Locally commensurate charge-density wave with three-unit-cell periodicity in YBa2Cu3Oy.

In order to identify the mechanism responsible for the formation of charge-density waves (CDW) in cuprate superconductors, it is important to understand which aspects of the CDW's microscopic structure are generic and which are material-dependent. Here, we show that, at the local scale probed by NMR, long-range CDW order in YBa2Cu3Oy is unidirectional with a commensurate period of three unit cells (λ = 3b), implying that the incommensurability found in X-ray scattering is ensured by phase slips (discommensurations). Furthermore, NMR spectra reveal a predominant oxygen character of the CDW with an out-of-phase relationship between certain lattice sites but no specific signature of a secondary CDW with λ = 6b associated with a putative pair-density wave. These results shed light on universal aspects of the cuprate CDW. In particular, its spatial profile appears to generically result from the interplay between an incommensurate tendency at long length scales, possibly related to properties of the Fermi surface, and local commensuration effects, due to electron-electron interactions or lock-in to the lattice.

Laser cooling of antihydrogen atoms.

The photon-the quantum excitation of the electromagnetic field-is massless but carries momentum. A photon can therefore exert a force on an object upon collision1. Slowing the translational motion of atoms and ions by application of such a force2,3, known as laser cooling, was first demonstrated 40 years ago4,5. It revolutionized atomic physics over the following decades6-8, and it is now a workhorse in many fields, including studies on quantum degenerate gases, quantum information, atomic clocks and tests of fundamental physics. However, this technique has not yet been applied to antimatter. Here we demonstrate laser cooling of antihydrogen9, the antimatter atom consisting of an antiproton and a positron. By exciting the 1S-2P transition in antihydrogen with pulsed, narrow-linewidth, Lyman-α laser radiation10,11, we Doppler-cool a sample of magnetically trapped antihydrogen. Although we apply laser cooling in only one dimension, the trap couples the longitudinal and transverse motions of the anti-atoms, leading to cooling in all three dimensions. We observe a reduction in the median transverse energy by more than an order of magnitude-with a substantial fraction of the anti-atoms attaining submicroelectronvolt transverse kinetic energies. We also report the observation of the laser-driven 1S-2S transition in samples of laser-cooled antihydrogen atoms. The observed spectral line is approximately four times narrower than that obtained without laser cooling. The demonstration of laser cooling and its immediate application has far-reaching implications for antimatter studies. A more localized, denser and colder sample of antihydrogen will drastically improve spectroscopic11-13 and gravitational14 studies of antihydrogen in ongoing experiments. Furthermore, the demonstrated ability to manipulate the motion of antimatter atoms by laser light will potentially provide ground-breaking opportunities for future experiments, such as anti-atomic fountains, anti-atom interferometry and the creation of antimatter molecules.

Orbital symmetries of charge density wave order in YBa2Cu3O6+x.

Charge density wave (CDW) order has been shown to compete and coexist with superconductivity in underdoped cuprates. Theoretical proposals for the CDW order include an unconventional d-symmetry form factor CDW, evidence for which has emerged from measurements, including resonant soft x-ray scattering (RSXS) in YBa2Cu3O6+x (YBCO). Here, we revisit RSXS measurements of the CDW symmetry in YBCO, using a variation in the measurement geometry to provide enhanced sensitivity to orbital symmetry. We show that the (0 0.31 L) CDW peak measured at the Cu L edge is dominated by an s form factor rather than a d form factor as was reported previously. In addition, by measuring both (0.31 0 L) and (0 0.31 L) peaks, we identify a pronounced difference in the orbital symmetry of the CDW order along the a and b axes, with the CDW along the a axis exhibiting orbital order in addition to charge order.

Thermal Hall conductivity in the cuprate Mott insulators Nd2CuO4 and Sr2CuO2Cl2.

The heat carriers responsible for the unexpectedly large thermal Hall conductivity of the cuprate Mott insulator La2CuO4 were recently shown to be phonons. However, the mechanism by which phonons in cuprates acquire chirality in a magnetic field is still unknown. Here, we report a similar thermal Hall conductivity in two cuprate Mott insulators with significantly different crystal structures and magnetic orders - Nd2CuO4 and Sr2CuO2Cl2 - and show that two potential mechanisms can be excluded - the scattering of phonons by rare-earth impurities and by structural domains. Our comparative study further reveals that orthorhombicity, apical oxygens, the tilting of oxygen octahedra and the canting of spins out of the CuO2 planes are not essential to the mechanism of chirality. Our findings point to a chiral mechanism coming from a coupling of acoustic phonons to the intrinsic excitations of the CuO2 planes.

