Superconducting incommensurate organic composite crystals based on the methylenedithio-tetraselenafulvalene (MDT-TSF) series donors, where the energy band filling deviates from the usual 3/4-filled, are reviewed. The incommensurate anion potential reconstructs the Fermi surface for both (MDT-TSF)(AuI2)0.436 and (MDT-ST)(I3)0.417 neither by the fundamental anion periodicity q nor by 2 q , but by 3 q , where MDT-ST is 5H-2-(1,3-dithiol-2-ylidene)-1,3-diselena-4,6-dithiapentalene, and q is the reciprocal lattice vector of the anion lattice. The selection rule of the reconstructing vectors is associated with the magnitude of the incommensurate potential. The considerably large interlayer transfer integral and three-dimensional superconducting properties are due to the direct donor-donor interactions coming from the characteristic corrugated conducting sheet structure. The materials with high superconducting transition temperature, Tc, have large ratios of the observed cyclotron masses to the bare ones, which indicates that the strength of the many-body effect is the major determinant of Tc. (MDT-TS)(AuI2)0.441 shows a metal-insulator transition at TMI=50 K, where MDT-TS is 5H-2-(1,3-diselenol-2-ylidene)-1,3,4,6-tetrathiapentalene, and the insulating phase is an antiferromagnet with a high Néel temperature (TN=50 K) and a high spin-flop field (Bsf=6.9 T). There is a possibility that this material is an incommensurate Mott insulator. Hydrostatic pressure suppresses the insulating state and induces superconductivity at Tc=3.2 K above 1.05 GPa, where Tc rises to the maximum, Tcmax=4.9 K at 1.27 GPa. This compound shows a usual temperature-pressure phase diagram, in which the superconducting phase borders on the antiferromagnetic insulating phase, despite the unusual band filling.
Keywords: Fermi surface; incommensurate composite crystal; metal-insulator transition; organic superconductor.