Theoretical Study of Hole-Pair System in a Periodical Lattice

Abstract

We investigate the statistics of the coupled hole pairs in a crystal lattice in high Tc superconductors, following the previously developed approach for the collective charge state (holon). The exact commutation relations for the hole pair operators correspond to a modified parafermi statistics of rank M′ (M′ is the number of sites in a “superlattice” formed by centers of mass for each hole pair), i.e. one state can be occupied by up to M′ pairs. Even in the absence of dynamic interaction, the system of hole pairs is characterized by some immanent interaction (kinematic interaction), which depends on the hole-pairs concentration. In spite of the kinematic interaction, there is no statistical prohibition on the Bose-Einstein condensation of coupled hole pairs.