  We examine the Fermi-surface effect called the nesting effect for the FFLO
state in strongly Pauli-limited Q2D superconductors, focusing on the effect of
3D factors, such as interlayer electron transfer, interlayer pairing, and
off-plane magnetic fields including those perpendicular to the most conductive
layers. We examine the systems with a large Maki parameter so that the orbital
pair-breaking effect is negligible, except for the locking of the direction of
the FFLO vector q in the field direction.It is known that the nesting effect
for the FFLO state can be strong in QLD systems in which the orbital
pair-breaking effect is suppressed by applying the mag. field parallel to the
layers. Hence, it has sometimes been suggested that the nesting effect may
hardly enhance the stability of the FFLO state for perpendicular fields. We
illustrate that, contrary to this view, the nesting effect can strongly
stabilize the FFLO state for perpendicular fields as well as for parallel
fields when tz is small so that the Fermi surfaces are open in the
kz-direction, where tz denotes the interlayer transfer energy. In particular,
the nesting effect in perpendicular fields can be strong in interlayer states.
For example, in systems with cylindrical Fermi surfaces warped by tz /= 0,
interlayer states with Dlt_k prop sin k_z exhibit mu_e Hc=1.65 Dlt_a0 for
perpendicular fields, which is much larger than typical values for parallel
fields, such as mu_e Hc=Dlt_s0 of the s-wave state and mu_e Hc = 1.28 Delta_d0
of the d-wave state in cylindrical systems with tz=0. The present result could
potentially provide a physical reason why the areas in the phase diagrams
occupied by the high-field phases for the perpendicular and parallel fields are
of the same order in CeCoIn5 and FeSe.
