New solutions for the superconducting order parameter in a high magnetic field

We demonstrate that for clean type II superconductors under a magnetic field, when the upper critical field H-c2 is mainly determined by the Pauli limit, a new type of solutions for the superconducting order parameter is realised at low temperatures. These solutions correspond to higher Landau level functions with an additional modulation along the field. It may be considered as a generalisation of the non-uniform Larkin-Ovchinnikov-Fulde-Ferrell state in the presence of an orbital effect. We predict the appearance of a cascade of transitions between different Landau level solutions with a change of field or temperature. Suitable systems for the observation of such effects are magnetic and heavy fermion superconductors.