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This Concept Map, created with IHMC CmapTools, has information related to: High temperature superconductivity.cmap, HIGH TEMPERATURE SUPERCONDUCTIVITY 1. Ordinary super-conducti- vity. a) Landau Ginzburg model and BCS theory as models. b) Electron Cooper pairs as carriers of supracurrent. Pho- non exchange creates the in- teraction binding electrons to gether. c) Cooper has vanishing total spin and is in s=0 wave. Sta- tistics favores opposite spins. d) Critical temperature and critical magnetic fields. SCs are of type I and II. SC does not allow the penetration of mag- netic field below critical value (Meissner effect). For SC of type I the magnetic field fills the entire super-conductor above critical value. For SC of type II it penetrates as flux quanta and fills it at higher cri- tical value. e) Interpretation: magnetic field destroys Cooper pairs since it tends to turn the spins in same direction., HIGH TEMPERATURE SUPERCONDUCTIVITY 2. High T_c superconducti- vity. a) 2-dimensional phenomenon. Supra current flows along pre- ferred lattice planes. Type II super-conductivity in question. Proper sizes of Cooper pairs (coherence lengths) are ξ=1-3 nm. Magnetic length λ is lon- ger than ξ/sqrt(2). b) Mechanism for the forma- tion of Cooper pairs is same water bed effect as in the case of ordinary SC. Phonons are on- ly replaced with spin-density waves for electrons with perio- dicity in general not that of the underlying lattice. Spin density waves relate closely to the un- derlying antiferromagnetic or- der. Spin density waves appe- ar near phase transition to an- ti-ferromagnetism. c) The relative orbital angular momentum of Cooper pair is L=2 (x^2-y^2 wave), and wave function vanishes at origin unlike for ordinary s wave SCs. The spin of the Cooper pair va- nishes., HIGH TEMPERATURE SUPERCONDUCTIVITY 3. TGD inspired proposal is roughly following. a) Basic notions: mag- netic flux tubes and pos- sibly also dark electrons forming Cooper pairs. b) The appearance of spin waves means sequences of electrons with opposite spins. The magnetic field associated with them can form closed flux tube con- taining both spins. Assu- me that spins are orthogo- nal to the lattice plane in which supra-current flows. Assume that the flux tube branches associated with electron with given spin branches so that it is sha- red with both neighboring electrons. c) Electrons of opposite spins at the two portions of the closed flux tube ha- ve magnetic interaction energy. The total energy is minimal when the spins are in opposite directions. Thus the flux tube tends to favore formation of Cooper pairs. d) Since magnetic interac- tion energy is proportional to h_eff=n×h, it would stabilize the Cooper pairs at high temperatures., HIGH TEMPERATURE SUPERCONDUCTIVITY 3. e) This does not yet give super-conductivity. The closed flux tubes asso- ciated with paired spins can however reconnect so that longer flux closed flux tubes are formed. If this occurs for entire sequences one obtains two flux tubes containing elect- rons with opposite spins forming Cooper pairs. Thee pairs would form sup- ra-current in long scales. f) The phase phase transi- tions generating the recon- nections could be percola- tion type phase transition. g) In TGD inspired quantum biology the U-shaped loops carrying opposite magnetic fluxes are the tool of form- ing connections between two systems. The interpre- tation is as physical correla- of directed attention or re- cognition the presence of second system. The U- shaped loops are naturally superconductors with S=0 and L=2 Cooper pairs with electrons at different legs of U-shaped loop which in reconnection process be- comes pair of parallel flux tubes connecting the two systems., HIGH TEMPERATURE SUPERCONDUCTIVITY 4. This picture might apply also in TGD base model of bio- super-conductivity. a) The stability of dark Cooper pairs assume to reside at magnetic flux tubes is a problem also now. Fermi statistics favors opposite spins but this means that mag- netic field tends to spit the pairs if the members of the pair are at the same flux tube. b) If the members of the pair are at diffe- rent flux tubes, the situation changes. One can have L=1 and S=1 with parallel spins (ferromagnetism like situation) or L=2 and S= state (antifer- romagnetism like situa- tion). Lɬ is necessary since electrons must reside at separate flux tubes.
