Current-dependent flux–flow resistance and resonant current steps in BSCCO

intrinsic Josephson junctions

Sunmi Kim a,*, Shinya Urayama a, Huabing Wang a, Shin-ichi Kawakami a, Kunihiro Inomata a,

Masanori Nagao a, Kyung Sung Yun a, Yoshihiko Takano a, Kiejin Lee b, Takeshi Hatano a

a National Institute for Materials Science, 1-2-1 Sengen, Tsukuba 305-0047, Japanb Department of Physics, Sogang University, CPO Box 1142, Seoul 121-742, South Korea

Abstract

We report a current dependence of flux–flow resistance (FFR) and transport properties in intrinsic Jospehson junctions (IJJs) under magnetic

fields parallel to an ab-plane. In Bi2Sr2CaCu2O8Cd IJJs with the ab-plane dimensions of 1.8!10.5 mm2, the oscillations of FFR have been

observed with two apparent periods of 0.382 T in low fields and 0.765 T in high fields. The dominant period HpZ0.765 T is decided by a sample

width and corresponds to the field for adding one flux quantum per layer. Under certain conditions, we also observed the mergence of two peaks on

the oscillating FFR with half period 1/2Hp into one peak with the period Hp in low fields and the inversions between bottoms and peaks in high

fields. We found that this current-dependent FFR implying information of vortex lattice correlates with the transport properties such as current

steps on current–voltage curves.

q 2005 Elsevier Ltd. All rights reserved.

Keywords: A. Superconductors; D. Electric properties; D. Magnetic properties.

1. Introduction

High Tc superconductors have been paid attention for high-

frequency applications up to THz regime due to their large

energy gaps [1]. Especially, since highly anisotropic Bi2Sr2-CaCu2O8Cd (BSCCO) compound consists of naturally stacked

intrinsic Josephson junctions (IJJs), high frequency generations

are expected with small signal line width and high power [2].

However, for high frequency application, it is essential to

synchronize all junctions in a stack to a so-called in-phase

state. As reported in references [3–5], one of the ways is to use

the collective motion of Josephson fluxons. In stacked IJJs

superconducting layers with a thickness dZ3 A is much

thinner than the London penetration depth lLZ1500–1700 A,

so the inductive coupling appears between neighbouring

junctions [5,6], and a mutual phase locking can be expected

in all junctions by collective Josephson vortex motion.

Recently, in the magnetic fields parallel to superconducting

layers, it is theoretically discussed that the moving Josephson

0022-3697/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jpcs.2005.10.052

* Corresponding author. Tel.:C81 298 51 3351x6674; fax: C81 298 59

2801.

E-mail address: kim.sunmi@nims.go.jp (S. Kim).

vortices under a c-axis bias current form a rectangular lattice

for the in-phase mode and a triangular lattice for the out-of-

phase mode [7]. Experimentally, the configuration of

Josephson vortex lattices in BSCCO IJJs was considered as a

triangular lattice, namely the ground state by the periodic

oscillation of flux–flow resistance (FFR) [8] and the oscillation

of FFR is explained as a dynamical matching of Josephson

vortex lattice with sample edges [9]. On the other hand, without

oscillation, the field dependence of flux–flow resistivity was

reported as linear field dependence in low field and quadratic

dependence in high field [10,11].

It was reported the moving vortex lattice generates an

electromagnetic wave when the velocity of the lattice

matches the plasma wave velocity [12,13] and it has been

intensively investigated about different modes of electro-

magnetic waves related to Fiske and flux–flow modes with

respect to the vortex motion [14–17]. Although there are

many researches about vortex lattice motion and Jospehson

plasma wave in the IJJs individually, it is still obscure for

the relation between them.

In this paper we study the magnetic field dependence of

FFR to characterize the Josephson vortex lattice in BSCCO

IJJs. We also discuss the current-dependent FFR containing

information of vortex lattice motion, and the transport

properties reflecting electromagnetic wave emission.

