The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered a huge amount of innovative scientific inquiry. In the almost three decades since, much has been learned about the novel forms of quantum matter that are exhibited in these strongly correlated electron systems. A qualitative understanding of the nature of the superconducting state itself has been achieved. However, unresolved issues include the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the 'normal' state at elevated temperatures.

BASIC NOTIONSTransition metal oxides (TMOs) are an ideal arena for the study of electronic correlations because the s-electrons of the transition metal ions are removed and transferred to oxygen ions, and hence the strongly correlated d-electrons determine their physical properties such as electrical transport, magnetism, optical response, thermal conductivity, and superconductivity. These electron correlations prohibit the double occupancy of metal sites and induce a local entanglement of charge, spin, and orbital degrees of freedom. This gives rise to a variety of phenomena, e.g., Mott insulators, various charge/spin/orbital orderings, metal-insulator transitions, multiferroics, and superconductivity. 1 In recent years, there has been a burst of activity to manipulate these phenomena, as well as create new ones, using oxide heterostructures. 2 Most fundamental to understanding the physical properties of TMOs is the concept of symmetry of the order parameter. As Landau recognized, the essence of phase transitions is the change of the symmetry. For example, ferromagnetic ordering breaks the rotational symmetry in spin space, i.e., the ordered phase has lower symmetry than the Hamiltonian of the system. There are three most important symmetries to be considered here. (i) Spatial inversion (I), defined as r  -r. In the case of an insulator, breaking this symmetry can lead to spontaneous electric SLAC-PUB-14626 SIMES,

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

An understanding of the nature of superconductivity in cuprates has been hindered by the apparent diversity of intertwining electronic orders in these materials. Here we combine resonant X-ray scattering (REXS), scanning-tunneling microscopy (STM), and angle-resolved photoemission spectroscopy (ARPES) to observe a charge order that appears consistently in surface and bulk, as well as momentum and real space, with the Bi2Sr2−xLaxCuO 6+δ cuprate family. The observed wavevector rules out simple antinodal nesting in the single particle limit, but matches well with a phenomenological model of a many-body instability of the Fermi arcs. Combined with earlier observations in other cuprate families, these findings suggest the existence of a generic charge-ordered state in underdoped cuprates, and uncover its connection to the pseudogap regime. PACS numbers:Since the discovery of cuprate high-temperature superconductors, several unconventional phenomena have been observed in the region of the phase diagram located between the strongly localized Mott insulator at zero doping and the itinerant Fermi-liquid state that emerges beyond optimal doping [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The so-called 'pseudogap' opens at the temperature T * and obliterates the Fermi surface at the antinodes (AN) of the d-wave superconducting gap function, leaving behind disconnected "Fermi arcs" centered around the nodes. In addition, charge order has been observed on the surface of Bi-and Clbased compounds [4][5][6][7][8], in the bulk of La-based compounds [9][10][11], and most recently in YBa 2 Cu 3 O 6+δ (YBCO) [17][18][19][20], indicating this might be the leading instability in underdoped cuprates. The similarity between the observed charge ordering wavevector and the antinodal nesting vector of the hightemperature Fermi surface has prompted suggestions that a conventional Peierls-like charge-density-wave (CDW) might be responsible for the opening of the pseudogap [7,8,12,19]. We use complementary bulk/surface techniques to examine the validity of this scenario, and explore the connection between charge ordering and fermiology.By applying a suite of complementary tools to a single cuprate material, Bi 2 Sr 2−x La x CuO 6+δ (Bi2201), we reveal that the charge order in this system emerges just below T * , and that its wavevector corresponds to the Fermi arc tips rather than the antinodal nesting vector. We quantify the Fermi surface using ARPES, and we look for charge modulations along the Cu-O bond directions in both real-and reciprocalspace, using STM and REXS. The single-layer Bi2201 is well suited to this purpose owing to: (i) its two-dimensionality and high degree of crystallinity [22,23], and (ii) the possibility of probing the temperature evolution across T * , which is bettercharacterized [15,16] and more accessible than in bilayer sys-

Electronic phases with symmetry properties matching those of conventional liquid crystals have recently been discovered in transport experiments on semiconductor heterostructures and metal oxides at milli-Kelvin temperatures. We report the spontaneous onset of a onedimensional, incommensurate modulation of the spin system in the high-temperature superconductor YBa 2 Cu 3 O 6.45 upon cooling below ~150 K, while static magnetic order is absent above 2 K. The evolution of this modulation with temperature and doping parallels that of the in-plane anisotropy of the resistivity, indicating an electronic nematic phase that is stable over a wide temperature range. The results suggest that soft spin fluctuations are a microscopic route towards electronic liquid crystals, and nematic order can coexist with high-temperature superconductivity in underdoped cuprates.The electronic states near the Fermi level of high-temperature superconductors derive from the hybridized d-and p-orbitals of copper and oxygen ions in a square-planar network. At a doping level of 1/8 hole per Cu ion, experimental work on a specific superconducting cuprate family, (La,Nd) 2-x (Sr,Ba) x CuO 4 (La214), has shown that the two-dimensional electron system in the CuO 2 layers can support a state with uniaxial spin (1-3) and charge (1,4,5) order ("stripes"). Static stripe order implies that both translational and rotational symmetries of the copper-oxide square lattice are spontaneously broken. More unusual "electronic liquid crystal" states (6) that break the rotational symmetry of the lattice while at least partially preserving its translational symmetry can arise from quantum fluctuations of stripes(6-8), or from Fermi surface instabilities (9-11). Electronic nematic states have recently been discovered in semiconductor heterostructures (12) and in the bulk transition metal oxide Sr 3 Ru 2 O 7 (13). In both cases, however, they are stable only at milli-Kelvin temperatures and in high magnetic fields, and have thus far only been probed by transport measurements. We use neutron scattering to address the role of magnetic degrees of freedom in driving the formation of electronic liquid crystals, and to explore the presence of liquid-crystalline order in the cuprates.In the prior experiments on semiconductor heterostructures and on Sr 3 Ru 2 O 7 , the nematic director was aligned by external magnetic fields, resulting in a strong macroscopic anisotropy of 2 the current flow (12,13), analogous to the alignment of nematic domains in conventional liquid crystals by electric fields or confining walls. In the cuprates, subtle crystallographic distortions can serve as aligning fields for symmetry-broken electronic phases. They reduce the fourfold rotational symmetry of the CuO 2 layer to a twofold rotational or mirror symmetry by introducing a slight (~1%) difference between the in-plane lattice parameters. In stripe-ordered La214, the stripe domains in every CuO 2 layer are aligned by such a twofold axis, but the layers are stacked in such a way that the glob...