. However, as a neutron is neutral, it does not detect charge but rather its associated lattice distortion 7 , so it is not known whether the stripes involve ordering of the doped holes. Here we present a study of the charge order in LBCO with resonant soft X-ray scattering (RSXS). We observe giant resonances near the Fermi level as well as near the correlated gap 8,9 , demonstrating significant modulation in both the doped-hole density and the 'Mottness', or the degree to which the system resembles a Mott insulator 10 . The peak-to-trough amplitude of the valence modulation is estimated to be 0.063 holes, which suggests 11 an integrated area of 0.59 holes under a single stripe, close to the expected 0.5 for half-filled stripes.The charge/spin superstructure in LNSCO 5 and LBCO 6 appears only in the low-temperature tetragonal (LTT) phase, is most stable at x = 1/8 and coincides with an anomalous suppression of the critical temperature T c (ref. 12). This phase is frequently interpreted as (quasi) static stripes that have been pinned by the LTT distortion. The charge reflections observed with neutron scattering are weak (∼6 times less intense than the magnetic reflections) as neutrons only detect the lattice distortion, which was estimated to be only about 0.004Å (ref. 7). However, one assumes that the hole modulation itself is significant. We point out, however, that the spin-density wave in elemental Cr also exhibits half-wavelength charge reflections that are weaker by about a factor of 4.1 and represent a distortion of similar size 13 . So, in the neutron Bragg peaks alone there is no clear difference between the phenomenon in LNSCO and a simple spin-density wave. To determine whether the doped holes are actually involved we have studied LBCO with RSXS near the O K (1s → 2p) and Cu L 3/2 (2p 3/2 → 3d x2−y2 ) edges, which provide direct sensitivity to valence electron ordering [14][15][16][17][18][19][20] .Single crystals of La 2−x Ba x CuO 4 with x = 1/8 were grown by the floating-zone method 21 . The sample used in this study had T c = 2.5 K indicating suppressed superconductivity and stabilized spin/charge order. The sample was cleaved in air revealing a surface with (0,0,1) orientation. RSXS measurements were performed on beam line X1B at the National Synchrotron Light Source, Brookhaven, using a 10-axis, ultrahigh-vacuumcompatible diffractometer. The sample was cooled with a He flow cryostat connected through Cu braids, providing a base temperature of 18 K. X-ray absorption spectra (XAS) were measured in situ in fluorescence yield mode at the O K and Cu L 3/2 edges and found to be consistent with previous studies 8 (see Figs 1, 3a). We will denote reciprocal space with Miller indices (H,K,L), which represent a momentum transfer Q = (2π/a H,2π/b K,2π/c L) where a = b = 3.788Å, c = 13.23Å. The incident X-ray polarization depends on Q but was approximately 60 • from the Cu-O bond for measurements at both edges.The O K XAS in the cuprates exhibits a mobile carrier peak (MCP) at 528.6 eV, corresponding to tran...

2 If a fluid of bosons is cooled to sufficiently low temperature, a significant fraction will condense into the lowest quantum state, forming a Bose condensate. Bose condensation is a consequence of the even symmetry of the many-body wave function of bosons under particle interchange, and allows for the manifestation of macroscopic quantum phenomena, the most striking being superfluidity.Traditionally, Bose condensates are said to come in two types. Bose-Einstein condensates (BECs) occur in systems of stable bosons, such as dilute atomic gases or liquid Excitons are bosons that are bound states between an electron and hole in a solid, and were predicted long ago to Bose condense (2,3,4). Because of their light mass and high binding energy, exciton condensates should be stable at higher temperature than traditional BEC or BCS phases (5,6).Different theories predict that a Bose condensate of excitons could be a superfluid (5) or innately insulating (7), so there is tremendous need for experimental input. Identifying an exciton condensate in nature could have a profound impact on future understanding of macroscopic quantum phenomena, as well the classic problem of the metal-insulator transition in band solids, in which exciton condensation has long been believed to play a fundamental role (2,3,4).Condensed phases of photogenerated excitons have been realized in semiconductor quantum wells in resonance with a Fabry-Perot cavity which, although not fully thermally equilibrated, have exhibited evidence for transient superfluidity (8). Excitonic phases have also been realized in quantumHall bilayers in a perpendicular magnetic field (9). Although the order in these two-dimensional structures is not strictly long-ranged, and the order parameter cannot be measured directly, compelling evidence for excitonic correlations has been observed in Coulomb drag experiments (9). Despite these 3 achievements, there is a great need to identify an exciton condensate in a fully thermalized, threedimensional system in which the order is long-ranged.An ideal approach would be to identify a material in which an exciton condensate forms "naturally." Long ago, a BCS condensate of excitons was predicted to arise spontaneously in semimetals in which an indirect band gap is tuned close to zero ( Fig. 1) (2,3,4). This condensate is expected to break a spatial symmetry, rather than the U(1) symmetry broken by a superconductor, and in the absence of pinning should exhibit perfect conductivity without a Meissner effect (10). This phase can be thought of as a solid crystal of excitons, which early authors dubbed "excitonium" (4), and is the two-band analogue of the Wigner crystal instability of an interacting electron gas (10). This condensate is closely related to that in bilayer quantum wells (9), the coherence developing between electrons and holes in different bands ( Fig. 1) rather than in different layers. If found, this exciton condensate would be threedimensional, guaranteed to reside in thermodynamic equilibrium, and could potentially...

