Two-dimensional superconductor in a tilted magnetic field: States with finite Cooper-pair momentum

Varying the angle $\theta$ between applied field and the conducting planes of a layered superconductor in a small interval close to the plane-parallel field direction, a large number of superconducting states with unusual properties may be produced. For these states, the pair breaking effect of the magnetic field affects both the orbital and the spin degree of freedom. This leads to pair wave functions with finite momentum, which are labeled by Landau quantum numbers $0<n<\mathrm{}\infty .$ The stable order-parameter structure and magnetic-field distribution for these states is found by minimizing the quasiclassical free energy near $H_{c2\mathrm{}}$ including nonlinear terms. One finds states with coexisting linelike and pointlike order-parameter zeros and states with coexisting vortices and antivortices. The magnetic response may be diamagnetic or paramagnetic depending on the position within the unit cell. The structure of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states at $\theta =0\mathrm{}$ is reconsidered. The transition $\overrightarrow{n}\infty$ of the paramagnetic vortex states to the FFLO limit is analyzed and the physical reason for the occupation of higher Landau levels is pointed out.