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Physical review. B, Solid state

Observation of a cosφ term in the current-phase relation for "Dayem"-type weak link contained in an rf-biased superconducting quantum interference device

Marty Nisenoff, S. A. Wolf

Published Sep 1, 1975• 30 citations
Publisher

Abstract

The presence of a $cos\ensuremath{\varphi}$ term in the current---quantum-mechanical phase relation for a superconducting weak link can be established from the frequency response of an rf-biased superconducting quantum interference device containing the structure. For narrow constrictions, the sign of the coefficient of the cosine term was determined to be negative.

DOI
10.1103/physrevb.12.1712

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The presence of a cos\ensuremathφcos\ensuremath{\varphi}cos\ensuremathφ term in the current---quantum-mechanical phase relation for a superconducting weak link can be established from the frequency response of an rf-biased superconducting quantum interference device containing the structure. For narrow constrictions, the sign of the coefficient of the cosine term was determined to be negative.
The rf impedance of superconducting point contacts has been measured as a function of the quantum-mechanical phase difference $\ensuremath{\varphi}$ across the point contact. By representing the point contact as a parallel combination of an inductor $\mathfrak{L}(\ensuremath{\varphi})=(\frac{\ensuremath{\hbar}}{2e}){(\frac{\ensuremath{\partial}{I}_{p}}{\ensuremath{\partial}\ensuremath{\varphi}})}^{\ensuremath{-}1}$ and a resistor $R\ensuremath{\equiv}\frac{1}{G(\ensuremath{\varphi})}$ the current-phase relation ${I}_{p}(\ensuremath{\varphi})$ and the phase-dependent conductance $G(\ensuremath{\varphi})$ have been determined from measurements at 30 MHz on phase-biased niobium point contacts. For point contacts with sufficiently small critical current Ic{I}_{c}Ic​, the inductance was $\mathfrak{L}(\ensuremath{\varphi})=\frac{\ensuremath{\hbar}}{2e{I}_{c}cos\ensuremath{\varphi}}$ yielding the expected negative inductance branch for $\frac{\ensuremath{\pi}}{2}\ensuremath{\le}\ensuremath{\varphi}\ensuremath{\le}\ensuremath{\pi}$ and a sinusoidal current-phase relation. For larger critical currents there were departures from the sinusoidal form for the measured ${I}_{p}(\ensuremath{\varphi})$. There was a phase-dependent conductance that is an increasing function of $\ensuremath{\varphi}$ corresponding to a negative coefficient for the $cos\ensuremath{\varphi}$ term in the Josephson current.
The magnetic properties of a rf superconducting quantum interference device containing one overdamped double-barrier junction are studied. The effective nonsinusoidal expression for the current-phase relation with an additional half harmonic term is used for the double-barrier junction. Devices with inhomogeneous double-barrier junctions show a characteristic feature: for fixed and not too high superconducting loop inductance values, transition from irreversible to reversible magnetic behavior can be induced by increasing the difference in the Josephson coupling of the two junctions.
The signal properties of radio frequency (rf) (SQUIDs) based on YBa2Cu3O7−x symmetrical 30° and asymmetrical 45° grain-boundary Josephson junctions have been experimentally investigated. Both amplitude as well as phase detection have been used to read out the SQUID output signal. Comparison of the SQUID output signals to each other is given. It is shown that peculiarities of the rf SQUID response of SQUIDs with a 45° grain-boundary Josephson junction are consistent with an unconventional current-phase relation (CPR) of the Josephson junction, namely, the CPR contains a finite amplitude of the second harmonic.
Based on the hypothesis that the macroscopic superconducting shielding current on the surface of a porous granular superconductor is short lived due to the action of thermal noise, a dispersive-mode theory for a high-temperature radio-frequency superconducting quantum interference device (rf SQUID) is suggested. In this theory, the effect of the SQUID ring on the resonant tank circuit is an effective inductance Le{L}_{e}Le​, Le{L}_{e}Le​=k2{k}^{2}k2FLT{\mathrm{FL}}_{T}FLT​, where k is the coupling coefficient between the SQUID ring and the resonant tank circuit with inductance LT{L}_{T}LT​, and F is a periodic function of external flux ${\ensuremath{\Phi}}_{\mathrm{dc}}$ with a period of flux quantum ${\ensuremath{\Phi}}_{0}$. The phenomena that the weak-link-rf-SQUID flux-receiving area defined by the hole of the SQUID ring and the bulk-rf-SQUID flux-receiving area, which is determined by an annular surface region with a thickness of the effective penetration depth ${\ensuremath{\lambda}}_{e}$, can be interpreted. The theory is qualitatively consistent with available experimental results.
Calibrated measurements of both the real and imaginary parts of the microwave impedance of proximity coupled superconducting weak links have been made. The measurements were compared with analytic calculations based on several different models for the supercurrent Is and quasiparticle current. For dc bias currents I1 less than the critical current Ic, the experimental results are consistent with the Josephson relation Is=Ic sinφ, where φ is the quantum phase angle. However, for I1≳Ic, the Fourier component of Is at the Josephson frequency is found to be significantly less (∼0.65±0.1) than would be predicted from Is=Ic sinφ, and consistent with Tinkham’s analysis of a phase slip process. The experimental results indicate that the phase-dependent part of the quasiparticle current, if it exists at all, is no more than 10% of the total quasiparticle current. These results do not necessarily contradict previous measurements made on true tunnel junctions because of the fundamental differences between the two types of devices.