Low-dimensional electron systems, as realized in layered materials, often tend to spontaneously break the symmetry of the underlying nuclear lattice by forming so-called density waves 1 ; a state of matter that at present attracts enormous attention 2-6 . Here we reveal a remarkable and surprising feature of charge density waves, namely their intimate relation to orbital order. For the prototypical material 1T-TaS 2 we not only show that the charge density wave within the two-dimensional TaS 2 layers involves previously unidentified orbital textures of great complexity. We also demonstrate that two metastable stackings of the orbitally ordered layers allow manipulation of salient features of the electronic structure. Indeed, these orbital e ects provide a route to switch 1T-TaS 2 nanostructures from metallic to semiconducting with technologically pertinent gaps of the order of 200 meV. This new type of orbitronics is especially relevant for the ongoing development of novel, miniaturized and ultrafast devices based on layered transition metal dichalcogenides 7,8 .Among the various transition metal dichalcogenides (TMDs), 1T-TaS 2 stands out because of its particularly rich electronic phase diagram as a function of pressure and temperature 9 . This phase diagram not only features incommensurate, nearly commensurate and commensurate charge density waves (CDWs), but also pressure-induced superconductivity below 5 K. In addition to this, it was proposed early on that the low-temperature commensurate CDW (C-CDW), which is illustrated in Fig. 1a,c, also features manybody Mott physics 10 . Experimental evidence for the presence of Mott physics in 1T-TaS 2 has indeed been obtained recently by timeresolved spectroscopies, which observed the ultrafast collapse of a charge excitation gap, which has been interpreted as a fingerprint of significant electron-electron interactions [11][12][13] . Even though the above scenario for the C-CDW is widely accepted, important experimental facts remain to be understood: the very strong suppression of the C-CDW with external pressure is puzzling. Already above 0.6 GPa, the C-CDW is no longer stable, although nesting conditions, band widths and lattice structure remain essentially unchanged. It is also not clear how ordered defects within the C-CDW, which emerge in the nearly commensurate phase (NC-CDW) on heating 14,15 and do not cause significant changes in the bandwidths, can render the electronelectron on-site interaction U completely ineffective 16 . In the following we will show that all these issues are explained consistently in terms of orbital textures that are intertwined with the CDW. Furthermore, we demonstrate that this new twist to the physics of

Superconductivity (SC) in so-called "unconventional superconductors" is nearly always found in the vicinity of another ordered state, such as antiferromagnetism, charge density wave (CDW), or stripe order. This suggests a fundamental connection between SC and fluctuations in some other order parameter. To better understand this connection, we used high-pressure x-ray scattering to directly study the CDW order in the layered dichalcogenide TiSe 2 , which was previously shown to exhibit SC when the CDW is suppressed by pressure [1] or intercalation of Cu atoms [2]. We succeeded in suppressing the CDW fully to zero temperature, establishing for the first time the existence of a quantum critical point (QCP) at P c = 5.1 ± 0.2 GPa, which is more than 1 GPa beyond the end of the SC region. Unexpectedly, at P = 3 GPa we observed a reentrant, weakly first order, incommensurate phase, indicating the presence of a Lifshitz tricritical point somewhere above the superconducting dome. Our study suggests that SC in TiSe 2 may not be connected to the QCP itself, but to the formation of CDW domain walls. *The term "unconventional superconductor" once referred to materials whose phenomenology does not conform to the Bardeen-Cooper-Schrieffer (BCS) paradigm for superconductivity. It is now evident that, by this definition, the vast majority of known superconductors are unconventional, notable examples being the copper-oxide, iron-arsenide, and iron-selenide high temperature superconductors, heavy Fermion materials such as CeIn 3 and CeCoIn 5 , ruthenium oxides, organic superconductors such as ϰ-(BEDT-TTF)2X, filled skutterudites, etc.Despite their diversity in structure and phenomenology, the phase diagrams of these materials all exhibit the common trait that superconductivity (SC) resides near the boundary of an ordered phase with broken translational or spin rotation symmetry. For example, SC resides near antiferromagnetism in CeIn 3 [3], near a spin density wave in iron arsenides [4], orbital order in ruthenates [5], and stripe and nematic order in the copper-oxides [6]. The pervasiveness of this "universal phase diagram" suggests that there exists a unifying framework -more general than BCS -in which superconductivity can be understood as coexisting with some ordered phase, and potentially emerging from its fluctuations.A classic example is the transition metal dichalcogenide family, MX 2 , where M=Nb, Ti, Ta, and X=Se, S, which exhibit a rich competition between superconductivity and Peierls-like charge density wave (CDW) order [7]. A recent, prominent case is 1T-TiSe 2 , which under ambient pressure exhibits CDW order below a transition temperature T CDW = 202 K [8]. This CDW phase can be suppressed either with intercalation of Cu atoms [2,9], or through the application of hydrostatic pressure [1,10], causing SC to emerge. These studies suggest that the emergence of SC coincides with a quantum critical point (QCP) at which T CDW goes to zero, suggesting that TiSe 2 exemplifies the universal phenomenon of superconductivity em...