De Haas–van Alphen effect in conventional and unconventional superconductors

Abstract

The damping of the amplitude of the magnetization oscillations in the mixed state of type-II superconductors is found. The magnitude of the order parameter is determined self-consistently from the system of Gor'kov equations taking into consideration the electron scattering by the nonmagnetic impurities, nonuniform distribution of the order parameter and the effects of Pauli spin paramagnetism. It is shown that for the superconductors with high value of the upper critical field and small value of Fermi energy the superconducting state is gapless in broad enough mixed state region below the upper critical field. Another important consequence of the theory is that the phase transition to the mixed state of clean enough type-II ordinary superconductor is of the first order below some tricritical point temperature depending on impurities concentration. In the unconventional superconducting states where the lines of extremal cross-section of Fermi-surface by the plane perpendicular to magnetic field coincide with lines of zeros of the order parameter the amplitude of the magnetization oscillations is practically the same as in a normal state. In the superconducting phases with an other distribution of zeros the damping of dHvA oscillations corresponds qualitatively to the ordinary superconductivity. Unlike to singlet pairing for a triplet equal spin pairing the phase transition into mixed state is always of the second order.