Anomalous behavior of the upper critical field in extreme type-II superconductors at low temperatures

We present a detailed numerical calculation of the upper critical field H_c2(T) for a bulk extreme type-II superconductor. Particular emphasis is placed on the high-field, low-temperature regime of the HT-phase diagram. In this regime, it is necessary to go beyond the standard semi-classical theory and include the effects of Landau quantization of the electronic motion on the superconducting state. The presence of Landau level quantization induces an upward curvature in H_c2(T) at ∼ 10% of T_c0 for those superconducting systems in which the slope of H_c2(T) at T_c0 is ≥ 0.2 T/K. We construct a simple analytical model that can account for this behavior based on the renormalization of the BCS coupling constant by the off-diagonal pairing of electrons on Landau levels.