By Arioli G., Szulkin A.
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Extra info for A semilinear Schrödinger equation in the presence of a magnetic field
3 Melt Processing of YBa2 Cu3 O7−δ 35 The sintering temperature was slightly below the melting temperature of YBa2 Cu3 O7−δ . The critical current densities which could be achieved with these samples were disappointingly low. The reason was that in these veryfine-grained materials a large number of high-angle grain boundaries are present, which carry nearly no supercurrent as is known from bicrystal experiments . 1 Melt Growth Processes All melt growth processes are based on the phase reactions described in Sect.
This melting transition is a first-order phase transition in pure materials; in the presence of pinning and strong disorder it turns into a second-order phase transition. A schematic outline of the vortex phase diagram in an HTSC is given in Fig. 3. magnetic field H normal phase Hc1 vortex liquid vortex glass (superconducting) Meissner phase temperature T Tc Fig. 3. Hypothetical vortex phase diagram in an HTSC In a pure superconductor the first-order phase transition from vortex solid to vortex liquid is expected to obey the Lindemann criterion [22, 171].
Therefore many theories on the mechanism of high-temperature superconductivity were put forward which did not consider electron–phonon coupling as the basic interaction for superconductivity as the BCS theory does. Among them there are bipolarons, anyons and marginal-Fermi-liquid theory. Recently the discussion has concentrated on either electron–phonon interaction and an extended BCS theory or spin fluctuations as the explanation for the high transition temperature and other properties of the HTSCs.
A semilinear Schrödinger equation in the presence of a magnetic field by Arioli G., Szulkin A.