Spatially inhomogeneous competition between superconductivity and the charge density wave in YBa2Cu3O6.67.

The charge density wave in the high-temperature superconductor YBa2Cu3O7-x (YBCO) has two different ordering tendencies differentiated by their c-axis correlations. These correspond to ferro- (F-CDW) and antiferro- (AF-CDW) couplings between CDWs in neighbouring CuO2 bilayers. This discovery has prompted several fundamental questions: how does superconductivity adjust to two competing orders and are either of these orders responsible for the electronic reconstruction? Here we use x-ray diffraction to study YBa2Cu3O6.67 as a function of magnetic field and temperature. We show that regions with F-CDW correlations suppress superconductivity more strongly than those with AF-CDW correlations. This implies that an inhomogeneous superconducting state exists, in which some regions show a fragile form of superconductivity. By comparison of F-CDW and AF-CDW correlation lengths, it is concluded that F-CDW ordering is sufficiently long-range to modify the electronic structure. Our study thus suggests that F-CDW correlations impact both the superconducting and normal state properties of YBCO.

Unusual Interplay between Superconductivity and Field-Induced Charge Order in YBa_{2}Cu_{3}O_{y}.

We present a detailed study of the temperature (T) and magnetic field (H) dependence of the electronic density of states (DOS) at the Fermi level, as deduced from specific heat and Knight shift measurements in underdoped YBa_{2}Cu_{3}O_{y}. We find that the DOS becomes field independent above a characteristic field H_{DOS}, and that the H_{DOS}(T) line displays an unusual inflection near the onset of the long-range 3D charge-density wave order. The unusual S shape of H_{DOS}(T) is suggestive of two mutually exclusive orders that eventually establish a form of cooperation in order to coexist at low T. On theoretical grounds, such a collaboration could result from the stabilization of a pair-density wave state, which calls for further investigation in this region of the phase diagram.

Influence of Spin-Orbit Coupling in Iron-Based Superconductors.

We report on the influence of spin-orbit coupling (SOC) in Fe-based superconductors via application of circularly polarized spin and angle-resolved photoemission spectroscopy. We combine this technique in representative members of both the Fe-pnictides (LiFeAs) and Fe-chalcogenides (FeSe) with tight-binding calculations to establish an ubiquitous modification of the electronic structure in these materials imbued by SOC. At low energy, the influence of SOC is found to be concentrated on the hole pockets, where the largest superconducting gaps are typically found. This effect varies substantively with the k_{z} dispersion, and in FeSe we find SOC to be comparable to the energy scale of orbital order. These results contest descriptions of superconductivity in these materials in terms of pure spin-singlet eigenstates, raising questions regarding the possible pairing mechanisms and role of SOC therein.

Observation of the 1S-2P Lyman-α transition in antihydrogen.

In 1906, Theodore Lyman discovered his eponymous series of transitions in the extreme-ultraviolet region of the atomic hydrogen spectrum1,2. The patterns in the hydrogen spectrum helped to establish the emerging theory of quantum mechanics, which we now know governs the world at the atomic scale. Since then, studies involving the Lyman-α line-the 1S-2P transition at a wavelength of 121.6 nanometres-have played an important part in physics and astronomy, as one of the most fundamental atomic transitions in the Universe. For example, this transition has long been used by astronomers studying the intergalactic medium and testing cosmological models via the so-called 'Lyman-α forest'3 of absorption lines at different redshifts. Here we report the observation of the Lyman-α transition in the antihydrogen atom, the antimatter counterpart of hydrogen. Using narrow-line-width, nanosecond-pulsed laser radiation, the 1S-2P transition was excited in magnetically trapped antihydrogen. The transition frequency at a field of 1.033 tesla was determined to be 2,466,051.7 ± 0.12 gigahertz (1σ uncertainty) and agrees with the prediction for hydrogen to a precision of 5 × 10-8. Comparisons of the properties of antihydrogen with those of its well-studied matter equivalent allow precision tests of fundamental symmetries between matter and antimatter. Alongside the ground-state hyperfine4,5 and 1S-2S transitions6,7 recently observed in antihydrogen, the Lyman-α transition will permit laser cooling of antihydrogen8,9, thus providing a cold and dense sample of anti-atoms for precision spectroscopy and gravity measurements10. In addition to the observation of this fundamental transition, this work represents both a decisive technological step towards laser cooling of antihydrogen, and the extension of antimatter spectroscopy to quantum states possessing orbital angular momentum.

Characterization of the 1S-2S transition in antihydrogen.

