Anomalous (H,T) phase diagram in bilayered superconducting systems

We demonstrate that in a superconducting multilayered system with alternating interlayer coupling a new type of nonuniform superconducting state can be realized under in-plane magnetic field. The Zeeman effect in this state is compensated by the energy splitting between bonding and antibonding levels. At low temperature such compensation mechanism leads to the field-induced superconductivity. We discuss the choice of the optimal coupling between the layers in order to observe the predicted phenomena in experiments