No abstract

No abstract

An outstanding problem in the field of high-transition-temperature (high-Tc) superconductivity is the identification of the normal state out of which superconductivity emerges in the mysterious underdoped regime. The normal state uncomplicated by thermal fluctuations can be studied using applied magnetic fields that are sufficiently strong to suppress long-range superconductivity at low temperatures. Proposals in which the normal ground state is characterized by small Fermi surface pockets that exist in the absence of symmetry breaking have been superseded by models based on the existence of a superlattice that breaks the translational symmetry of the underlying lattice. Recently, a charge superlattice model that positions a small electron-like Fermi pocket in the vicinity of the nodes (where the superconducting gap is minimum) has been proposed as a replacement for the prevalent superlattice models that position the Fermi pocket in the vicinity of the pseudogap at the antinodes (where the superconducting gap is maximum). Although some ingredients of symmetry breaking have been recently revealed by crystallographic studies, their relevance to the electronic structure remains unresolved. Here we report angle-resolved quantum oscillation measurements in the underdoped copper oxide YBa2Cu3O6 + x. These measurements reveal a normal ground state comprising electron-like Fermi surface pockets located in the vicinity of the nodes, and also point to an underlying superlattice structure of low frequency and long wavelength with features in common with the charge order identified recently by complementary spectroscopic techniques.

Peaks in the magnetoresistivity of the layered superconductor κ-(BEDT-TTF)2Cu(NCS)2, measured in fields ≤ 45 T applied within the layers, show that the Fermi surface is extended in the interlayer direction and enable the interlayer transfer integral (t ⊥ ≈ 0.04 meV) to be deduced. However, the quasiparticle scattering rate τ −1 is such thath/τ ∼ 6t ⊥ , implying that κ-(BEDT-TTF)2Cu(NCS)2 meets the criterion used to identify interlayer incoherence. The applicability of this criterion to anisotropic materials is thus shown to be questionable.PACS numbers: 74.70. Kn, 78.20.Ls, 71.20.Rv Many correlated-electron systems which are of fundamental interest have very anisotropic electronic bandstructure. Examples include the "high-T c " cuprates [1,2], layered ruthenates [3], and crystalline organic metals [2,4]. Such systems may be described by a tightbinding Hamiltonian in which the ratio of the interlayer transfer integral t ⊥ to the average intralayer transfer integral t || is ≪ 1 [2,4,5]. The inequalityh/τ > t ⊥ [6] where τ −1 is the quasiparticle scattering rate [1, 2, 5], frequently applies to such systems, suggesting that the quasiparticles scatter more frequently than they tunnel between layers. The question has thus arisen as to whether the interlayer charge transfer is coherent or incoherent, i.e. whether or not the Fermi surface (FS) extends in the interlayer direction [2,4,5]. In this paper we have used magnetoresistance data to estimate the interlayer transfer integral in the highly anisotropic organic superconductor κ-(BEDT-TTF) 2 Cu(NCS) 2 . We find that the material obeys the inequalityh/τ > t ⊥ ; moreover, mean-free path in the interlayer direction is < ∼ 20% of the unit-cell height. Nevertheless, our data demonstrate a FS which is extended in the interlayer direction.κ-(BEDT-TTF) 2 Cu(NCS) 2 was selected for our experiments because it is perhaps the most thoroughly characterised quasi-two-dimensional (Q2D) conductor [4]. In contrast to the cuprates, the FS topology is well known from Shubnikov-de Haas (SdH) and de Haas-van Alphen (dHvA) studies [4] and from angle-dependent magnetoresistance oscillation (AMRO) [8] and millimetre-wave (MMW) experiments [9]; it consists of a pair of quasione-dimensional (Q1D) electron sheets plus a Q2D hole pocket (see Fig. 1a [10, 11]). The κ-phase BEDT-TTF salts are considered to be leading contenders for interlayer incoherence [5], and optical data may be interpreted as consistent with this suggestion [12]. Moreover, models for unconventional superconductivity in κ-phase BEDT-TTF salts invoke the nesting properties of the FS [11,13,14]; the degree of nesting might depend on whether the FS is a 2D or 3D entity (see [4], Section 3.5). Experimental tests for coherence in κ-(BEDT-TTF) 2 Cu(NCS) 2 are thus far deemed to be inconclusive [5]; e.g. semiclassical models can reproduce AMRO [8] and MMW data [9] equally well when the interlayer transport is coherent or "weakly coherent" [5].To examine how interlayer coherence might be detected, we use a tight-binding dispersio...

We report quantum oscillations in the underdoped high-temperature superconductor YBa 2 Cu 3 O 6+x over a wide range in magnetic field 28Յ 0 H Յ 85 T corresponding to Ϸ12 oscillations, enabling the Fermi surface topology to be mapped to high resolution. As earlier reported by Sebastian et al. ͓Nature ͑London͒ 454, 200 ͑2008͔͒, we find a Fermi surface comprising multiple pockets, as revealed by the additional distinct quantum oscillation frequencies and harmonics reported in this work. We find the originally reported broad lowfrequency Fourier peak at Ϸ535 T to be clearly resolved into three separate peaks at Ϸ460, Ϸ532, and Ϸ602 T, in reasonable agreement with the reported frequencies of Audouard et al. ͓Phys. Rev. Lett. 103, 157003 ͑2009͔͒. However, our increased resolution and angle-resolved measurements identify these frequencies to originate from two similarly sized pockets with greatly contrasting degrees of interlayer corrugation. The spectrally dominant frequency originates from a pocket ͑denoted ␣͒ that is almost ideally two-dimensional in form ͑exhibiting negligible interlayer corrugation͒. In contrast, the newly resolved weaker adjacent spectral features originate from a deeply corrugated pocket ͑denoted ␥͒. On comparison with band structure, the d-wave symmetry of the interlayer dispersion locates the minimally corrugated ␣ pocket at the "nodal" point k nodal = ͑ / 2, / 2͒, and the significantly corrugated ␥ pocket at the "antinodal" point k antinodal = ͑ ,0͒ within the Brillouin zone. The differently corrugated pockets at different locations indicate creation by translational symmetry breaking-a spin-density wave has been suggested from the suppression of Zeeman splitting for the spectrally dominant pocket. In a broken-translational symmetry scenario, symmetry points to the nodal ͑␣͒ pocket corresponding to holes, with the weaker antinodal ͑␥͒ pocket corresponding to electrons-likely responsible for the negative Hall coefficient reported by LeBoeuf et al. ͓Nature ͑London͒ 450, 533 ͑2007͔͒. Given the similarity in ␣ and ␥ pocket volumes, their opposite carrier type and the previous report of a diverging effective mass in Sebastian et al. ͓Proc. Nat. Am. Soc. 107, 6175 ͑2010͔͒, we discuss the possibility of a secondary Fermi surface instability at low dopings of the excitonic insulator type, associated with the metal-insulator quantum critical point. Its potential involvement in the enhancement of superconducting transition temperatures is also discussed.