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Low Temperature Physics

Current- and magnetic-field-controlled superconducting multi-terminal microstructures

E. D. Vol, A. N. Omel’yanchuk

Published Feb 1, 1994• 10 citations
Publisher

Abstract

We study theoretically superconducting microstructures of a special configuration, viz., Josephson multi-terminals (JMT), which are systems of interconnected microbridges. The nonlinear interaction of individual bridge junctions in JMT is due to fact that they have a common center and, hence, that the superconducting order parameter in each weak link is a function of the currents through all other microbridges. JMT is a nonlinear parametric element controlled by the current and the magnetic field. Dynamic equations have been derived, which govern the behavior of JMT versus the control parameters, viz., transport control currents or fluxes of an external magnetic field. We consider various JMT working regimes: synchronization of Josephson oscillations, degeneration of metastable states, and broken symmetry of the ground state in magnetic field.

DOI
10.1063/10.0033584

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We study theoretically superconducting microstructures of a special configuration, viz., Josephson multi-terminals (JMT), which are systems of interconnected microbridges. The nonlinear interaction of individual bridge junctions in JMT is due to fact that they have a common center and, hence, that the superconducting order parameter in each weak link is a function of the currents through all other microbridges. JMT is a nonlinear parametric element controlled by the current and the magnetic field. Dynamic equations have been derived, which govern the behavior of JMT versus the control parameters, viz., transport control currents or fluxes of an external magnetic field. We consider various JMT working regimes: synchronization of Josephson oscillations, degeneration of metastable states, and broken symmetry of the ground state in magnetic field.
Abstract The progressive miniaturization of superconducting quantum interference devices (SQUIDs) used, e.g. for magnetic imaging on the nanoscale or for the detection of the magnetic states of individual magnetic nanoparticles causes increasing problems in realizing a proper flux-bias scheme for reading out the device. To overcome the problem, a multi-terminal, multi-junction layout has been proposed and realized recently for the SQUID-on-tip configuration, which uses constriction-type Josephson junctions (JJ). This geometry is also interesting for SQUIDs based on overdamped superconductor—normal metal—superconductor (SNS) JJ. We fabricated four-terminal, four-junction SQUIDs based on a trilayer Nb/HfTi/Nb process and study their static and dynamic transport properties in close comparison with numerical simulations based on the resistively and capacitively shunted junction model. Simulations and measurements are in very good agreement. However, there are large differences to the transport properties of conventional two-junction SQUIDs, including unusual phase-locked and chaotic dynamic states which we describe in detail. We further extract the current-phase relation of our SNS junctions, which turns out to be purely sinusoidal within the experimental error bars.
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We have analyzed the quantum interference effects in the macroscopic “superconducting molecule.” The composite system consists of two massive superconducting rings, each interrupted by a Josephson junction, which are at the same time weakly coupled with one another. The special case of coupling via the Josephson four-terminal junction is considered. The structure of the macroscopic quantum states in an applied magnetic field is calculated. It is shown that, depending on the values of the magnetic fluxes through each ring, the system displays two groups of states, the “orthostates” with both induced currents going in the same direction, and the “parastates” with the opposite currents and with the total induced flux locked to zero value. The transition to the flux locked state with changing of the total applied flux is sudden and is preserved in a certain interval which is determined by the difference of the fluxes applied through each ring. It makes the system sensitive to small gradients of the external magnetic field.
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We describe in this paper how the nonlinear Josephson inductance is the crucial circuit element for all Josephson qubits. We discuss the three types of qubit circuits, and show how these circuits use this nonlinearity in unique manners. We give a brief derivation of the BCS theory, highlighting the appearance of the macroscopic phase parameter. The Josephson equations are derived using standard first and second order perturbation theory that describe quasiparticle and Cooper-pair tunneling. An exact calculation of the Josephson effect then follows using the quasiparticle bound-state theory, and then expand upon this theory to describe quasiparticle excitations as transitions from the ground to excited bound states from nonadiabatic changes in the bias. Although quasiparticle current is typically calculated only for a constant DC voltage, the advantage to this approach is seen where we qualitatively describe quasiparticle tunneling with AC voltage excitations, as appropriate for the qubit state. This section describes how the Josephson qubit is typically insensitive to quasiparticle damping, even to the extent that a phase qubit can be constructed from microbridge junctions.