The concept that superconductivity competes with other orders in cuprate superconductors has become increasingly apparent, but obtaining direct evidence with bulk-sensitive probes is challenging. We have used resonant soft x-ray scattering to identify two-dimensional charge fluctuations with an incommensurate periodicity of similar to 3.2 lattice units in the copper-oxide planes of the superconductors (Y,Nd)Ba2Cu3O6+x, with hole concentrations of 0.09 to 0.13 per planar Cu ion. The intensity and correlation length of the fluctuation signal increase strongly upon cooling down to the superconducting transition temperature (T-c); further cooling below T-c abruptly reverses the divergence of the charge correlations. In combination with earlier observations of a large gap in the spin excitation spectrum, these data indicate an incipient charge density wave instability that competes with superconductivity

The resistivity of the heavy-fermion superconductor CeCoIn5 was measured as a function of temperature, down to 25 mK and in magnetic fields of up to 16 T applied perpendicular to the basal plane. With increasing field, we observe a suppression of the non-Fermi liquid behavior, rho approximately T, and the development of a Fermi liquid state, with its characteristic rho=rho(0)+AT2 dependence. The field dependence of the T2 coefficient shows critical behavior with an exponent of 1.37. This is evidence for a field-induced quantum critical point (QCP), occurring at a critical field which coincides, within experimental accuracy, with the superconducting critical field H(c2). We discuss the relation of this field-tuned QCP to a change in the magnetic state, seen as a change in magnetoresistance from positive to negative, at a crossover line that has a common border with the superconducting region below approximately 1 K.

Recently, charge density wave (CDW) order in the CuO(2) planes of underdoped YBa(2)Cu(3)O(6+δ) was detected using resonant soft x-ray scattering. An important question remains: is the chain layer responsible for this charge ordering? Here, we explore the energy and polarization dependence of the resonant scattering intensity in a detwinned sample of YBa(2)Cu(3)O(6.75) with ortho-III oxygen ordering in the chain layer. We show that the ortho-III CDW order in the chains is distinct from the CDW order in the planes. The ortho-III structure gives rise to a commensurate superlattice reflection at Q=[0.33 0 L] whose energy and polarization dependence agrees with expectations for oxygen ordering and a spatial modulation of the Cu valence in the chains. Incommensurate peaks at [0.30 0 L] and [0 0.30 L] from the CDW order in the planes are shown to be distinct in Q as well as their temperature, energy, and polarization dependence, and are thus unrelated to the structure of the chain layer. Moreover, the energy dependence of the CDW order in the planes is shown to result from a spatial modulation of energies of the Cu 2p to 3d(x(2)-y(2)) transition, similar to stripe-ordered 214 cuprates.

