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.
Coherence in the quasiparticle scattering by the vortex lattice in pure type-II superconductors
The effect of quasiparticle (QP) scattering by the vortex lattice on the de Haas-van Alphen (dHvA) oscillations in a pure type-II superconductor is investigated within a mean-field asymptotic perturbation theory. Using a two-dimensional (2D) electron-gas model it is shown that, due to a strict phase coherence in the many particle correlation functions, the scattering effect in the asymptotic limit ({radical}(E{sub F}/{h_bar}{omega}{sub c}){gt}1) is much weaker than what is predicted by the random vortex-lattice model proposed by Maki and Stephen, which destroys this coherence. The coherent many particle configuration is a collinear array of many particle coordinates, localized within a spatial region with size of the order of the magnetic length. The amplitude of the magnetization oscillations is sharply damped just below H{sub c2} because of strong 180{degree} out of phase magnetic oscillations in the superconducting condensation energy, which tend to cancel the normal electron oscillations. Within the ideal 2D model used it is found, however, that because of the relative smallness of the quartic and higher order terms in the expansion, the oscillations amplitude at lower fields does not really damp to zero, but only reverses sign and remains virtually undamped well below H{sub c2}. This conclusion may be changedmore » if disorder in the vortex lattice, or vortex line motion is taken into account. The reduced QP scattering effect may be responsible for the apparent crossover from a strong damping of the dHvA oscillations just below H{sub c2} to a weaker damping at lower fields observed experimentally in several 3D superconductors. {copyright} {ital 1997} {ital The American Physical Society}« less
Refinement of crystal structure parameters using convergent‐beam electron diffraction: the low‐temperature phase of SrTiO3
The method to refine crystal structure parameters (atom positions and Debye–Waller factors) using convergent-beam electron diffraction (CBED), which is applicable to crystal structure analysis of a small specimen area down to a few nm in diameter, is studied. The line profiles of higher-order Laue-zone reflections are recorded using imaging plates. Theoretical intensities are calculated based on the dynamical theory of electron diffraction with the aid of the generalized Bethe approximation to shorten calculation time. The structural parameters are determined by fitting the experimental profiles with the theoretical ones using a nonlinear least-squares method. The present method has been applied to the low-temperature phase of SrTiO3. The structural parameter or the rotation angle of the oxygen octahedron has been determined to be \varphi = 1.12 (4)°, which shows good agreement with that obtained from electron spin resonance experiments.