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 two- and quasi-two-dimensional metals and superconductors
Abstract An analytical form of the quantum magnetization oscillations (de Haas van Alphen effect) is derived for two- and quasi-two-dimensional metals in normal and superconducting mixed states. The theory is developed under condition μ/ωc ≫ 1 (μ is the chemical potential and ωc the cyclotron frequency), which is proved to be valid for using grand canonical ensemble in the systems of low dimensionality. The effects of the impurities, temperature, spin splitting and vortex lattice (in the case of superconductors of type II) are taken into account. Contrary to the three-dimensional case, the oscillations in sufficiently pure systems of low dimensionality and at sufficiently low temperatures are characterized by a sawtooth waveform, which became smoother with increasing temperature and increasing concentration of impurities. In the normal quasi-two-dimensional systems, the expression for the magnetization oscillations includes an extra factor expressed through the transfer integral between the layers. The additional damping effect due to the vortex lattice is found. The criterion of proximity to the upper critical field for the observation of the de Haas–van Alphen effect in the superconducting mixed state is established.
Kinemamtic analysis of flying-saw vehicle
The paper analyzes the kinematic motion of the flying-saw vehicle.After the analysis,it is concluded that the ac- celerating periods and decelerating periods in both forward and backward directions will follow sin~2αcurve and,in order to increase the sawing dimensional accuracy,flying-saw vehicle must come back as soon as possible while acceleration remains constant.Based on this premise,the paper gives out the equations of kinematic motion of the flying-saw vehicle in every sta- ges and one example result in a common situation.By now this method has been used in the real situation.