Superconductivity with On- and Inter-Site Attractions in a Two-Dimensional Square Lattice

Abstract

We investigate superconductivity in a two-dimensional square lattice characterized by both an on-site attractive interaction (- V 1 ) of the BCS type and an inter-site attractive interaction (- V 2 ). We evaluate the phase diagram in the ( V 1 , V 2 , T ) space, which shows that there appear three kinds of superconducting states, i.e. a pure s -state, a pure d -state and a mixed state, depending on the values of V 1 , V 2 and T . For some appropriate values of V 1 and V 2 , two types of transitions take place on the reduction of temperature; from a normal state to a pure state and then from a pure state to a mixed state. We calculate several physical quantities in order to study their behaviors at these transition points. Implication of the present theory is discussed in relation with high- T c superconductivity.