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Magnetic field effect on phase-slip processes in superconducting microbridges
PHItSIlII
Physica C 185-189 (1991) 2713-2714 North-Holland
M A G N E T I C FIELD E F F E C T ON P H A S E - S L I P P R O C E S S E S IN S U P E R C O N D U C T I N G M I C R O B R I D G E S
Takahiro YAMAMOTO and Takafumi AOMINE Department of Physics, Kyushu University, Fukuoka 812, Japan We have observed the resistive regular steps in current-voltage characteristics of an indium variablethickness microbridge in the presence of a magnetic field H near the critical temperature. From the differential resistance of steps, we obtained the H dependence of size of dissipative region, and compared it with the phase-slip model with the modified pair-breaking time and quasiparticle-diffusion length. 1. I N T R O D U C T I O N
to transport current I.
Superconducting microbridges with the small width
The geometry and size (length L, width W, thick-
and thickness compared to the coherence length tiT) ac-
ness g) of microbridge (NB-9) are shown in the inset of
company the dissipative state with the electric field pene-
Fig. 1, of which critical current & was proportional to
tration. This nonequilibrium phenomenon can be under-
(1- T / T ¢ ) 312 in the temperature region 0.993 < T/T~ 0.999, where T~ is the critical temperature 3.592 K.
stood in terms of phenomenological model of Phase-Slip
<
Centers (PSCs). The length of microbridge is supposed
Figure 1 shows the l - v characteristic at H = 0. Two
ta be large compared to the ~(T), and dc Josephson ef-
resistive steps corresponding to two PSCs were observed.
fect is not considered. The intrinsic hysteresis of current-
The third voltage jump of l - V characteristic at T~ - T =
voltage ( I - V ) characteristics was observed due to an ac
17 mK indicated that the narrow part of microbridgc be-
effect of PSCs.
came in the normal state completely. The rounding of
Since the Cooper-pah breaking arises from not only i
the electron-phonon interaction but also magnetic field H, the dynamic structure of PSCs is changed by H. The
%
> a0
field H +. We have recently explained the temperature T dependence of H +. 2
20
The PSCs are composed of both the phase-slip region and the electric field penetration region as shown in inset of Fig.1. The phase-slip region of PSC, which has been assumed to be the length of ~(T) or 2 {(T), is not clear.
I
I
i
!
60
intrinsic hysteresis of I - v characteristics vanishes at the H larger than the nonequilibrium transition magnetic
~
0
i
Ii111' /2I .'"
--a ~ - - - /
[exc Ic 0
i,'V=8.!~m
--" ~i
Iexc
200
¢/
-,
.-"-J
L - ""
i,
[c a00
I/~
In this work, in order to reveal the size of PSC, we
~ "T c - T
/
600
A
investigate t h e / / d e p e n d e n c e of the structure of PSCs in an indium superconducting rnicmbridge, and compare it with both the phenomenological theory ~ and microscopic theory a of PSCs. 2. E X P E R I M E N T A L PdBSULTS A N D D I S C U S S I O N
Our indium variable-thickness microbr;.dge ",,~-~ fabricated as described elsewhere. ~ The external magnetic field H was parallel to the film surface and perpendicular
FI~[JRG 1 Typical I" v characteristic of an indium rrficrobridge. Arrows show the direction of cu,rrent sweep. Scheme of microbridge geometry is shown in the right side of inset. Shadowed area represents the region of a phase-slip center (PSC). Left side of inset is the top view of narrow part of microbridge, which has one PSC with the leng~h of A. Narrow shadowed and wide shadowed area represent the phas~slip region and the char W imbalance region, respectively. S-region adjacent {o the PSC is in the superconducting state.
0921-4534/91/$03.50 © 1991 - Elsevier Science Publishem B.V. All fights reserved.
