Quantum oscillations in underdoped YBa$_{2}$Cu$_{3}$O$_{6}$$_{.}$$_{5}$ Cyril Jaudet, 1 Julien Levallois, 1 Alain Audouard, 1 David Vignolles, 1 Baptiste Vignolle, 1 Ruixing Liang, 2, 3 D.A. Bonn, 2, 3 W.N. Hardy, 2, 3 N.E. Hussey, 4 Louis Taillefer, 3, 5 and Cyril Proust 1, 3,$_{∗}$ $^{1}$Laboratoire National des Champs Magn´ etiques Intenses (CNRS), Toulouse, France $^{2}$Department of Physics and Astronomy, University of British Columbia, Vancouver, Canada $^{3}$Canadian Institute for Advanced Research, Toronto, Canada $^{4}$H. H. Wills Physics Laboratory, University of Bristol, Bristol, U.K. $^{5}$D´ epartement de physique & RQMP, Universit´ e de Sherbrooke, Sherbrooke, Canada Shubnikov-de Haas and de Haas-van Alphen effects have been measured in the underdoped high temperature superconductor YBa 2 Cu 3 O 6 . 51 . Data are in agreement with the standard Lifshitz- Kosevitch theory, which confirms the presence of a coherent Fermi surface in the ground state of underdoped cuprates. A low frequency F = 530 ± 10 T is reported in both measurements, pointing to small Fermi pocket, which corresponds to 2% of the first Brillouin zone area only. This low value is in sharp contrast with that of overdoped Tl 2 Ba 2 CuO 6+ δ , where a high frequency F = 18 kT has been recently reported and corresponds to a large hole cylinder in agreement with band structure calculations. These results point to a radical change in the topology of the Fermi surface on opposing sides of the cuprate phase diagram. PACS numbers: 74.25.Jb, 74.25.Bt, 74.25.Ha, 74.72.Bk [9]. We used two detwinned single crystals of YBa$_{2}$Cu$_{3}$O$_{6}$$_{.}$$_{51}$ flux-grown in a non-reactive BaZrO$_{3}$ crucible [12]. The dopant oxygen atoms are ordered into an ortho-II superstructure of alternating full and empty CuO chains which corresponds to a superconducting temperature of T$_{c}$ = 57 . 5 K and therefore a doping of about p ∼ 0 . 1[13]. Fig. 1(a) shows raw data of torque (defined as τ = | − → M × − → B | where M is the magnetization) in one sample of YBa$_{2}$Cu$_{3}$O$_{6}$$_{.}$$_{51}$ at different temperatures. The torque signal displays clear dHvA oscillations in high magnetic fields. Above 30 T, the torque varies almost linearly with magnetic field which allow us to subtract a monotonic background from the data in order to derive the oscilla- tory part. Eight oscillations can be resolved at T = 0 . 5 K. Fig. 1(b) and Fig. 1(c) show raw data of the Hall re- sistance and of the transverse magnetoresistance, respec- tively, in another sample of YBa$_{2}$Cu$_{3}$O$_{6}$$_{.}$$_{51}$ at different temperatures. Oscillatory parts of R$_{xy}$ and R$_{xx}$ are ob- tained after substraction of a polynomial background. The oscillatory part of the resistance (Δ R ) and of the magnetization (Δ M ) are analyzed in the framework of the standard Lifshitz-Kosevich (LK) theory for a two- dimensional generalized Fermi liquid [14]: where F is the oscillation frequency and γ a phase fac- tor. The amplitude is given by A ∝ R$_{T}$R$_{D}$ , where R$_{T}$ = αTm ∗ /B sinh[ αTm ∗ /B ] and R$_{D}$ =exp[ − αT$_{D}$m ∗ /B ] are the thermal and Dingle damping factors, respectively. m ∗ is the cyclotron effective mass, T$_{D}$ is the Dingle tem- Transverse magnetoresistance ( R$_{xx}$ ) and Hall resis- tance ( R$_{xy}$ ) were measured down to 1 . 5 K in pulsed mag- netic fields up to 60 T. Current and field were applied along the a axis and normal to the CuO$_{2}$ planes, respec- tively. A commercial piezoresistive microcantilever [11] was used for torque measurements in a dilution fridge down to 0 . 5 K in pulsed magnetic fields up to 59 T. The crystal was glued to the beam of the cantilever with an angle of approximately θ ∼ 5 o between the direction of the magnetic field and the normal to the CuO$_{2}$ planes In this paper we report a set of new data of Shubnikov- de Haas (SdH) in an underdoped cuprate YBa$_{2}$Cu$_{3}$O$_{6}$$_{.}$$_{51}$ obtained both in the in-plane and Hall resistances. We compare the results with measurements of the dHvA at the same doping level published in ref. [9]. The first unambiguous observation of quantum oscil- lations (QO) in underdoped YBa$_{2}$Cu$_{3}$O$_{6}$$_{.}$$_{5}$ [1] has cre- ated a lot of interest concerning the exact nature and the origin of the Fermi surface (FS) in the pseudogap phase of cuprates. If QO are interpreted as the usual consequence of the quantization of closed orbits in a mag- netic field, they show that the FS consists of small pock- ets. It contrasts with angle-resolved photoemission spec- troscopy (ARPES) which shows an apparent destruction of the FS producing a set of disconnected Fermi arcs [2]. The apparent contradiction between the two sets of mea- surements is not yet resolved [3–5]. Shubnikov-de Haas effect has been confirmed in the stoichiometric compound YBa$_{2}$Cu$_{4}$O$_{8}$ [6, 7], indicating that QO are generic to the CuO$_{2}$ planes rather than some feature of the band struc- ture specific to YBa$_{2}$Cu$_{3}$O$_{6}$$_{.}$$_{5}$ [6, 8]. More recently, de Haas-van Alphen effect (dHvA) has been reported in un- derdoped YBa$_{2}$Cu$_{3}$O$_{6}$$_{.}$$_{5}$ [9, 10], which confirmed the ex- istence of a well-defined, closed, and coherent, FS via a thermodynamic probe. Δ R, Δ M ∝ R$_{T}$R$_{D}$cos [ 2 π ( F B − γ ) ] (1) arXiv:1001.1508v1 [cond-mat.supr-con] 10 Jan 2010