Exact results on superconductivity due to interband coupling.

We present a family of exactly solvable models at arbitrary filling in any dimensions which exhibit novel superconductivity with interband pairing. By the use of the hidden SU(2) algebra the Hamiltonians were diagonalized explicitly. The zero-temperature phase diagrams and the thermodynamic properties are discussed. Several new properties are revealed which are different from those of the BCS-type superconductor. Typeset using REVTEX 1 Superconductivity is one of the most remarkable phenomena in condensed matter physics. Recently possibilities of a novel superconductor are proposed by Kohmoto and Takada [1]. They investigated the superconducting instability of insulators by the mean-field treatment. A two-band system which is insulating without interactions becomes superconducting by a sufficiently large interband attraction. It has many properties which are different from those of the BCS-type superconductors [2]. Note that the Cooper instability is irrelevant here, since there is no Fermi surface. In Ref. [3], possible realization in organic materials is discussed, which is an extension of the Little’s idea for the room-temperature superconductor [4]. We have constructed a family of exactly solvable models at arbitrary filling in any dimensions which includes the models proposed in Ref. [1] and Ref. [3]. We have obtained the ground state and the thermodynamic quantities explicitly. Several new properties have been revealed. An instability without a Fermi surface, which was proposed by Kohmoto and Takada, is realized in the models. This instability is quite different from the Cooper instability. A finite strength of attraction is needed to produce the superconductivity in contrast to the BCS-type superconductivity. Let us consider a two-band model described by the Hamiltonian H = Hkin +Hint, (1) Hkin = ∑ k ǫ(k)c (v) k c (v) k + ∑ k ǫ(k)c (c) k c (c) k , (2)