Antiferromagnetically induced electron pairing

Abstract

Abstract A naive counting of valence electrons, in the materials currently displaying high temperature superconductivity, would suggest a near half-filled-band metallic state whereas many of the observed properties are suggestive of semiconducting or at best poor metallic behaviour. In addition, the undoped La 2 CuO 4 and YBa 2 Cu 3 O 6 are both antiferromagnetic. We therefore consider the possibility of electron pairing in the itinerant antiferromagnetic state within the Hubbard model. The superconducting pairing obtained is similar to the formation of bipolarons in doped Peierls distorted insulators. Within the generalised Hartree-Fock approximation we derive a pair of gap equations corresponding to the superconducting and antiferromagnetic gaps. The existence of the superconducting gap depends essentially on the antiferromagnetic order which provides an effective interaction for electrons near to the Fermi surface. We study the model with a two-dimensional band structure appropriate to the layered structure of high- T c superconductors. We find that superconducting solutions are only possible when account is taken of the presence of more than one orbital in the unit cell. Furthermore these solutions are found only near half band filling.