2714
Z Yamamoto, T. Aomine / Magnetic.field effect on phase.sh'p proeesses
the second step of t - v characteristic at T¢-T = 25 mK was
i
i
i
I
NB-9
probably due to the interaction between the two PSCs _
in the narrow part of microbridge.
o
:
I
experiment
=
'""
~ ('[') ~
D
Figure 2 shows the H dependence of size A of PSC
theory
E
I
A(o) T/Tc=0.993 =
/
13
a
{1
0.5 3 / ~ m
a a
dL~sipative region which was obtained from the differen-
•
<
tial resistance of the first resistive step of the l-V characteristic at T[T¢ = 0.993. Here, the h decreased monotonically with increasing H. At T/T~ = 0.999, however, it was almost constant against H.
0 I
I
I
-15
-10
I
I
-H +
In order to explain these results, we modify the basic
0
H+
I
I
10
15
H/Oe
equation ~ of charge imbalance due to a PSC. In the previous works, 2 we introduced the modified Cooper-pair
breaking in the phase-slip region, where m is the inelas-
FIGURE 2 Magnetic-field dependence of size of dissipative region due to one PSC. Theoretical curves of A vs. H are also shown for the PSC, assuming the phase slip region with length of ((T) (solid line) and 2 ((T) (dashed line).
tic electron-phonon collision time and ~ is the magneticfield pair-breaking time. Then, in the right-hand side of
and theoretical curves is as in the following; the estima-
the charge imbalance equation, eq. (33) of Ref. 1 we re-
tion of rz might be slightly large, or the phase-slip region
placed the *x by the rdH+), and in the left-hand side
given by eq. (2) might have a more complex form. Ivlev
we substituted a new form Aq(H) = ~ for the quasiparticle diffusion length AQ, where D is a diffusion
and Kopnin developed the microscopic picture of PSCs on the basis of the time-dependent Ginzburg-Landaa
constant. Assuming the relaxation of charge imbalance
equations. 3 Their theory predicted that the size of phase-
is mainly caused by inelastic electron-phonon collision
slip region was enhanced by the pair-breaking energy.
and magnetic-field pair-breaking, we have a simple form
The excess current I~xc due to the quasiparticle excita-
breaking time n(H +) = (l/2rs + 1/~) -t in the phase-slip model for taking account into the magn,tic-field pair-
tion was also predicted to be 0.68 I¢, which was close to
AQ(m= AQ(o){I+ ( ~_-TO, o "~( H---"~R-'/~,", ,~,r+J J '
O)
where ro is the superconducting response time. According to the Baratoff's discussion, 4 no charge
our experimental value 0.7 It, where I¢ was the critical current. 3. C O N C L U S I O N
imbalance occurs in the phase-slip region. It means that
Introducing the rl(H +) in the PSC model, we ex-
the damping of quasiparticle density starts at the ends
plained qualitatively that the monotonic decreasing of h
of the phase-slip region. So, the size of dissipative region due to PSCs is given by
against H was due to the decreasing of the electric field penetration depth.
A(H, T) = 2 Aq(H) + ((T), and has the T dependence at ~" ~_ T~. P. . . . . .
O) t l~
and (2), we obtained theoretical curves shown in Fig. 2. Here, we used r~ = 140 ps. This behavior of A(H,T) has
REFERENCES 1. A. M. Kadin, L. N. Smith, and W. J. Skocpol, 1 T.~u~ Tt,w~,~
Ph,,¢
q £ ( 1 0 ~ n ~ A.q'7
2. T. Yamamoto and T. Aomine, J. Low Temp. Phys. 79 (1990) 55; T. Yamamoto, K. Mizuno, and
the same tendency as the experimental result mentioned
T. Aomine, Proc. 4th Asia Pacific Phys. Conf.
above, i.e., at T[T¢ = 0.993 (rz > to) the A decreases
Seoul (World Scientific, Singapore, 1991) pp. 547.
with the increasing H, but at T[T¢ = 0.999 (re = to) the A becomes constant against H.
3. B. I. Ivlev and N. B. Kopnin, Soy. Phys. Usp. 27
The reason of discrepancy between the experimental
(1984) 206; Advances in Physics 33 (1984) 47. 4. A. Baratoff, PSys. Rev. Lett. 48 (1982)434.
