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Japanese Journal of Applied Physics

Numerical Investigation and Model Approximation for the Hysteretic Current-Voltage Characteristics of Josephson Junctions with Nonlinear Quasiparticle Resistance

Yoshinao Mizugaki, Koji Nakajima

Published Jan 1, 1997• 5 citations
Publisher

Abstract

We present a model analysis for the current-voltage (I-V) characteristics of Josephson junctions having superconductor-insulator-superconductor (SIS) structure. The numerical result for the V m value, which is the product of the maximum supercurrent and the observed subgap resistance, shows a marked decrease with increasing junction critical current density (J c). The marked decrease is independent of leak current. Increasing J c reduces the junction capacitance C J and enlarges the amplitude of the junction voltage oscillation. Nonlinearity of the quasiparticle resistance restricts the voltage oscillation amplitude to the gap voltage, which results in the rapid decrease of the V m value. In this paper, we introduce a sinusoidal oscillation model for the junction voltage, and derive the approximated expressions for the V m value. The model approximation results agree well with the numerical results.

DOI
10.1143/jjap.36.110

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We present a model analysis for the current-voltage (I-V) characteristics of Josephson junctions having superconductor-insulator-superconductor (SIS) structure. The numerical result for the V m value, which is the product of the maximum supercurrent and the observed subgap resistance, shows a marked decrease with increasing junction critical current density (J c). The marked decrease is independent of leak current. Increasing J c reduces the junction capacitance C J and enlarges the amplitude of the junction voltage oscillation. Nonlinearity of the quasiparticle resistance restricts the voltage oscillation amplitude to the gap voltage, which results in the rapid decrease of the V m value. In this paper, we introduce a sinusoidal oscillation model for the junction voltage, and derive the approximated expressions for the V m value. The model approximation results agree well with the numerical results.
We present a Verilog-A based compact model for the superconductor-insulator-superconductor (SIS) Josephson junction. The model can generate both hysteretic and non-hysteretic current-voltage (I-V) response for the SIS junctions utilizing the Stewart-McCumber parameter. We calibrate our model with different SIS samples and demonstrate accurate matching between the simulated and experimental results. We implement temperature effect on the energy gap and the critical current of the superconductor to explore the dynamic trends in device characteristics. We calculate the junction inductance and energy as functions of junction current and temperature. We simulate the read/write operations of an SIS junction based cryogenic memory cell to illustrate the usability of our model.
We present a quantitative study of the current-voltage characteristics (CVC) of diffusive superconductor/insulator/ferromagnet/superconductor (SIFS) tunnel Josephson junctions. In order to obtain the CVC we calculate the density of states (DOS) in the F/S bilayer for arbitrary length of the ferromagnetic layer, using quasiclassical theory. For a ferromagnetic layer thickness larger than the characteristic penetration depth of the superconducting condensate into the F layer, we find an analytical expression which agrees with the DOS obtained from a self-consistent numerical method. We discuss general properties of the DOS and its dependence on the parameters of the ferromagnetic layer. In particular we focus our analysis on the DOS oscillations at the Fermi energy. Using the numerically obtained DOS we calculate the corresponding CVC and discuss their properties. Finally, we use CVC to calculate the macroscopic quantum tunneling (MQT) escape rate for the current biased SIFS junctions by taking into account the dissipative correction due to the quasiparticle tunneling. We show that the influence of the quasiparticle dissipation on the macroscopic quantum dynamics of SIFS junctions is small, which is an advantage of SIFS junctions for superconducting qubits applications.
The effect of the voltage-dependent junction resistance R/sub j/ on the critical current decay of Josephson junctions was studied. In the thermal regime, the author has obtained a simple expression for the lifetime of the zero-voltage state which takes into account the nonlinear dependence of R/sub j/ on the voltage, removing an assumption of the resistivity shunted junction model (RSJ), which assumes an ohmic shunt resistance to describe the junction dissipation. These results are confirmed by experimental data which also show the relevance of the intrinsic dissipation due to the presence of quasiparticles. This latter aspect is relevant, because it allows extremely underdamped systems to be obtained at low temperatures. These conditions are particularly interesting to study a macroscopic quantum aspect, namely the effects of the presence of quantized energy levels on the supercurrent decay. The dependence of this latter effect on the junction resistance is also briefly discussed.
Abstract This study is devoted to the investigation of tunneling superconductor–insulator–superconductor (SIS) Josephson junctions with a new type of shunt based on an additional superconductor–insulator–normal metal (SIN) junction placed around the SIS junction. In the course of study, the parameters of such shunted junctions are numerically calculated and their current–voltage characteristics (IVC) are simulated. The designed structures are assembled in real samples and their parameters are studied; the IVC of junctions with different degrees of shunting are measured, and the behavior of these junctions under the influence of high-frequency signals in the subterahertz range is studied.
We have measured Nb–AlOx–Nb Josephson tunnel junctions which have resistive shunts with different parasitic inductances. Numerical simulations reveal that specific features in the experimental current–voltage (I–V) characteristics of these devices are dc signatures of complex ac behavior. Depending on the inductance of the shunt loop and the capacitance of the junction, these features may either appear or disappear as the temperature of the device is increased. Examination of the simulated voltage waveforms allows us to map regions of the parameter space which exhibit complicated behavior. These regions should be avoided when a nearly sinusoidal voltage waveform is desired, as is the case for Josephson junction-based oscillators. The agreement of the experimental and simulated I–V curves also enables us to accurately determine the inductance of the shunts and the capacitance of the junctions.
Quantum fluctuations of the charge at a current-biased Josephson junction and of the Josephson current couple to the quasiparticle tunneling when the system is at equilibrium in the zero-voltage state. The effect of reducing the capacitance of the junction is studied by means of a model Hamiltonian. When this becomes smaller, charge fluctuations are reduced, but the effective dissipation is also lowered so that the junction displays an underdamped behavior. The Josephson branch is shifted at the voltage e/2C because of charging due to the quasiparticles. A path-integral formulation of the model leads to a high dynamical subgap resistance at I\ensuremath{\rightarrow}0, as recently found experimentally.