Realization of a two-channel Kondo model with Josephson junction networks

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 in Phys. Rev. Lett., 110 (2013) 147202. 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.