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Superconductor Science and Technology

Ratchet potential in superconducting quantum interference devices containing a double-barrier junction

Roberto De Luca

Published Jul 15, 2009• 3 citations
Publisher

Abstract

The periodic effective potential of a superconducting quantum interference device containing an underdamped Josephson junction in the first branch and a double-barrier junction in the second is studied. An effective non-sinusoidal expression for the current–phase relation with an additional half harmonic term is used for the double-barrier junction. The system allows voltage rectification under opportunely chosen parameter values.

DOI
10.1088/0953-2048/22/8/085008

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The periodic effective potential of a superconducting quantum interference device containing an underdamped Josephson junction in the first branch and a double-barrier junction in the second is studied. An effective non-sinusoidal expression for the current–phase relation with an additional half harmonic term is used for the double-barrier junction. The system allows voltage rectification under opportunely chosen parameter values.
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Integer and half-integer Shapiro step amplitudes in the current-voltage characteristics of symmetric superconducting quantum interference devices (SQUIDS), containing more than one Josephson junction on each arm, are analytically calculated for small values of the parameter β and in the absence of noise. This analysis is made possible by the reduction of the dynamical equations of the multiple-junction SQUID to the dynamical equation of a single Josephson junction possessing a nonconventional current-phase relation.
We have calculated the dc Josephson current through multi-barrier superconducting junctions (MBSJs). The current-phase relationship of the MBSJs has been obtained numerically from the probability amplitude of the process in which an electron-like quasiparticle is reflected as a hole-like quasiparticle (Andreev reflection) in the junctions. Moreover, using the obtained current-phase relationship of MBSJs, the characteristics of superconducting quantum interference devices containing MBSJs have also been analyzed.
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Conventional superconductor/insulator/superconductor (SIS) Josephson junctions, devices where two superconductors are separated by a tunnel barrier are technologically important as elements in quantum circuits, particularly with their key role in superconducting qubits. An important characteristic of Josephson junctions is the relation between the supercurrent Is and the phase difference ϕϕϕ between them. For SIS junctions, the current-phase relation is sinusioidal and 2πππ periodic. Other types of Josephson junctions, where the material between the superconductors is a weak link or a normal metal (N) may have non-sinusoidal current-phase relations that are still 2πππ periodic. We show here that a multi-terminal diffusive SNS Josephson junction with 4 superconducting contacts can show a current phase relation between two of the contacts that is a superposition of 2πππ and 4πππ periodic components whose relative strength is controlled by the phase difference between the other two contacts, becoming 2πππ or 4πππ periodic for certain values of this phase difference. This tunability might have applications in tailoring the Hamiltonians of superconducting quantum circuits.
The Hamiltonian of a superconducting thin loop interrupted by a double-barrier Josephson junction is derived. The parameter ε, which takes account of the difference in the Josephson coupling of the two single junctions in the SISIS structure, is seen to allow variation of the energy gap ΔE01 between the ground state and the first excited flux number state of the system. An additional parameter γ, describing the coupling between the outer electrodes of the double-barrier Josephson junction, is introduced. Persistent currents in the system are studied in terms of the usual parameter α, representing the ratio between the Josephson energy and the magnetic energy, and of the externally applied flux.