  We study conductance spectroscopy of a two-dimensional junction between a
normal metal and a strongly-correlated superconductor in an applied magnetic
field in the Pauli limit. Depending on the field strength the superconductor is
either in the Bardeen-Cooper-Schrieffer (BCS), or in the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of the Fulde-Ferrell (FF) type.
The strong correlations are accounted for by means of the Gutzwiller method
what leads naturally to the emergence of the spin-dependent masses (SDM) of
quasiparticles when the system is spin-polarized. The case without strong
correlations (with the spin-independent masses, SIM) is analyzed for
comparison. We consider both the s-wave and the d-wave symmetries of the
superconducting gap and concentrate on the parallel orientation of the Cooper
pair momentum Q with respect to the junction interface. The junction
conductance is presented for selected barrier strengths (i.e., in the contact,
intermediate, and tunneling limits). The conductance spectra in the cases with
and without strong correlations differ essentially. Our analysis provides thus
an experimentally accessible test for the presence of strong-correlations in
the superconducting state. Namely, correlations alter the distance between the
conductance peaks (or related conductance features) for carriers with spin-up
and spin-down. In the uncorrelated case, this distance is twice the Zeeman
energy. In the correlated case, the corresponding distance is about 30-50%
smaller, but other models may provide even stronger difference, depending on
details of the system electronic structure. It turns out that the strong
correlations manifest themselves most clearly in the case of the junction with
the BCS, rather than the FFLO superconductor, what should make the experimental
verification of the present results simpler.
