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arXiv:1304.4046 · Physical Review B

Phase sticking in one-dimensional Josephson junction chains

Adem Ergül, David J. Schaeffer, Magnus Lindblom, David B. Haviland, Jack Lidmar, Jan Johansson

Published Sep 3, 2013• 16 citations
arXivHTMLPDF

Abstract

We studied current-voltage characteristics of long one-dimensional Josephson junction chains with Josephson energy much larger than charging energy, ${E}_{J}\ensuremath{\gg}{E}_{C}$. In this regime, typical I-V curves of the samples consist of a supercurrent-like branch at low-bias voltages followed by a voltage-independent chain current branch, ${I}_{\mathrm{chain}}$ at high bias. Our experiments showed that ${I}_{\mathrm{chain}}$ is not only voltage-independent but it is also practically temperature-independent up to $T=0.7{T}_{C}$. We have successfully model the transport properties in these chains using a capacitively shunted junction model with nonlinear damping.

DOI
10.1103/physrevb.88.104501

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We studied current-voltage characteristics of long one-dimensional Josephson junction chains with Josephson energy much larger than charging energy, EJ\ensuremath≫EC{E}_{J}\ensuremath{\gg}{E}_{C}EJ​\ensuremath≫EC​. In this regime, typical I-V curves of the samples consist of a supercurrent-like branch at low-bias voltages followed by a voltage-independent chain current branch, Ichain{I}_{\mathrm{chain}}Ichain​ at high bias. Our experiments showed that Ichain{I}_{\mathrm{chain}}Ichain​ is not only voltage-independent but it is also practically temperature-independent up to T=0.7TCT=0.7{T}_{C}T=0.7TC​. We have successfully model the transport properties in these chains using a capacitively shunted junction model with nonlinear damping.
For the observation of the charging effect on a Josephson junction, the charging energy (E c) must be much larger than the Josephson coupling energy (E J) and thermal energy (k B T). We investigated the properties of submicron-sized Bi2Sr2CaCu2O8+δ intrinsic Josephson junctions (IJJs) at low temperature. The current–voltage curve of IJJs with a junction area of 0.06 µm2 showed a much higher resistance state near the zero bias voltage regions when the measurement temperature decreased to 72.6 mK. The ratios of E c/E J and E c/k B T were 7.04 and 5.78, respectively, which indicates that the charging effect is dominant. In addition, a characteristic voltage structure due to the charging effect in one-dimensional junction array, which is composed of the offset voltage and the threshold voltage of the junction, was observed.
We studied quantum phase-slip (QPS) phenomena in long one-dimensional Josephson junction series arrays with tunable Josephson coupling. These chains were fabricated with as many as 2888 junctions, where one sample had a separately tunable link in the middle of the chain. Measurements were made of the zero-bias resistance, R 0 , as well as current–voltage characteristics (IVC). The finite R 0 is explained by QPS and shows an exponential dependence on with a distinct change in the exponent at R 0 = R Q = h /4 e 2 . When R 0 > R Q , the IVC clearly shows a remnant of the Coulomb blockade, which evolves to a zero-current state with a sharp critical voltage as E J is tuned to a smaller value. The zero-current state below the critical voltage is due to coherent QPSs and we show that these are enhanced when the central link is weaker than all other links. Above the critical voltage, a negative, differential resistance is observed, which nearly restores the zero-current state.
This thesis presents the results of the experimental studies on two kindof Superconducting circuits: one-dimensional Josephson junction chains andsuperconducting coplanar waveguide (CPW) resonators. One-dimensionalJosephson junction chains are constructed by connecting many Superconducting quantum interference devices (SQUIDs) in series. We have studied DC transport properties of the SQUID chains and model their nonlineardynamics with Thermally Activated Phase-Slips (TAPS). Experimental andsimulated results showed qualitative agreement revealing the existence of auniform phase-slipping and phase-sticking process which results in a voltage-independent current on the dissipative branch of the current-voltage char-acteristics (IVC). By modulating the effective Josephson coupling energy ofthe SQUIDs (EJ ) with an external magnetic field, we found that the ratio EJ /EC is a decisive factor in determining the qualitative shape of theIVC. A quantum phase transition between incoherent Quantum Phase