Field-induced superconducting phase in superconductor-normal metal and superconductor-superconductor bilayers

We study the proximity effect in a superconductor (S)-normal metal (N) bilayer system under in-plane magnetic field and demonstrate that a compensation between the Zeeman effect and the energy splitting between bonding and antibonding levels may lead to a magnetic-field-induced superconducting phase well above the standard paramagnetic limit. It occurs that the nonuniform Fulde-Ferrell-Larkin-Ovchinikov superconducting state also exists in the field-induced phase. The presence of the impurity scattering shrinks the region of field-induced superconductivity existence in S-N and S-S bilayers.