Journal of Physics and Chemistry of Solids 67 (2006) 438–441

www.elsevier.com/locate/jpcs

S. Kim et al. / Journal of Physics and Chemistry of Solids 67 (2006) 438–441 439

2. Experiment

BSCCO whiskers were grown by annealing the sintered Te-

doped BSCCO precursors and a detailed growth method was

reported in Ref. [18]. A whisker with clean and flat surface was

etched by focused ion beam (FIB) in form of In-line junction

with dimensions of 1.8!10.5 mm2. Measured by a scanning

ion microscope (SIM), the thickness of the fabricated IJJs was

estimated to be 0.22 mm, implying about 146 junction numbers

involved in the stack. A critical temperature Tc and a critical

current density Jc of BSCCO IJJs are 81 K and 1.784 kA/cm2 in

zero field at 10 K. With general parameters, superconducting

layer dZ3 A, and the (in-plane) London penetration depth

labZ1500 A, the Josephson penetration depth lJzðF0d=4pm0jcl

2abÞ

1=2 is about 0.31 mm [19]. Therefore our

sample, about 5.8 times larger than the calculated lJ, can be

regarded as long Josephson junctions.

Electric transport properties were measured using a Physical

Property Measurement System (PPMS) of Quantum Design

with a four-terminal configuration. The sample was set on a

holder, which can be rotated with a resolution of 0.0018. In

order to enhance the effect from the edges, which were

regarded as barriers for Josepshon vortex motions [9], we

applied magnetic fields parallel to the ab-plane and along the

longer side (i.e., a-axis) of BSCCO IJJs as shown in the inset of

Fig. 1. The in-plane alignment was precisely determined by

measuring the angular dependence of FFR at a constant bias

current of 1 mA and a magnetic field of 1 T at 60 K.

Fig. 1 shows the misalignment effect on FFR oscillation

with (a) qZ08 and (b) qZ0.358 at 40 K. Even such a small

misalignment qZ0.358 can smear the oscillation of FFR at

high field as shown in Fig. 1b. To our knowledge, it is caused

Fig. 1. Magnetic field dependence of flux–flow resistance (FFR) at 40 K when

(a) qZ08 and (b) qZ0.358, clearly indicating misalignment effect is remarkable

even q is quite small, where q orientation angle between magnetic fields and the

ab-plane. The inset is a side view of BSCCO IJJs fabricated by FIB etching.

Magnetic field was applied along the longer side of junction to enhance edge

effect.

by pancake vortices formed from the c-axis component of the

misaligned field.

3. Result and discussion

3.1. Periodic oscillation of FFR

The field dependence of the flux–flow resistance with c-axis

bias current of 1 mA (about 0.52% of IcZ193 mA in zero field)

at 50 K is shown in Fig. 2. Observed were two kinds of clear

oscillation periods of FFR: 0.382 T in low fields of H/Hp!2.5,

and 0.765 T in high fields of H/HpO2.5. The dominant

oscillation period HpZ0.765 T in high fields is in good

agreement with the calculated period HPZ(F0/ws)Z0.766 T

with wZ1.8 mm and sZ15 A, where F0, w, and s are the flux

quantum, the junction width, and the layer periodicity along the

c-axis, respectively. The small discrepancy results from the

FIB etching process. Since Hp corresponds to the field for

adding one flux quantum per junction, formed in the IJJs can be

a rectangular configuration of Josephson vortex lattice i.e.in-

phase motion of Josephson vortices. The observed period at

low field 0.382 T is 1/2 Hp, implying triangular Josephson

vortex lattice formed in the stack as described in Ref. [8]. Our

results also show that the period of triangular one in low fields

transforms to be the rectangular one in high fields. The detailed

mechanism of this phenomenon will be published elsewhere by

Hatano et al., [20].

3.2. Current dependence of FFR

In principle the c-axis current exerts Lorentz force on a

Josephson vortex lattice sliding along the ab-plane. The

increase of the current bias gives rise to not only an

increase of the velocity of the sliding Jospehson vortex but

also the configuration change of the vortex lattice. The

effect of the c-axis bias current on Josephson vortex flow is

Fig. 2. FFR as a function of magnetic field with c-axis bias current of 1 mA at

50 K. Magnetic fields were normalized by an oscillation period HpZ0.765 T.

Cur

rent

(µA

)

Voltage (mV)

(ii) H/HP=4

dI/d

V (

arb.

uni

ts)

(i) H/HP=3

(iii) H/HP=5

(i)

(ii)

(iii)

0 20 40 60–20

–10

0

10

20(b)

(a)

H/Hp

0

3

6

9

Flux

-flo

w r

esis

tanc

e (k

Ω)

10µA9µA8µA7µA6µA5µA4µA3µA1µA

2 3 4 5 6

Fig. 4. (a) FFR at various currents of 1–10 mA at 50 K, in relatively high fields

(H/HpZ2–6). (b) I–V characteristics and their differential conductance dI/dV at

fields H/HpZ3, 4, 5, showing strong current steps.

