Slave-boson mean-field theory for the negative-U Hubbard model

We study the negative-U Hubbard model for arbitrary values of the attractive interaction U and band filling by means of the slave-boson mean-field theory. We analyze both the normal and the superconducting states. We show that for the superconducting state our approach gives results similar to those obtained in the usual BCS mean field; only small renormalization of the bare parameters are obtained for U of the order of the bandwidth W. The energy difference between the normal and the superconducting states is maximum for UW. This energy difference is a measure of the superconducting critical temperature, which increases exponentially for small U and decreases as 1/U for large U. We discuss briefly the pair-breaking excitations.