The electrical resistance of two samples of ortho-II ordered YBa 2 Cu 3 O 6.5 was measured in a magnetic field up to 62 T applied normal to the CuO 2 planes (B || c).(Sample characteristics and details of the measurements are given in the Methods section below.) With a T c of 57.5 K, these samples have a hole doping per planar copper atom of p = 0.10, i.e., they are well into the underdoped region of the phase diagram (see Fig. 1a). ARPES data for underdoped Na 2-x Ca x Cu 2 O 2 Cl 2 (Na-CCOC) at precisely the same doping (reproduced in Fig. 1b from ref. 6) shows most of the spectral intensity to be concentrated in a small region near the nodal position (π/2, π/2), suggesting a Fermi surface broken up into disconnected arcs, while ARPES studies on overdoped Tl 2 Ba 2 CuO 6+δ at p = 0.25 reveal a large, continuous cylinder (reproduced in The Hall resistance R xy as a function of magnetic field is displayed in Fig. 2 for sample A, and in Fig. S1 for sample B, where oscillations are clearly seen above the resistive superconducting transition. Note that a vortex liquid phase is believed to extend well above the irreversibility field, beyond our highest field of 62 T, which may explain why R xy is negative at these low temperatures, as opposed to positive at temperatures above T c . Nevertheless, quantum oscillations are known to exhibit the very same diagnostic characteristics of frequency in the vortex state as in the field-induced normal state above H c2 (0) (e.g. ref. 7). They are caused by the passage of quantized Landau levels across the Fermi level as the applied magnetic field is varied, and as such 3 they are considered the most robust and direct signature of a coherent Fermi surface (FS). The inset of Fig. 2 shows the 2-K isotherm and a smooth background curve. We extract the oscillatory component, plotted in Fig. 3a as a function of inverse field, by subtracting the monotonic background (shown for all temperatures in Fig. S2). This shows that the oscillations are periodic in 1/B, as expected of oscillations that arise from Landau quantization. A Fourier transform yields the power spectrum, displayed in Fig. 3b, which consists of a single frequency, F = 530 ± 10 T. In Fig. 3c, we plot the amplitude of the oscillations as a function of temperature, from which we deduce a carrier mass m* = 1.9 ± 0.1 m 0 , where m 0 is the bare electron mass. Within error bars, both F and m* are the same in sample B, for which J || b (see Fig. S1). Oscillations of the same frequency are also observed in R xx (in both samples), albeit with a smaller amplitude. We note that while at 7.5 K the oscillations are still perceptible, they are absent at 11 K, as expected from thermally damped quantum oscillations (see Fig. S5).While quantum oscillations in YBa 2 Cu 3 O 6+y (YBCO) have been the subject of a number of earlier studies 8 , 9 , 10 , the data reported so far do not exhibit clear oscillations as a function of 1/B and, as such, have not been accepted as convincing evidence for a Fermi surface 11 . Furthermore, we note that a...

High-temperature superconductivity in copper oxides occurs when the materials are chemically tuned to have a carrier concentration intermediate between their metallic state at high doping and their insulating state at zero doping. The underlying evolution of the electron system in the absence of superconductivity is still unclear, and a question of central importance is whether it involves any intermediate phase with broken symmetry. The Fermi surface of the electronic states in the underdoped 'YBCO' materials YBa2Cu3O(y) and YBa2Cu4O8 was recently shown to include small pockets, in contrast with the large cylinder that characterizes the overdoped regime, pointing to a topological change in the Fermi surface. Here we report the observation of a negative Hall resistance in the magnetic-field-induced normal state of YBa2Cu3O(y) and YBa2Cu4O8, which reveals that these pockets are electron-like rather than hole-like. We propose that these electron pockets most probably arise from a reconstruction of the Fermi surface caused by the onset of a density-wave phase, as is thought to occur in the electron-doped copper oxides near the onset of antiferromagnetic order. Comparison with materials of the La2CuO4 family that exhibit spin/charge density-wave order suggests that a Fermi surface reconstruction also occurs in those materials, pointing to a generic property of high-transition-temperature (T(c)) superconductors.

The effect of sample size and surface roughness on the phonon thermal conductivity κp of Nd2CuO4 single crystals was studied down to 50 mK. At 0.5 K, κp is proportional to √ A, where A is the cross-sectional area of the sample. This demonstrates that κp is dominated by boundary scattering below 0.5 K or so. However, the expected T 3 dependence of κp is not observed down to 50 mK. Upon roughing the surfaces, the T 3 dependence is restored, showing that departures from T 3 are due to specular reflection of phonons off the mirror-like sample surfaces. We propose an empirical power law fit, to κp ∼ T α (where α < 3) in cuprate single crystals. Using this method, we show that recent thermal conductivity studies of Zn doping in YBa2Cu3Oy re-affirm the universal heat conductivity of d-wave quasiparticles at T → 0. To understand the pairing mechanism in a superconductor, it is essential to know the symmetry of the order parameter. In this context, measurements of lowtemperature thermal conductivity κ, which probes the low-energy quasiparticle excitations, has emerged as a powerful probe of the order parameter in superconductors. For conventional s-wave superconductors with a fully gapped excitation spectrum, the linear-temperature electronic contribution to thermal conductivity is zero at T → 0, i.e. the residual linear term κ 0 /T = 0. This can be seen in the single-gap s-wave superconductor Nb,

Phys. Rev. B 77, 134501 ͑2008͔͒, Sun and Ando estimate that the phonon mean free path at low temperature is roughly half the width of the single crystal used in our study, from which they argue that phonon scattering cannot be dominated by sample boundaries. Here we show that their use of specific-heat data on Nd 2 CuO 4 , which contains a large magnetic contribution at low temperature that is difficult to reliably extract, leads to an underestimate of the mean free path by a factor 2 compared to an estimate based on the specific-heat data of the nonmagnetic isostructural analog Pr 2 CuO 4 . This removes the apparent contradiction raised by Sun and Ando.