Superconductivity in a very high magnetic field

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Abstract
An external magnetic field does not destroy superconductivity. As the field increases, the diamagnetic pair breaking is eliminated and the Abrikosov flux lattice crosses over into a new quantum limit, characterized by a transition temperature that is an increasing function of the field, the virtual absence of the Meissner effect, and a supercurrent flow along the field direction. The transition temperature remains finite in an arbitrarily strong external field as long as both spin states are present. Such a superconducting state in a very high magnetic field can occur irrespective of the nature of the ground state at low fields. We study various properties of this new state and discuss the relevance of our results for experimental work in high magnetic fields.