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 presence or absence of a quantum critical point and its location in the phase diagram of high-temperature superconductors have been subjects of intense scrutiny. Clear evidence for quantum criticality, particularly in the transport properties, has proved elusive because the important low-temperature region is masked by the onset of superconductivity. We present measurements of the low-temperature in-plane resistivity of several highly doped La2-xSrxCuO4 single crystals in which the superconductivity had been stripped away by using high magnetic fields. In contrast to other quantum critical systems, the resistivity varies linearly with temperature over a wide doping range with a gradient that scales monotonically with the superconducting transition temperature. It is maximal at a critical doping level (pc) approximately 0.19 at which superconductivity is most robust. Moreover, its value at pc corresponds to the onset of quasi-particle incoherence along specific momentum directions, implying that the interaction that first promotes high-temperature superconductivity may ultimately destroy the very quasi-particle states involved in the superconducting pairing.

The absence of resistivity saturation in many strongly correlated metals, including the hightemperature superconductors, is critically examined from the viewpoint of optical conductivity measurements. Coherent quasiparticle conductivity, in the form of a Drude peak centred at zero frequency, is found to disappear as the mean free path (at ω = 0) becomes comparable to the interatomic spacing. This basic loss of coherence at the so-called Mott-Ioffe-Regel (MIR) limit suggests that the universality of the MIR criterion is preserved even in the presence of strong electron correlations. We argue that the shedding of spectral weight at low frequencies, induced by strong correlation effects, is the primary origin of the extended positive slope of the resistivity to high temperatures observed in all so-called 'bad metals'.Moreover, in common with those metals which exhibit resistivity saturation at high temperatures, the scattering rate itself, as extracted from optical spectra, saturates at a value consistent with the MIR limit. We consider possible implications that this ceiling in the scattering rate may have for our understanding of transport within a wide variety of bad metals and suggest a better method for analysing their optical response.

Neutron scattering is used to characterize the magnetism of the vortices for the optimally doped high-temperature superconductor La(2-x)Sr(x)CuO4 (x = 0.163) in an applied magnetic field. As temperature is reduced, low-frequency spin fluctuations first disappear with the loss of vortex mobility, but then reappear. We find that the vortex state can be regarded as an inhomogeneous mixture of a superconducting spin fluid and a material containing a nearly ordered antiferromagnet. These experiments show that as for many other properties of cuprate superconductors, the important underlying microscopic forces are magnetic.

All conventional metals are known to possess a three-dimensional Fermi surface, which is the locus in reciprocal space of the long-lived electronic excitations that govern their electronic properties at low temperatures. These excitations should have well-defined momenta with components in all three dimensions. The high-transition-temperature (high-T(c)) copper oxide superconductors have unusual, highly two-dimensional properties above the superconducting transition. This, coupled with a lack of unambiguous evidence for a three-dimensional Fermi surface, has led to many new and exotic models for the underlying electronic ground state. Here we report the observation of polar angular magnetoresistance oscillations in the overdoped superconductor Tl2Ba2CuO6+delta in high magnetic fields, which firmly establishes the existence of a coherent three-dimensional Fermi surface. Analysis of the oscillations reveals that at certain symmetry points, however, this surface is strictly two-dimensional. This striking form of the Fermi surface topography, long-predicted by electronic band structure calculations, provides a natural explanation for a wide range of anisotropic properties both in the normal and superconducting states. Our data reveal that, despite their extreme electrical anisotropy, the high-T(c) materials at high doping levels can be understood within a framework of conventional three-dimensional metal physics.

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In the quest to increase the critical temperature T c of cuprate superconductors, it is essential to identify the factors that limit the strength of superconductivity. The upper critical field H c2 is a fundamental measure of that strength, yet there is no agreement on its magnitude and doping dependence in cuprate superconductors. Here we show that the thermal conductivity can be used to directly detect H c2 in the cuprates YBa 2 Cu 3 O y , YBa 2 Cu 4 O 8 and Tl 2 Ba 2 CuO 6 þ d , allowing us to map out H c2 across the doping phase diagram. It exhibits two peaks, each located at a critical point where the Fermi surface of YBa 2 Cu 3 O y is known to undergo a transformation. Below the higher critical point, the condensation energy, obtained directly from H c2 , suffers a sudden 20-fold collapse. This reveals that phase competitionassociated with Fermi-surface reconstruction and charge-density-wave order-is a key limiting factor in the superconductivity of cuprates.

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.