Cur

rent

(µA

)

Voltage (mV)

1.5 2.5

0

40

1.251.752.250

40

2 3

(ii)

2nd4th

1st3rd

(i)

(iii)

H/Hp

0 80 160 240 320 400

0

40

(b)

Flux

-flo

w r

esis

tanc

e (k

Ω)

H/Hp

1 1.5 2 2.5 3.50

0.5

1

1.5

2

2.5(a) 10µA9µA8µA7µA6µA5µA4µA3µA1µA

3

Fig. 3. (a) FFR at various currents of 1–10 mA at 50 K, in relatively low fields

(H/HpZ1–3.5), where there is peak transformation. (b) I–V characteristics at

different fields; (i) H/HpZ1.75, 2.25, 2.75, (ii) H/HpZ1.5, 2.5, and (iii)

H/HpZ2, 3.

S. Kim et al. / Journal of Physics and Chemistry of Solids 67 (2006) 438–441440

shown in Figs. 3a and 4a. As shown in Fig. 3a, in low

fields (H/Hp!2.5) the two peaks of FFR with half period 1/

2Hp merge into one peak with the period Hp at high bias

current. It indicates a transformation from the triangular

period to the rectangular one by higher bias current and it

agrees with the structural change of the Josephson vortex

lattice in Ref. [21].

On the other hand, in high fields H/HpO2.5 shown in

Fig. 4a, the oscillation peaks of FFR are inverted as bottoms

and vice versa by the bias current. There is no change of the

oscillation period. This inversion of the oscillation peaks of

FFR is caused by the velocity change of the sliding Josephson

vortices since the flux–flow voltage and FFR are proportional

to vortex velocity [9]. In addition, we found that these FFR

anomalies correlated with the transport properties such as

resonant current steps on the I–V characteristics.

3.3. The relation between FFR oscillation and transport

properties

Shown in Fig.3b are the I–V characteristics measured at

specific fields parallel to the layers. Considering the FFR

oscillation, we classified the fields as (i) H/HpZ1.75, 2.25,

2.75, where FFR peaks are with half period (1/2Hp)

corresponding to the triangular lattice, (ii) H/HpZ1.5, 2.5,

and (iii) H/HpZ2, 3 where both bottoms and peaks of FFR

oscillation with a period for the rectangular lattice.

The increase of magnetic field decreased the hysteresis

on I–V characteristics as well as the critical current then

finally, the hysteresis disappeared above 2.5 H/Hp. We

observed the pronounced current steps on the I–V

characteristics only in rectangular period’s case as shown

in (ii) and (iii) of Fig. 3b. In particular, odd steps came out

at peak fields H/HpZn, and even steps revealed at bottom

fields H=HpZnC1=2 where n is integer number. Note that

bottoms of FFR are transformed to peaks by increasing the

bias current, with the oscillation period unchanged. In non-

hysteretic region the current step is obvious. In the case of

triangular lattice, no steps were observed. It is understood

from our results that the I–V curves were modulated by the

parallel magnetic fields forming Josephson vortex lattice,

and especially the current steps appear in the specific fields

S. Kim et al. / Journal of Physics and Chemistry of Solids 67 (2006) 438–441 441

where are characterized by the oscillation of FFR

corresponding to the period of the rectangular vortex lattice.

Fig. 4b shows the I–V characteristics with steps and their

differential conductance dI/dV at the fields H/HpZ3, 4, and 5.

These steps are expected as a strong enhancement of

superconducting current at fixed voltage when the Josephson

frequencies match the resonant frequencies of cavity modes in

parallel fields, i.e., Fiske steps [12,15,16]. The detailed

discussion on Fiske steps with regarding the vortex motion

will be reported elsewhere. In present experiments, we paid

close attention to the strong enhancement of dI/dV at fixed

voltages. As shown in Fig. 4b, maximum conductance appears

at 12.1, 8.6 and 6.6 mA for H/HpZ3, 4, and 5. Compared with

current-dependent FFR, the current levels of each steps in

Fig. 4b actually coincide with the currents where the inversion

from peak to bottom of FFR oscillation takes place, as marked

in Fig. 4a.

