BCS theory of superconductivity as modified by Coulomb interaction in cuprates

In cuprate superconductors the intraband Coulomb interaction causes a hole to make transitions to other band states of various energies and momenta. The interband interaction causes an indirect interaction between such holes. The net result is that in the superconducting state there will be, on the average, hole pairs with various binding energies along with unbound holes. A modified BCS theory has been developed for such a system. Assuming a phenomenological form for the transition probabilities, the normal-to-superconducting tunneling conductance and the low-temperature specific heat have been calculated for ${\mathrm{La}}_{1.85}$ ${\mathrm{Sr}}_{0.15}$ ${\mathrm{CuO}}_4$ and ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$. The results are in qualitative agreement with measurements.