Charge-ordered ground states permeate the phenomenology of 3d-based transition metal oxides, and more generally represent a distinctive hallmark of stronglycorrelated states of matter. The recent discovery of charge order in various cuprate families fueled new interest into the role played by this incipient broken symmetry within the complex phase diagram of high-T c superconductors.Here we use resonant X-ray scattering to resolve the main characteristics of the charge-modulated state in two cuprate families: Bi 2 Sr 2−x La x CuO 6+δ (Bi2201) and YBa 2 Cu 3 O 6+y (YBCO). We detect no signatures of spatial modulations along the nodal direction in Bi2201, thus clarifying the inter-unit-cell momentum-structure of charge order. We also resolve the intra-unit-cell symmetry of the charge ordered state, which is revealed to be best represented by a bond-order with modulated charges on the O-2p orbitals and a prominent d-wave character. These results provide insights on the microscopic description of charge order in cuprates, and on its origin and interplay with superconductivity.Complex oxides exhibit a mosaic of exotic electronic phases with various symmetry-broken ground states that revolve around three main instabilities: antiferromagnetism, charge order, and superconductivity. In particular, charge order -the tendency of the valence electrons to segregate into periodically-modulated structures -is found in various classes of strongly-correlated 3d-oxides, such as manganites [1], nickelates [2], and cobaltates [3]. The original discovery of period-4 stripe-like charge correlations in the La-based materials [4][5][6][7] confirmed the central role played by chargeordered states in the physics of underdoped cuprates, as anticipated by earlier theoretical work [8][9][10][11][12]. Following further indications by surface-sensitive scanning tunnelling microscopy (STM) [13, 14], the field was recently revived by the detection of charge-modulated states in YBCO using nuclear magnetic resonance [15] and resonant X-ray scattering (RXS), with wavevector Q * ∼ 0.31 reciprocal lattice units (r.l.u., used hereafter) [16][17][18][19][20][21]. Even more recently, this phenomenology was confirmed in Bi-based materials (with Q * ∼ 0.26 and 0.3 in single-and double-layer compounds, respectively), following observations in both bulk/momentum space (with RXS) FIG. 1:Charge ordering patterns and wavevectors. a, Schematics of a RXS experiment. b, Low-temperature RXS (at photon energy hν = 931.5 eV) from an underdoped Bi2201-UD15K sample, mapping reciprocal-space features along the two high-symmetry directions: (H, 0), antinodal, green (reproduced from Ref. 22, the full line represents a Gaussian fit plus background); and (H, H), nodal, orange. c,e, Modulation of the charge density ∆ρ(x, y), with functional form given by a sum (c) and product (e) of cosines, and a wavevector magnitude Q * = 0.265 r.l.u. (black bars indicate the period and direction of the spatial modulation, expressed in terms of the lattice parameter a = 3.86Å). The blu...

We derive diffusion equations, which describe spin-charge coupled transport on the helical metal surface of a three-dimensional topological insulator. The main feature of these equations is a large magnitude of the spin-charge coupling, which leads to interesting and observable effects. In particular, we predict a new magnetoresistance effect, which manifests in a nonohmic correction to a voltage drop between a ferromagnetic spin-polarized electrode and a nonmagnetic electrode, placed on top of the helical metal. This correction is proportional to the cross-product of the spin polarization of the ferromagnetic electrode and the charge current between the two electrodes. We also demonstrate tunability of this effect by applying a gate voltage, which makes it possible to operate the proposed device as a transistor.Time-reversal invariant topological insulator (TI) is a new state of matter, distinguished from a regular band insulator by a nontrivial topological invariant, which characterizes its bandstructure [1]. Its theoretical [2] and experimental [3] discovery has accordingly generated a great deal of excitement in the condensed matter physics community. The most robust observable consequence of a nontrivial topological character of these materials is the presence of gapless helical edge states, whose gaplessness is protected by time-reversal symmetry and is thus robust to perturbations that do not break this symmetry. In particular, the surface of a three-dimensional (3D) TI, such as Bi 2 Se 3 or Bi 2 Te 3 [4], is a 2D metal, whose bandstructure consists of an odd number of Dirac cones, centered at time-reversal invariant momenta in the surface Brillouin zone [2]. Assuming the Fermi surface encloses only one Dirac point, the low-energy Hamiltonian, describing such a 2D metal, is given by:whereẑ is along the normal to the surface, v F is the Fermi velocity, τ is the vector of Pauli matrices, summation over repeated spin indices is implicit, and we useh = 1 units henceforth. The eigenstates of this Hamiltonian are labeled by helicity, i.e. projection of the spin of the electron on the direction of its momentum, hence the name helical metal (HM). The most obvious physical property of a HM is a strong coupling between the spin and orbital degrees of freedom, the energy scale characterizing this coupling being the Fermi energy ǫ F . Spin-orbit (SO) coupling of such a magnitude is unprecedented among known materials and it is thus extremely interesting to work out its possible observable consequences. Some work on this subject has already appeared in the literature [5,6]. In this Letter we will focus on spin and charge transport phenomena in a 2D HM. In this setting, it is useful to note that the Hamiltonian of a HM Eq.(1) is very similar to the Rashba Hamiltonian [7], which has been studied extensively in the context of spin transport in semiconductor-based two-dimensional electron gas (2DEG) systems [8][9][10]. The main difference is the magnitude of the SO term: while in a semiconductor 2DEG it is only a weak per...