  We study properties of normal, superconducting (SC) and CDW states for an
attractive Hubbard model on the square lattice, using a variational Monte Carlo
method. In trial wave functions, we introduce an interspinon binding factor,
indispensable to induce a spin-gap transition in the normal state, in addition
to the onsite attractive and intersite repulsive factors. It is found that, in
the normal state, as the interaction strength $|U|/t$ increases, a first-order
spin-gap transition arises at $|U_{\rm c}|\sim W$ ($W$: band width) from a
Fermi liquid to a spin-gapped state, which is conductive through hopping of
doublons. In the SC state, we confirm by analysis of various quantities that
the mechanism of superconductivity undergoes a smooth crossover at around
$|U_{\ma{co}}|\sim |U_{\rm c}|$ from a BCS type to a Bose-Einstein condensation
(BEC) type, as $|U|/t$ increases. For $|U|<|U_{\ma{co}}|$, quantities such as
the condensation energy, a SC correlation function and the condensate fraction
of onsite pairs exhibit behavior of $\sim \exp(-t/|U|)$, as expected from the
BCS theory. For $|U|>|U_{\ma{co}}|$, quantities such as the energy gain in the
SC transition and superfluid stiffness, which is related to the cost of phase
coherence, behave as $\sim t^2/|U|\propto T_{\rm c}$, as expected in a bosonic
scheme. In this regime, the SC transition is induced by a gain in kinetic
energy, in contrast with the BCS theory. We refer to the relevance to the
pseudogap in cuprate superconductors.

Strongly Correlated Electrons