Slip, QPS (supercurrent branch with a finite slope) to coherent QPS (IVC withwell-developed Coulomb blockade) via an intermediate state (supercurrentbranch with a remnant of Coulomb blockade) is observed as the EJ /EC ratio is tuned. This transition from incoherent QPS to the intermediate-statehappens around R0 ∼ RQ (RQ = h/4e^2 = 6.45kΩ). We also fabricated structured chains where a SQUID at the middle of the chain (central SQUID) has different junction size and loop area compared to other SQUIDs in the chain. Results showed that with these structured chains it is possible to localize andtune the amplitude of both TAPS and QPS at the central SQUID. The second part of the thesis describes the fabrication process and themeasurement results of superconducting CPW resonators. Resonators withdifferent design parameters were fabricated and measured. The transmissionspectra showed quality factors up to, Q ∼ 5 × 10^5 . We have observed bendingof the resonance curves to the lower frequencies due to existence of a nonlinear kinetic inductance. The origin of the nonlinear kinetic inductance isthe nonlinear relation between supercurrent density, Js, and superfluid veloc-ity, vs , of the charge carriers on the center line of the resonators. A simplemodel based on the Ginzburg-Landau theory is used in order to explain ob-served nonlinear kinetic inductance and estimates using this model showedgood agreement with the experimental results.
The Josephson effect, tunnelling of a supercurrent through a thin insulator layer between two superconducting islands, is a phenomena characterized by a spatially distributed phase of the superconducting condensate. In recent years, there has been a growing focus on Josephson junction devices particularly for the applications of quantum metrology and superconducting qubits. In this study, we report the development of Josephson junction circuit formed by serially connecting many Superconducting Quantum Interference Devices, SQUIDs. We present experimental measurements as well as numerical simulations of a phase-slip center, a SQUID with weaker junctions, embedded in a Josephson junction chain. The DC transport properties of the chain are the result of phase slips which we simulate using a classical model that includes linear external damping, terminating impedance, as well as internal nonlinear quasiparticle damping. We find good agreement between the simulated and the experimental current voltage characteristics. The simulations allow us to examine the spatial and temporal distribution of phase-slip events occurring across the chains and also the existence of travelling voltage pulses which reflect at the chain edges.
We have measured the current-voltage $(I\ensuremath{-}V)$ characteristics of small-capacitance single Josephson junctions at low temperatures (T=0.02−−0.6K),(T=0.02--0.6\mathrm{K}),(T=0.02−−0.6K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc superconducting quantum interence devices (SQUIDs). The single-junction $I\ensuremath{-}V$ curve is sensitive to the impedance of the environment, which can be tuned in situ. We have observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, where the zero-bias resistance ${R}_{0}^{\ensuremath{'}}$ of the SQUID arrays is much higher than the quantum resistance ${R}_{K}\ensuremath{\equiv}{h/e}^{2}\ensuremath{\approx}26\mathrm{k}\ensuremath{\Omega}.$ The negative differential resistance is evidence of the coherent single-Cooper-pair tunneling within the theory of current-biased single Josephson junctions. Based on this theory, we have calculated the $I\ensuremath{-}V$ curves numerically in order to compare then with the experimental ones at ${R}_{0}^{\ensuremath{'}}\ensuremath{\gg}{R}_{K}.$ The numerical calculation agrees with the experiments qualitatively. We also discuss the ${R}_{0}^{\ensuremath{'}}$ dependence of the single-Josephson-junction $I\ensuremath{-}V$ curve in terms of the superconductor-insulator transition driven by changing the coupling to the environment.
The supercurrent of a Josephson junction is reduced by phase diffusion. For ultrasmall capacitance junctions the current may be further decreased by Coulomb blockade effects. We calculate the Cooper pair current by means of time-dependent perturbation theory to all orders in the Josephson coupling energy and obtain the current-voltage characteristic in closed form in a range of parameters of experimental interest. The results comprehend phase diffusion of the coherent Josephson current in the classical regime as well as the supercurrent peak due to incoherent Cooper pair tunneling in the Coulomb blockade regime.