Physica C 185-189 (1991) 2713-2714 North-Holland
M A G N E T I C FIELD E F F E C T ON P H A S E - S L I P P R O C E S S E S IN S U P E R C O N D U C T I N G M I C R O B R I D G E S
Takahiro YAMAMOTO and Takafumi AOMINE Department of Physics, Kyushu University, Fukuoka 812, Japan We have observed the resistive regular steps in current-voltage characteristics of an indium variablethickness microbridge in the presence of a magnetic field H near the critical temperature. From the differential resistance of steps, we obtained the H dependence of size of dissipative region, and compared it with the phase-slip model with the modified pair-breaking time and quasiparticle-diffusion length. 1. I N T R O D U C T I O N
to transport current I.
Superconducting microbridges with the small width
The geometry and size (length L, width W, thick-
and thickness compared to the coherence length tiT) ac-
ness g) of microbridge (NB-9) are shown in the inset of
company the dissipative state with the electric field pene-
Fig. 1, of which critical current & was proportional to
tration. This nonequilibrium phenomenon can be under-
(1- T / T ¢ ) 312 in the temperature region 0.993 < T/T~ 0.999, where T~ is the critical temperature 3.592 K.
stood in terms of phenomenological model of Phase-Slip
<
Centers (PSCs). The length of microbridge is supposed
Figure 1 shows the l - v characteristic at H = 0. Two
ta be large compared to the ~(T), and dc Josephson ef-
resistive steps corresponding to two PSCs were observed.
fect is not considered. The intrinsic hysteresis of current-
The third voltage jump of l - V characteristic at T~ - T =
voltage ( I - V ) characteristics was observed due to an ac
17 mK indicated that the narrow part of microbridgc be-
effect of PSCs.
came in the normal state completely. The rounding of
Since the Cooper-pah breaking arises from not only i
the electron-phonon interaction but also magnetic field H, the dynamic structure of PSCs is changed by H. The
%
> a0
field H +. We have recently explained the temperature T dependence of H +. 2
20
The PSCs are composed of both the phase-slip region and the electric field penetration region as shown in inset of Fig.1. The phase-slip region of PSC, which has been assumed to be the length of ~(T) or 2 {(T), is not clear.
I
I
i
!
60
intrinsic hysteresis of I - v characteristics vanishes at the H larger than the nonequilibrium transition magnetic
~
0
i
Ii111' /2I .'"
--a ~ - - - /
[exc Ic 0
i,'V=8.!~m
--" ~i
Iexc
200
¢/
-,
.-"-J
L - ""
i,
[c a00
I/~
In this work, in order to reveal the size of PSC, we
~ "T c - T
/
600
A
investigate t h e / / d e p e n d e n c e of the structure of PSCs in an indium superconducting rnicmbridge, and compare it with both the phenomenological theory ~ and microscopic theory a of PSCs. 2. E X P E R I M E N T A L PdBSULTS A N D D I S C U S S I O N
Our indium variable-thickness microbr;.dge ",,~-~ fabricated as described elsewhere. ~ The external magnetic field H was parallel to the film surface and perpendicular
FI~[JRG 1 Typical I" v characteristic of an indium rrficrobridge. Arrows show the direction of cu,rrent sweep. Scheme of microbridge geometry is shown in the right side of inset. Shadowed area represents the region of a phase-slip center (PSC). Left side of inset is the top view of narrow part of microbridge, which has one PSC with the leng~h of A. Narrow shadowed and wide shadowed area represent the phas~slip region and the char W imbalance region, respectively. S-region adjacent {o the PSC is in the superconducting state.
0921-4534/91/$03.50 © 1991 - Elsevier Science Publishem B.V. All fights reserved.
