We report the observation of Shubnikov-de Haas oscillations in the underdoped cuprate superconductor YBa2Cu4O8 (Y124). For fields aligned along the c axis, the frequency of the oscillations is 660+/-30 T, which corresponds to approximately 2.4% of the total area of the first Brillouin zone. The effective mass of the quasiparticles on this orbit is measured to be 2.7+/-0.3 times the free electron mass. Both the frequency and mass are comparable to those recently observed for ortho-II YBa2Cu3O6.5 (Y123-II). We show that although small Fermi surface pockets may be expected from band-structure calculations in Y123-II, no such pockets are predicted for Y124. Our results therefore imply that these small pockets are a generic feature of the copper oxide plane in underdoped cuprates.

In doped SrTiO3 superconductivity persists down to an exceptionally low concentration of mobile electrons. This restricts the relevant energy window and possible pairing scenarios. We present a study of quantum oscillations and superconducting transition temperature, Tc as the carrier density is tuned from 10 17 to 10 20 cm −3 and identify two critical doping levels corresponding to the filling thresholds of the upper bands. At the first critical doping, which separates the single-band and the two-band superconducting regimes in oxygen-deficient samples, the steady increase of Tc with carrier concentration suddenly stops. Near this doping level, the energy dispersion in the lowest band displays a downward deviation from parabolic behavior. The results impose new constraints for microscopic pairing scenarios.Superconductiviy is induced in insulating SrTiO 3 by introducing n-type charge carriers through chemical doping[1] and survives over three orders of magnitude of carrier concentration. The transition temperature, T c , peaks to 0.45 K around a carrier density of n H ∼ 10 20 cm −3 [2]. A superconducting dome has also been detected in the metallic interfaces of SrTiO 3 [3] when the carrier density is modulated by a gate voltage bias [4]. In unconventional superconductors, such as high-T c cuprates, superconducting domes are often attributed to the proximity of a magnetic order or a Mott insulator. The recent discovery of superconducting dome in gate-tuned MoS 2 [5] in absence of a competing order, however, highlights the limits of our current understanding of the interplay between carrier concentration and superconductivity and motivates a fresh reexamination of superconducting domes. In the specific case of SrTiO 3 , superconductivity occurs in the vicinity of an aborted ferroelectric order[6] and survives deep inside the dilute metallic regime when the Fermi temperature becomes more than one order of magnitude lower than the Debye temperature [7]. This is a second puzzle in addition to the one raised by the drop in T c on the overdoped side. These two questions, raised at the opposite limits of the superconducting dome, remain unsettled.According to band calculations[9-11], doping SrTiO 3 with n-type carriers can fill three bands one after the other. Once the critical threshold for the occupation of a band is attained, a new Fermi surface concentric with the previous one emerges. Previous studies of quantum oscillations in bulk doped SrTiO 3 [7, 12-14] have detected both multiple-frequency [7,13,14] and singlefrequency [7,14] oscillations at different doping levels, but did not determine these critical doping levels. Moreover, according to tunneling experiments, doped SrTiO 3 beyond a carrier density of 10 19 cm −3 is a multi-gap superconductor [8]. The interplay between multi-band occupation in the normal state and multi-gap superconductivity has been a subject of recent theoretical attention [20].We present a systematic study of quantum oscillations and superconducting transition as a function of carrier con...