Phase transition into the superconducting mixed state and the de Haas-van Alphen effect
Abstract The Landau expansion for the free energy of the superconducting mixed state near the upper critical field in powers of the sauare modulus of the order parameter averaged over an Abrikosov lattice is derived. The analytical calculations have been carried out in the framework of the Gor'kov formalism for a 3-dimensional isotropic BCS model beyond the limits of the quasiclassical approximation, that is, with Landau auantization of the auasiparticle energy levels taken into consideration. The derivation is performed at Iow temperature for finite but high enough crystal purity. The effect of Pauli paramagnetic terms is taken into account. The quantum oscillations of the critical temperature, the order parameter's amplitude and the magnetization (de Haas-van Alphen effect) in the mixed state are found. The limitation for the validity of a mean field approach due to critical fluctuations (Ginzburg criterion) for the phase transition under consideration is established.
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.
Fermi-surface measurements in normal and superconducting 2H-NbSe/sub 2/
Landau quantum oscillations are observed for the first time in the layered, superconducting, incommensurate-charge-density-wave compound 2H-NbSe$sub 2$. The oscillations are observed clearly above H/subc/$sub 2$ but also below H/ subc/$sub 2$, with somewhat increased scattering. This is interpreted as scattering of the orbiting normal electrons from the flux lattice. The observed sheet of Fermi surface can be explained if Mattheiss's augmented-plane-wave band structure is modified slightly. (AIP)