Quantum limit of a flux lattice: Superconductivity and magnetic field in a new relationship

An external magnetic field does not destroy superconductivity in type-II superconductors. As the field increases, the Abrikosov flux lattice crosses over into a new quantum limit, characterized by a transition temperature which is an increasing function of the field, the absence of the Meissner effect, and a supercurrent flow along the field direction. The transition temperature remains finite in an arbitrarily strong external field. We discuss the relevance of our results for the studies of a flux lattice in high-temperature superconductors and other superconducting systems.