  Motivated by the accumulating hints of new sterile neutrino species at the eV
scale, we explore the consequences of such an hypothesis on the solar sector
phenomenology. After introducing the theoretical formalism needed to describe
the MSW conversion of solar neutrinos in the presence of one (or more) sterile
neutrino state(s) located "far" from the (nu_1,nu_2) "doublet", we perform a
quantitative analysis of the available experimental results, focusing on the
electron neutrino mixing. We find that the present data posses a sensitivity to
the amplitude of the lepton mixing matrix element U_e4 --- encoding the
admixture of the electron neutrino with a new mass eigenstate --- which is
comparable to that achieved on the standard matrix element U_e3. In addition,
and more importantly, our analysis evidences that, in a 4-flavor framework, the
current preference for |U_e3|>0 is indistinguishable from that for |U_e4|>0,
having both a similar statistical significance (which is ~ 1.3 sigma adopting
the old reactor fluxes determinations, and ~ 1.8 sigma using their new
estimates). We also point out that, differently from the standard 3-flavor
case, in a 3+1 scheme the Dirac CP-violating phases cannot be eliminated from
the description of solar neutrino conversions.
