Shubnikov-de Haas oscillations for two well-defined frequencies, corresponding, respectively, to areas of 0.8 and 1.36% of the first Brillouin zone, were observed in single crystals of Na 0:3 CoO 2 . The existence of Na superstructures in Na 0:3 CoO 2 , coupled with this observation, suggests the possibility that the periods are due to the reconstruction of the large Fermi surface around the ÿ point. An alternative interpretation in terms of the long sought-after " 0 g pockets is also considered but found to be incompatible with existing specific heat data. DOI: 10.1103/PhysRevLett.97.126401 PACS numbers: 71.18.+y, 71.30.+h, 72.15.Gd A number of theoretical treatments have suggested that the nature of the superconducting pairing mechanism in hydrated Na x CoO 2 is unconventional and that it probably corresponds to a spin-triplet state [1][2][3][4]. Nevertheless, the experimental situation remains unclear with heat capacity experiments in the superconducting state suggesting that the electronic contribution can either be described in terms of an order parameter having nodal lines [5], a hypothesis supported by muon spin resonance ( SR) experiments [6], or simply in terms of inhomogeneity in the Na content [7]. Measurements of the 59 Co nuclear magnetic resonance Knight shift supports either spin-triplet [8] or singlet pairing [9]. At the same time SR experiments [10] find no indication of static moments in the superconducting state, implying that time reversal symmetry is not broken.For conventional superconductivity, as well as for most unconventional superconductivity scenarios, the pairing mechanism and consequently the superconducting transition temperature critically depend on the electronic structure near the Fermi level. An accurate description of the Fermi surface (FS) is therefore critical for the superconductivity of the hydrated Na 0:3 CoO 2 whose FS size and precise shape still is a central but unsettled issue. Localdensity approximation (LDA) calculations [11] for the unhydrated NaCo 2 O 4 compound indicate that two-bands, the A 1g and one of the " 0 g bands, cross the Fermi level creating, respectively, a large hexagonal Fermi surface around the ÿ point of the Brillouin zone (BZ) and six small elliptical pockets of holes near the K point.This Fermi surface geometry is the starting point for several of the proposed theories of unconventionally mediated superconductivity [1], where the existence of small nearly perfectly elliptical hole pockets resulting from the " 0 g band is essential. [3,4] However, angle-resolved photoemission (ARPES) on Na x CoO 2 (for 0:3 x 0:72) reveals only a single FS centered around the ÿ point whose area changes with x according to the Luttinger theorem [12,13], while the " 0 g band and the associated FS pockets were found to sink below the Fermi energy independently of the doping level or temperature [13]. This discrepancy between ARPES and LDA calculations were claimed to result either from strong electronic correlations [14 -16] or Na disorder [17].For over half a c...