V.~-with or without an external magnetic field. First two peaks correspond to transverse and longitudinal phonons. Then, followed by a few phonon harmonics, a drastic change around VT 20 mV is observed. This corresponds to the threshold for the appearance of a voltage in the superconducting film. After the transition, the curve coincides with that in the normal state obtained by applying magnetic field. The rapid increase of a voltage after the transition in fig. 1 may be qualitatively understood by assuming
[5] A.1. Golovashkin, K.V. Mitsen and G.P. Motulevich, Zh. Eksp. Teor. Fiz. 68 (1975) 1408 [Soy. Phys. JETP 41 (1976) 7011.
[6] W.H. Parker, Solid State Commun. 15 (1974) 1003. [71 C.S. Owen and DJ. Scalapino,Phys. Rev. Lett. 28
(1972) 1559. [8] W.H. Parker, Phys. Rev. B12 (1975) 3667. [91 I. Iguchi, Phys. Lett. 50A (1974) 247. [10] 1. Iguchi,44(1975)141. Proc. 6th Conf. Solid State Devices, Suppi. JJ.A.P. [111K.H. Gundlach, private communication. [121A. Rothwarf, G.A. Sai-Halasz and D.N. Langenberg, Phys. Rev. Lett. 33 (1974) 212.
315
PHYSICS LETTERS
13 December 1976
QUASIPARTICLE INJECTION AND DISAPPEARANCE OF SUPERCONDUCTIVITY IN SUPERCONDUCTING TUNNELING JUNCTIONS 1. IGUCHI and K. HARA Department of Mathematical Engineering and Instrumentation Physics, University of Tokyo, Tokyo, Japan Received 28 September 1976 The destruction of superconductivity by heavy current injection in superconducting tunneling junctions is reported. The analysis based on Parker’s modified heating theory is also presented.
Recently considerable attention has been given to nonequilibrium properties of superconductors. In the study of a strongly perturbed system from thermal equilibrium, Testardi [I] observed super-normal transition in thin superconducting films by pulsed laser light. Then many experiments using optical radiation [2—6] were reported. Owen and Scalapino [7] proposed the model based an the BCS theory in which the excess quasiparticle density is maintained by an external source. Its essential features are a decrease of the gap with an increase of the excess quasiparticle density and first order transition to the normal state. The latter result, however, so far contradicts to the experimental observations. In the phonon-trapping regime, Parker [8] proposed another model which he called “modified heating theory”. He divided phonons into two groups. The phonons with energies greater than 2~are in equilibrium with the quasipartides at an effective temperature T*, while the phonons with energies less than 2~are characterized by the bath temperature T. This model provides second order transition as well as a dependence of the gap on the excess quasiparticle density. In recent papers [9, 10] we reported the appearance of a dc voltage in the superconducting films of the tunneling junctions with low resistance ~ 1 ~2 carrying high tunneling current density. The critical current densities are typically 102_103 A/cm2, depending on the sample materials and their conditions. The effect is observed in both cross- and linear-type junctions and does not depend on the superconducting materials, being qualitatively the same. Fig. 1 shows the general behavior of this effect for the samples with glass substrates. The differential peak in the lower curve of fig. 1(c) corresponds to the transition of a ,
V ____________
/s ~
7
i~-
V
I _______________
(a) ?
v
~
d l~
_________
,,/~ I~ Ib) (C)
Fig. 1. (a) Cross-type junction geometry, (b) linear-type junction geometry, (c) the general behavior of the current-voltage characteristic. ‘T is the tunneling current and V is the voltage.
superconducting film to the normal state. For the samples with sapphire substrates, the finite voltage behavior in d V/dIT versus ‘T curve becomes almost linear except near the transition region. The same phenomenon has also been observed by Gundlach using Pb-Cu junctions [11]. If the injection of quasiparticles is so large that the excess number of quasiparticles in the steady state may become of the order of N(0)z~,where N(0) is the single-spin density of states at the Fermi level and ~ is the BCS gap parameter, it may be possible that supernormal transition occurs~1.Roughly speaking, the ~ See following page.
313
Volume 59A, number 4
P1-IYSICS LETTERS
tunneling current density corresponding to this critical value is given by J~ edN(0)~/reff, where e is the electronic charge, d the thickness of a superconducting film and Teff is the effective recombination time. The estimated order of magnitude for 1~agree with that observed experimentally.
utilizing 2and were stainless prepared steel masks vacuum withevaporation their thicknesses 0.1thin 0.03mm andby immersed in liquid heliX 0.1 The mm samples with the typical dimension urn. The film thicknesses are 2000 to 3000 0.1 A. Although the local heating problem may be important, the dissipated power per unit area at the threshold is usually around I W/crn2 at the temperatures far below T~.The measurement using 5Ops pulse yields the same result as obtained by dc measurement. The finite voltage behavior in fig. I also denies the possibility of simple heating effect. We often used sapphire subalso cooled the sample below lambda ternperature. Most of our experimental results showed second order transition~2.Following Parker’s theory [8},we may obtain the relation between the tunneling current density J andwith the effective temperature T* at which the phonons energies greater than 2~are in equilibriurn with the quasiparticles. At T 0, this relation becomes simple and is given by strates and
r
J(O) = 1 (T*) ~ x2dx J~(0) 2~(3) T 2~T*)/kBT* ex 1 ~
(I)
—
where Tc is the critical temperature, ~(3) = 1 .202 ... and L~(T*)is the BCS temperature dependent energy gap. J~(0)is the critical tunneling current density at
T = 0 which is given by
13 December 1976
J~(T)
Sn
~I?i5~ i
~2 ~
(2)
0.5~—
0L~ 02
0.4
101, we speculated the phenomenon as a locally induced flux flow phenomenon due to an inhomogeneous current flow, which proved to be completely wrong by the later experiments, *2 When the samples are cooled down below lambda temperature, some of them exhibited first order transition. We believe that this phenomenon is closely related to the predictions by the Owen-Scalapino model [7J and the research along this line is under way.
