  LiFeAs is unique among the arsenic based Fe-pnictide superconductors because
it is the only nearly stoichiometric compound which does not exhibit magnetic
order. This is at odds with electronic structure calculations which and a very
stable magnetic state and predict cylindrical hole- and electron-like Fermi
surface sheets whose geometry suggests spin uctuations and a possible
instability toward long-range ordering at the nesting vector. In fact, a
complex magnetic phase-diagram is indeed observed in the isostructural NaFeAs
compound. Previous angle resolved photoemission (ARPES) experiments revealed
the existence of both hole and electron-like surfaces, but with rather distinct
cross-sectional areas and an absence of the nesting that is thought to underpin
both magnetic order and superconductivity in the pnictide family of
superconductors. These ARPES observations were challenged by subsequent de Haas
van Alphen (dHvA) measurements which detected a few, electron like Fermi
surface sheets in rough agreement with the original band calculations. Here, we
show a detailed dHvA study unveiling additional, small and nearly isotropic
Fermi surface sheets in LiFeAs single crystals, which ought to correspond to
hole-like orbits, as previously observed by ARPES. Therefore, our results
conciliate the apparent discrepancy between ARPES and the previous dHvA
results5. The small size of these Fermi surface pockets suggests a prominent
role for the electronic correlations in LiFeAs. The absence of gap nodes, in
combination with the coexistence of quasi-two-dimensional and three-dimensional
Fermi surfaces, favor a s-wave pairing symmetry for LiFeAs. But similar
electron-like Fermi surfaces combined with very different hole pockets between
LiFeAs and LiFeP, suggest that the nodes in the gap function of LiFeP might be
located on the hole-pockets.
