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 2q, but by 3q, 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 = 3.2K above 1.05 GPa, where Tc rises to the maximum, T max
c = 4.9K 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.
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