0.6
0.8
1.0
T/T~ Fig. 2. Temperature dependence of the critical tunneling current density Jc(T) normalized by Jc(0). The theoretical curve
corresponds to eq. (3).
where is the net transition probability for phonons to be lost out of the energy range >2~by processes other than pair excitation and c 5 is the average sound velocity. In a good approximation, ~ is well represented by 4d/r~c5where i~is the average phonon transmission probability at the interface [12] With this approximation,J~(0)depends on only one parameter i~in the phonon-trapping regime. For tin 2. at Most T = 0,ofassuming 17 0.1 J~(0)are1 .4coated X I 0~A/cm our samples, however, by photoresist in order to prevent the film surface from chemical reaction. This reduces 17 considerably and the estimated i~are 0.03—0.08. At finite temperatures, T increases with an increase ofJ in a similar manner as in T = 0, whose behavior with the experimental observationsqualitatively obtained byagrees the method using two indepen-
,
‘—j
dent currents. The temperature dependence of the critical current density ~C(fl is easily calculated and the result becomes
~~(°) =
—
I /T 2~(3) C
*1 In the preliminary works of the cross-type junctions [9,
Cu
sample P~.72
kBT~3 =
-
sample No.104
0.
‘~
j
x2 dx
2~s(fl/kBT ex
—
.
1
(3)
2 shows the expermiental data for Sn-Cu junctions curve given by eq. (3). The data are normalized at the lowest experimental Fig.
together with the theoretical
temperature to fit the theory. The agreement between the experiments and the theory is good. Below lambda temperature (T/Tc ~ 0.58), i~is greatly enhanced owing to superfluid helium and ~c increases to higher values. Fig. 3 shows the second derivative d2 VT/dir2 of a
314
Volume 59A, number 4
PHYSICS LETTERS
13 December 1976
the scattering due to excess phonons. To analyze the
f~Yi
Pb1-NICrCLJ 2 1~=4 2K Area 0.1 xO.1mm
d I.~?
(arb.units)
four terminallayer method, inelastic phonon experimental data correctly, the corrections fortaken thein an insulating and the other effects should effect be into account. In the preliminary papers [9, 10] lots of strange current-voltage characteristics were reported, all of which can be interpreted by the four terminal calculations. It is noted that the phenomenon calls attention to measurements of superconducting properties using tunneling junctions carrying relatively high current density. A detailed paper will be published elsewhere. ,
We wish to thank Prof. Y. Wada and Dr. T. Fujita for helpful discussions and Dr. K.H. Gundlach for sending us his experimental data.
References Pb positive
*—
I
I
-30
-20
-10
0
.10
I
‘20 .30 VT IN mV
Fig. 3. The second derivative d2 V’r/dI~rversus VT of a tunneling characteristic. VT is the voltage across the junction.
[11 L.R. Testardi, Phys. Rev. B4 (1971) 2189. [2] W.H. Parker and W.D. Wffliams, Phys. Rev. Lett. 29 (1972) 924. [31 G.A. Sai-Flalasz, C.C. Chin, A. Denenstein and D.N. Langenberg, Phys. Rev. Left. 33(1974) 215. [41 P. Hu, R.C. Dynes and V. Narayanamurti, Phys. Rev. BlO (1974) 2786.
tunneling characteristic versus the tunneling voltage V.~-with or without an external magnetic field. First two peaks correspond to transverse and longitudinal phonons. Then, followed by a few phonon harmonics, a drastic change around VT 20 mV is observed. This corresponds to the threshold for the appearance of a voltage in the superconducting film. After the transition, the curve coincides with that in the normal state obtained by applying magnetic field. The rapid increase of a voltage after the transition in fig. 1 may be qualitatively understood by assuming
[5] A.1. Golovashkin, K.V. Mitsen and G.P. Motulevich, Zh. Eksp. Teor. Fiz. 68 (1975) 1408 [Soy. Phys. JETP 41 (1976) 7011.
[6] W.H. Parker, Solid State Commun. 15 (1974) 1003. [71 C.S. Owen and DJ. Scalapino,Phys. Rev. Lett. 28
(1972) 1559. [8] W.H. Parker, Phys. Rev. B12 (1975) 3667. [91 I. Iguchi, Phys. Lett. 50A (1974) 247. [10] 1. Iguchi,44(1975)141. Proc. 6th Conf. Solid State Devices, Suppi. JJ.A.P. [111K.H. Gundlach, private communication. [121A. Rothwarf, G.A. Sai-Halasz and D.N. Langenberg, Phys. Rev. Lett. 33 (1974) 212.
315