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arXiv:1308.1739 · Journal of Physics Condensed Matter

I–Vcharacteristics of short superconducting nanowires with different bias and shunt: a dynamic approach

Shi‐Zeng Lin, Lev N. Bulaevskii

Published Mar 27, 2014• 1 citation
arXivHTMLPDF

Abstract

We derived the I-V characteristics of short nanowire in a circuit with and without resistive and inductive shunt. For this we used numerical calculations in the framework of time-dependent Ginzburg-Landau equations with different relaxation times for the amplitude and phase dynamics. We also derived the dependence of the I-V characteristics on flux in a superconducting quantum interference device made of two such weak links.

DOI
10.1088/0953-8984/26/15/155703

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We derived the I-V characteristics of short nanowire in a circuit with and without resistive and inductive shunt. For this we used numerical calculations in the framework of time-dependent Ginzburg-Landau equations with different relaxation times for the amplitude and phase dynamics. We also derived the dependence of the I-V characteristics on flux in a superconducting quantum interference device made of two such weak links.
The electrical equations of a resonant circuit fed with a radio-frequency current and inductively coupled to a weakly superconducting loop have been derived. The current-voltage characteristic of the rf superconducting quantum interference device can then be calculated and studied as a function of the junction resistance or of the resonance frequency, enabling its behavior to be better understood. As shown by Kurkijärvi, the large positive slope of the steps and the rounding of the characteristic result from thermal noise. However, in order to explain quantitatively the experimental results concerning, namely, point contact weak links which are generally oxidized or which have several contact points, it is useful to remark that the connection between the two superconductors constituting the Josephson junction may be made from n resistive paths. The mean thermal energy of the fluctuating flux is then close to nkbT instead of kbT if the inductances linking the contact points are large enough, that is, on the order of 10−11 H.
Inspired by recent discoveries of the quasi-Josephson effect in shunted nanowire devices, we propose a superconducting nanowire interference device in this study, which is a combination of parallel ultrathin superconducting nanowires and a shunt resistor. A simple model based on the switching effect of nanowires and fluxoid quantization effect is developed to describe the behavior of the device. The current–voltage characteristic and flux-to-voltage conversion curves are simulated and discussed to verify the feasibility. Appropriate parameters of the shunt resistor and inductor are deduced for fabricating the devices.
We report here numerical calculations on the properties of superconducting weak links as mixers with external local oscillators (LO). Our calculations are based on the resistively shunted-junction model. We assume that the LO and the signal are ideal current sources of amplitudes ILO and IS and of frequencies ωLO and ωs, respectively. We calculate the IF voltage across the weak link as a function of the bias current, the LO current amplitude ILO, and the normalized signal frequency Ωs = ħωs/(2 e Ic R), where Ic is the critical current and R is the shunt resistance. If ωIF/ωLO and Is/Ic are small, we find a linear IF response. Using this method we find the frequency dependence of the IF response, estimate the conversion efficiency for the matched case in both the absence and the presence of noise, and calculate the required LO power. We have fabricated thin-film constrictions by using electron lithography. We have made constrictions of indium films with thicknesses of ~ 1 200 A with widths as narrow as 2 000 A and lengths as short as 1 000 A and have studied their I-V characteristics in the presence of RF radiation and measured their X-band mixing properties. We have measured an NEP of 10-13 W/Hz1/2 and a dynamic range of 23 dB (3 dB deviation from linearity) and estimate that, with optimum matching, these would become 3 × 10-18 W/Hz1/2 and 74 dB, respectively.
The quantum phase-coherent behavior of superconducting weak links (WLs) is often quenched in the finite voltage state, due to the heat dissipation and related thermal hysteresis. The latter can be reduced by improving heat evacuation and/or by lowering the critical current so a phase-dynamic regime is obtained, albeit over a narrow bias-current and temperature range. Here we demonstrate that an inductive shunt with well-chosen parameters introduces unexpected nonlinear dynamics that destabilize an otherwise stable fixed point in the dissipative branch. This leads to a nonhysteretic behavior with large voltage oscillations in intrinsically hysteretic WL-based micron-size superconducting quantum interference devices. A dynamic thermal model quantitatively describes our observations and further allows us to elaborate on the optimal shunting conditions.
Controlling both the amplitude and the phase of the superconducting quantum order parameter ψ in nanostructures is important for next-generation information and communication technologies. The lack of electric resistance in superconductors, which may be advantageous for some technologies, hinders convenient voltage-bias tuning and hence limits the tunability of ψ at the microscopic scale. Here, we demonstrate the local tunability of the phase and amplitude of ψ, obtained by patterning with a single lithography step a Nb nano-superconducting quantum interference device (nano-SQUID) that is biased at its nanobridges. We accompany our experimental results by a semi-classical linearized model that is valid for generic nano-SQUIDs with multiple ports and helps simplify the modelling of non-linear couplings among the Josephson junctions. Our design helped us reveal unusual electric characteristics with effective zero inductance, which is promising for nanoscale magnetic sensing and quantum technologies.
The experimental results obtained with low noise dc superconducting quantum interference devices (dc-SQUIDs) are sometimes not well understood. In particular, when the critical current is high, very irregular voltage versus flux characteristics can be measured. On the other hand, when the critical current is low, the characteristics follow perfectly the resistively shunted junction model. We have studied the dynamics of a dc-SQUID in the presence of stray capacitance and shunting resistors imbalance. The equations describing a circuit model for this physical system are integrated numerically and the results are compared with voltage versus flux characteristics obtained from fabricated devices. We find that the theoretical analysis accounts very well for previously misunderstood experimental features of the dc-SQUID. This model can give more physical sense to the various regimes of behavior of the dc-SQUID giving more insight into the experimental results.