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arXiv:cond-mat/0501378 · Nuclear Physics B

Effective boundary field theory for a Josephson junction chain with a weak link

Domenico Giuliano, Pasquale Sodano

Published Feb 15, 2005• 39 citations
arXivHTMLPDF
DOI
10.1016/j.nuclphysb.2005.01.037

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The authors present a model for a series-parallel array of small metallic (nontunneling) Josephson junctions. The transmission and configuration of pair electrons between small superconducting regions are considered assuming the presence of a strong interaction between the electrostatic energy (2e)/sup 2//2C and the Josephson effect in a network of metallic weak links. The model predicts that the same behavior as that of a single junction is obtained with a superconducting weak-link device comprising multiple small superconducting regions joined by conductive bridges. In an experiment in the 100- and 320-GHz frequency ranges, the constriction of a YBCO film formed with a network of grain-boundary Josephson weak links showed that the AC Josephson effect is the same as for a single Josephson element. It is confirmed that the constriction works as a harmonic mixer at 318 GHz and that a network of high-T/sub c/ superconducting weak links can be used for a practical device operating at submillimeter-wave frequencies.>
Hybrid superconductor-semiconductor nanowire Josephson junctions exhibit skewed and \phi_0 ϕ 0 -shifted current phase relations when an in-plane magnetic field is applied along the weak link’s spin-orbit effective field direction. These junctions can have an asymmetric Josephson potential with odd-order nonlinearities. A dominant third-order nonlinearity can be achieved by tuning the magnetic field to a sweet spot. Sweet spots persist when higher order Josephson harmonics are included. This makes it possible to have a single Josephson junction dipole element with three-wave mixing capability, which is favorable for pump-efficient amplification. Electrostatic gate tunability of the semiconductor weak link can make it operable within an extended range of working frequencies, and the inclusion of micromagnets can facilitate near-zero magnetic field operation.
We show that- in the quantum regime- a Josephson junction rhombi chain (i.e. a Josephson junction chain made by rhombi formed by joining 4 Josephson junctions) may be effectively mapped onto a quantum Hamiltonian describing Ising spins in a transverse magnetic field with open boundary conditions. Then, we elucidate how a Y-shaped network fabricated with 3 Josephson Junction Rhombi chains may be used as a quantum device realizing the two channel Kondo model recently proposed by Tsvelik. We point out that the emergence of a 2 channel Kondo effect in this superconducting network may be probed through the measurement of a pertinent Josephson current.