4. Conclusion

We measured a current dependence of FFR and transport

properties determined by the dynamics of Josephson vortex

lattice in BSCCO IJJs. We observed the transformation of

FFR oscillation by increasing the bias current. In low fields

H/Hp!2.5 the oscillation period corresponds to a triangular

lattice and it is transformed to the period of a rectangular

lattice by higher bias current. While in high fields H/HpO2.5 we observed that the oscillation peaks showing the

period of rectangular lattice are inverted to bottoms by

current bias. From I–V characteristics we found clear

current steps in the specific fields where exhibit the

oscillation period of FFR corresponding to not triangular

period but rectangular one. These steps were considered to

be Fiske steps related with geometric resonance.

The conductance enhancement of these current steps

happened at constant voltage results in the inversion from the

peaks to the bottoms of FFR oscillation. This inversion was

considered to be the resonance of ac Jospephson frequency

exited by the moving vortex lattice with the sample width (for

rectangular lattice) and it maybe is from energy dissipation due

to the Josephson plasma excitation. These results supply

important information for possible high-frequency application

of BSCCO IJJs.

Acknowledgements

The authors would like to thank T. Yamashita and M.

Tachiki for valuable discussion.

References

[1] S. Beuven, O. Harnack, L. Amatuni, H. Kohlstedt, M. Darula, IEEE

Trans. Appl. Supercond. 7 (1997) 2591.

[2] K.K. Likharev, Dynamics of Josephson Junctions and Circuits, Gordon &

Breach, 1986.

[3] M. Machida, T. Koyama, A. Tanaka, M. Tachiki, Physica C 330 (2000)

85.

[4] R. Kleiner, P. Muller, H. Kohlstedt, N.F. Pedersen, S. Sakai, Phys. Rev. B

50 (1994) 3942.

[5] S. Heim, M. Moßle, T. Clauß, R. Kleiner, Supercond. Sci. Technol. 15

(2002) 1226.

[6] S. Sakai, A.V. Ustinov, N. Thyssen, H. Kohlstedt, Phys. Rev. B 58 (1998)

5777.

[7] J.H. Kim, Phys. Rev. B 65 (2002) 100509.

[8] S. Ooi, T. Mochiku, K. Hirata, Phys. Rev. Lett. 89 (2002) 247002.

[9] M. Machida, Phys. Rev. Lett. 90 (2003) 037001.

[10] A.E. Koshelev, Phys. Rev. B 62 (2000) R3616.

[11] Yu.I. Latyshev, A.E. Koshelev, L.N. Bulavskii, Phys. Rev. B 68 (2003)

134604.

[12] A.E. Koshelev, I.S. Aranson, Phys. Rev. Lett. 85 (2000) 3938.

[13] T. Koyama, M. Tachiki, Solid State Commun. 96 (1995) 367.

[14] V.M. Kransnov, N. Mros, A. Yurgens, D. Winkler, Phys. Rev. B 59

(1999) 8463.

[15] M.D. Fiske, Rev. Mod. Phys. 36 (1964) 221.

[16] I.O. Kulik, JETP Lett. 2 (1965) 84.

[17] A. Irie, Y. Hirai, G. Oya, Appl. Phys. Lett. 72 (1998) 2159.

[18] M. Nagao, M. Sato, H. Maeda, S. Kim, T. Yamashita, Appl. Phys. Lett. 79

(2001) 2612.

[19] A. Irie, S. Heim, S. Schromm, M. Moßle, T. Nachtrab, M. Godo,

R. Kleiner, P. Muller, G. Oya, Phys. Rev. B 62 (2000) 6681.

[20] T. Hatano, M.B. Wang, S.M. Kim, S. Urayama, S. Kawakami, S.-J. Kim,

M. Nagao, K. Inomata, Y. Takano, T. Yamashita, M. Tachiki, IEEE

Trans. Appl. Supercond. 15 (2005) 912.

[21] K. Hirata, S. Ooi, E.H. Sadki, T. Mochiku, Physica B 329–333 (2003)

1332.