2714
Z Yamamoto, T. Aomine / Magnetic.field effect on phase.sh'p proeesses
the second step of t - v characteristic at T¢-T = 25 mK was
i
i
i
I
NB-9
probably due to the interaction between the two PSCs _
in the narrow part of microbridge.
o
:
I
experiment
=
'""
~ ('[') ~
D
Figure 2 shows the H dependence of size A of PSC
theory
E
I
A(o) T/Tc=0.993 =
/
13
a
{1
0.5 3 / ~ m
a a
dL~sipative region which was obtained from the differen-
•
<
tial resistance of the first resistive step of the l-V characteristic at T[T¢ = 0.993. Here, the h decreased monotonically with increasing H. At T/T~ = 0.999, however, it was almost constant against H.
0 I
I
I
-15
-10
I
I
-H +
In order to explain these results, we modify the basic
0
H+
I
I
10
15
H/Oe
equation ~ of charge imbalance due to a PSC. In the previous works, 2 we introduced the modified Cooper-pair
breaking in the phase-slip region, where m is the inelas-
FIGURE 2 Magnetic-field dependence of size of dissipative region due to one PSC. Theoretical curves of A vs. H are also shown for the PSC, assuming the phase slip region with length of ((T) (solid line) and 2 ((T) (dashed line).
tic electron-phonon collision time and ~ is the magneticfield pair-breaking time. Then, in the right-hand side of
and theoretical curves is as in the following; the estima-
the charge imbalance equation, eq. (33) of Ref. 1 we re-
tion of rz might be slightly large, or the phase-slip region
placed the *x by the rdH+), and in the left-hand side
given by eq. (2) might have a more complex form. Ivlev
we substituted a new form Aq(H) = ~ for the quasiparticle diffusion length AQ, where D is a diffusion
and Kopnin developed the microscopic picture of PSCs on the basis of the time-dependent Ginzburg-Landaa
constant. Assuming the relaxation of charge imbalance
equations. 3 Their theory predicted that the size of phase-
is mainly caused by inelastic electron-phonon collision
slip region was enhanced by the pair-breaking energy.
and magnetic-field pair-breaking, we have a simple form
The excess current I~xc due to the quasiparticle excita-
breaking time n(H +) = (l/2rs + 1/~) -t in the phase-slip model for taking account into the magn,tic-field pair-
tion was also predicted to be 0.68 I¢, which was close to
AQ(m= AQ(o){I+ ( ~_-TO, o "~( H---"~R-'/~,", ,~,r+J J '
O)
where ro is the superconducting response time. According to the Baratoff's discussion, 4 no charge
our experimental value 0.7 It, where I¢ was the critical current. 3. C O N C L U S I O N
imbalance occurs in the phase-slip region. It means that
Introducing the rl(H +) in the PSC model, we ex-
the damping of quasiparticle density starts at the ends
plained qualitatively that the monotonic decreasing of h
of the phase-slip region. So, the size of dissipative region due to PSCs is given by
against H was due to the decreasing of the electric field penetration depth.
A(H, T) = 2 Aq(H) + ((T), and has the T dependence at ~" ~_ T~. P. . . . . .
O) t l~
and (2), we obtained theoretical curves shown in Fig. 2. Here, we used r~ = 140 ps. This behavior of A(H,T) has
REFERENCES 1. A. M. Kadin, L. N. Smith, and W. J. Skocpol, 1 T.~u~ Tt,w~,~
Ph,,¢
q £ ( 1 0 ~ n ~ A.q'7
2. T. Yamamoto and T. Aomine, J. Low Temp. Phys. 79 (1990) 55; T. Yamamoto, K. Mizuno, and
the same tendency as the experimental result mentioned
T. Aomine, Proc. 4th Asia Pacific Phys. Conf.
above, i.e., at T[T¢ = 0.993 (rz > to) the A decreases
Seoul (World Scientific, Singapore, 1991) pp. 547.
with the increasing H, but at T[T¢ = 0.999 (re = to) the A becomes constant against H.
3. B. I. Ivlev and N. B. Kopnin, Soy. Phys. Usp. 27
The reason of discrepancy between the experimental
(1984) 206; Advances in Physics 33 (1984) 47. 4. A. Baratoff, PSys. Rev. Lett. 48 (1982)434.