Influence of Unconventional Current-Phase Relation on Return Current of Tunnel Josephson Junctions
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ORIGINAL PAPER
Influence of Unconventional Current-Phase Relation on Return Current of Tunnel Josephson Junctions I. N. Askerzade 1,2 Received: 7 May 2020 / Accepted: 22 July 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this study, we carried out the analysis of the return current of Josephson junction with unconventional current-phase relation. We analyzed two types of current-phase relation with additional terms to first harmonic sinφ: the case of second harmonic sin2φ and the case of fractional term sin φ2 . Numerical methods were employed for the calculations of return current by considering the different amplitudes of the second term in unconventional current-phase relation. It is shown that there is an opposite relation between the return current of Josephson junction with unconventional current-phase relation and the amplitude value of the second term. It can be stated that the return current of Josephson junction can be decreased by increasing the amplitude of the second term. Keywords Josephson junction . Current-phase relation . Return current
1 Introduction It is well known that the dynamics of Josephson junction with harmonic current-phase relation I = I c0 sin φ is described by the equation of resistively shunted junction (RSJ) model [1, 2] ::
β0 φ þ φ˙ þ sinφ ¼ ie :
ð1Þ
RSJ model can correctly describes the tunnel Josephson junctions when the junctions are shunted by resistor Rs, which, however, is not very low and therefore providing McCumber 2 parameter β0 value much higher than 1, i.e., β 0 ¼ 2e ℏ I c0 Rs C >> 1. In Eq. (1), the following notations were introduced: ie is normalized external current via Josephson junction in units of critical current Ic0, dots over φ corresponds to the derivative with respect to dimensionless time 2πIΦc00 Rs t, and Φ0 is the magnetic flux quantum. The McCumber parameter β 0 of
* I. N. Askerzade [email protected] 1
Department of Computer Engineering and Center of Excellence of Superconductivity Research, Ankara University, 06100 Ankara, Turkey
2
Institute of Physics Azerbaijan National Academy of Sciences, 33, H.Cavid 33, AZ1143 Baku, Azerbaijan
Josephson junction determines the size of the hysteresis in IV curve. It is well known that the case of β0 >> 1 corresponds to tunnel junction [1, 2]. In the case of β0 > 1 (high capacitance limit), numerical solution of Eq. (1) shows that the I-V curve has two separate branches: S (superconducting) and R (resistive) branch. An important parameter of the I-V curve of the Josephson junction is the return current IR0, at which arises switching from R-state to S-state [1, 2]. Calculation of the return current IR0 using simple RSJ model (Eq. (1)) for tunnel junctions β0 > > 1 leads to result [1], 4 I R0 ¼ pffiffiffiffiffi I c0 π β0
ð2Þ
This result is in good agreement for the Josephson junction based on low-temperature superconductors [1]. The presence of the return current on the I-V curve leads to a lowering of the clock frequency in latching logic circuits based on tunnel Jos
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