Inversion in a four terminal superconducting device on the quartet line: II. Quantum dot and Floquet theory

Abstract

In this paper, we consider a quantum dot connected to four superconducting terminals biased at opposite voltages on the quartet line. The grounded superconductor contains a loop threaded by the magnetic flux $\Phi$. We provide Keldysh microscopic calculations and physical pictures for the voltage-$V$ dependence of the quartet current. Superconductivity is expected to be stronger at $\Phi /{\Phi }_0=0$ than at $\Phi /{\Phi }_0=1/2$. However, inversion $I_{q,c}(V,0)<I_{q,c}(V,1/2)$ is obtained in the critical current $I_{q,c}(V,\Phi /{\Phi }_0)$ on the quartet line in the voltage-$V$ ranges which match avoided crossings in the Floquet spectrum at $(V,\Phi /{\Phi }_0=0)$ but not at $(V,1/2)$. A reduction in $I_{q,c}$ appears in the vicinity of those avoided crossings, where Landau-Zener tunneling produces dynamical quantum mechanical superpositions of the Andreev bound states. In addition, $\pi$-$0$ and $0$-$\pi$ cross-overs emerge in the current-phase relations as $V$ is further increased. The voltage-induced $\pi$-shift is interpreted as originating from the nonequilibrium Floquet populations produced by voltage biasing. The numerical calculations reveal that the inversion is robust against strong Landau-Zener tunneling and many levels in the quantum dot. Our theory provides a simple ``Floquet level and population'' mechanism for inversion tuned by the bias voltage $V$, which paves the way towards more realistic models for the recent Harvard group experiment where the inversion is observed.

18 pages, 9 figures, Supplemental Material as ancillary file (7 pages, 4 figures). Improved presentation

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Cited by in corpus (12)

• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Inversion in a four-terminal superconducting device on the quartet line: I. Two-dimensional metal and the quartet beam splitter
• A quantum interferometer for quartets in superconducting three-terminal Josephson junctions
• Ultralong-distance quantum correlations in three-terminal Josephson junctions
• Proposal for detecting the $\pi -$shifted Cooper quartet supercurrent
• Subgap dynamics of double quantum dot coupled between superconducting and normal leads
• Quartet Tomography in Multiterminal Josephson Junctions
• Magnetointerferometry of multiterminal Josephson junctions
• Ballistic Andreev interferometers
• Nonequilibrium Andreev resonances in ballistic graphene Andreev interferometers
• Dynamical Stabilization of Multiplet Supercurrents in Multi-terminal Josephson Junctions
• Revisiting the adiabatic limit in ballistic multiterminal Josephson junctions