How to describe the noise rounding in the I-V data or HTS Josephson junction of micron dimensions at a temperature close to its critical temperature? How could we justify the Resistively shunted junction (RSJ) model in the rounding part of the experimental data?
Maybe you can take a look at this work here: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.87.134517. Rounding effects in the IV curve may be due to phase diffusion dynamics.
Near critical temperature, a Josephson junction (JJ) is mostly nonhysteretic. The so-called thermally activated phase slip (TAPS) process in this regime becomes dominant. This TAPS leads to the generation of voltage but not fully switching to the resistive state. Thus, an average voltage between zero and IcRn appears below the transition. This is basically a mixed regime of superconducting and normal phase, which leads to rounding in the IVC. This can be one explanation, even for HTS-based JJ.
RCSJ or RSJ model won't give you rounding near (below) transition in IV curve unless you solve the equation with a current noise term, simulate the Langevin equation, etc. Clarke's book, The SQUID handbook, describes the RCSJ model with noise that gives rise to rounding.
In the RSJ model, the junction is represented as a resistor (R) and a capacitor (C) in parallel with a Josephson junction, and the I-V characteristic is given by:
$$I = I_c \sin\phi + \frac{V}{R} + C\frac{dV}{dt}$$
where I is the current through the junction, $I_c$ is the critical current, $\phi$ is the phase difference across the junction, V is the voltage across the junction, and t is time.
At low voltages and currents, the junction behaves as an ideal Josephson junction, and the I-V characteristic is described by:
$$I = I_c \sin\phi$$
However, as the voltage or current increases, the junction begins to behave more like a resistor, and the I-V curve begins to round off.
The rounding in the I-V data can be described by adding a noise term to the RSJ equation:
$$I = I_c \sin\phi + \frac{V}{R} + C\frac{dV}{dt} + \eta(t)$$
where $\eta(t)$ is the noise term.
The Resistively Shunted Junction model is justified in the rounding part of the experimental data because it takes into account the effects of thermal noise and resistance in the junction. The noise term in the RSJ model represents the effect of thermal fluctuations in the junction, which cause random variations in the current through the junction. The resistor in the RSJ model represents the effects of resistance in the junction, which can cause the I-V curve to round off at high currents or voltages.
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