BCS Stripe Phase in Coupled Bilayer Superconductors

As a signature of competing correlations, stripes occur in a variety of strongly correlated systems, such as high temperature superconductors (SCs) and quantum Hall effect. We study a double layer SC in the presence of a parallel magnetic field $B$ within the Bogoliubov-de Gennes framework. We find that for low $B$ the system remains in the ``Bardeen-Cooper-Schrieffer (BCS) phase" with a spatially uniform gap, but with increasing $B$, a transition occurs into a phase which contains stripes of the BCS phase separated by regions where the interlayer phase difference rotates by $2\pi$ due to the presence of inter-layer vortices. This stripe phase is predicted to manifest through oscillations in the amplitude of the SC gap and an alternating pattern of supercurrents. We will comment on the relation to previous works based on the Landau-Ginzburg formalism as well as on the possible experimental realization and signature of this phase.