Phase-dependent magnetoconductance fluctuations in a chaotic Josephson junction

Motivated by recent experiments by Den Hartog et al., we present a random-matrix theory for the magnetoconductance fluctuations of a chaotic quantum dot that is coupled by point contacts to two superconductors and one or two normal metals. There are aperiodic conductance fluctuations as a function of the magnetic field through the quantum dot and 2 pi-periodic fluctuations as a function of the phase difference phi of the superconductors. If the coupling to the superconductors is weak compared to the coupling to the normal metals, the phi dependence of the conductance is harmonic, as observed in the experiment. In the opposite regime, the conductance becomes a random 2 pi-periodic function of phi, in agreement with the theory of Altshuler and Spivak. The theoretical method employs an extension of the circular ensemble which can describe the magnetic-field dependence of the scattering matrix.