In 1928, Dirac published an equation 1 that combined quantum mechanics and special relativity. Negative-energy solutions to this equation, rather than being unphysical as initially thought, represented a class of hitherto unobserved and unimagined particles-antimatter. The existence of particles of antimatter was confirmed with the discovery of the positron 2 (or anti-electron) by Anderson in 1932, but it is still unknown why matter, rather than antimatter, survived after the Big Bang. As a result, experimental studies of antimatter3-7, including tests of fundamental symmetries such as charge-parity and charge-parity-time, and searches for evidence of primordial antimatter, such as antihelium nuclei, have high priority in contemporary physics research. The fundamental role of the hydrogen atom in the evolution of the Universe and in the historical development of our understanding of quantum physics makes its antimatter counterpart-the antihydrogen atom-of particular interest. Current standard-model physics requires that hydrogen and antihydrogen have the same energy levels and spectral lines. The laser-driven 1S-2S transition was recently observed 8 in antihydrogen. Here we characterize one of the hyperfine components of this transition using magnetically trapped atoms of antihydrogen and compare it to model calculations for hydrogen in our apparatus. We find that the shape of the spectral line agrees very well with that expected for hydrogen and that the resonance frequency agrees with that in hydrogen to about 5 kilohertz out of 2.5 × 1015 hertz. This is consistent with charge-parity-time invariance at a relative precision of 2 × 10-12-two orders of magnitude more precise than the previous determination 8 -corresponding to an absolute energy sensitivity of 2 × 10-20 GeV.

Enhanced Control and Reproducibility of Non-Neutral Plasmas.

The simultaneous control of the density and particle number of non-neutral plasmas confined in Penning-Malmberg traps is demonstrated. Control is achieved by setting the plasma's density by applying a rotating electric field while simultaneously fixing its axial potential via evaporative cooling. This novel method is particularly useful for stabilizing positron plasmas, as the procedures used to collect positrons from radioactive sources typically yield plasmas with variable densities and particle numbers; it also simplifies optimization studies that require plasma parameter scans. The reproducibility achieved by applying this technique to the positron and electron plasmas used by the ALPHA antihydrogen experiment at CERN, combined with other developments, contributed to a 10-fold increase in the antiatom trapping rate.

Logarithmic Upturn in Low-Temperature Electronic Transport as a Signature of d-Wave Order in Cuprate Superconductors.

In cuprate superconductors, high magnetic fields have been used extensively to suppress superconductivity and expose the underlying normal state. Early measurements revealed insulatinglike behavior in underdoped material versus temperature T, in which resistivity increases on cooling with a puzzling log(1/T) form. We instead use microwave measurements of flux-flow resistivity in YBa_{2}Cu_{3}O_{6+y} and Tl_{2}Ba_{2}CuO_{6+δ} to study charge transport deep inside the superconducting phase, in the low-temperature and low-field regime. Here, the transition from metallic low-temperature resistivity (dρ/dT>0) to a log(1/T) upturn persists throughout the superconducting doping range, including a regime at high carrier dopings in which the field-revealed normal-state resistivity is Fermi-liquid-like. The log(1/T) form is thus likely a signature of d-wave superconducting order, and the field-revealed normal state's log(1/T) resistivity may indicate the free-flux-flow regime of a phase-disordered d-wave superconductor.

Erratum: Observation of the hyperfine spectrum of antihydrogen.

This corrects the article DOI: 10.1038/nature23446.

Spin susceptibility of charge-ordered YBa2Cu3O y across the upper critical field.

The value of the upper critical field Hc2, a fundamental characteristic of the superconducting state, has been subject to strong controversy in high-Tc copper oxides. Since the issue has been tackled almost exclusively by macroscopic techniques so far, there is a clear need for local-probe measurements. Here, we use 17O NMR to measure the spin susceptibility [Formula: see text] of the CuO2 planes at low temperature in charge-ordered YBa2Cu3O y We find that [Formula: see text] increases (most likely linearly) with magnetic field H and saturates above field values ranging from 20 T to 40 T. This result is consistent with the lowest Hc2 values claimed previously and with the interpretation that the charge density wave (CDW) reduces Hc2 in underdoped YBa2Cu3O y Furthermore, the absence of marked deviation in [Formula: see text] at the onset of long-range CDW order indicates that this [Formula: see text] reduction and the Fermi-surface reconstruction are primarily rooted in the short-range CDW order already present in zero field, not in the field-induced long-range CDW order. Above [Formula: see text], the relatively low values of [Formula: see text] at [Formula: see text] K show that the pseudogap is a ground-state property, independent of the superconducting gap.

Antihydrogen accumulation for fundamental symmetry tests.

Antihydrogen, a positron bound to an antiproton, is the simplest anti-atom. Its structure and properties are expected to mirror those of the hydrogen atom. Prospects for precision comparisons of the two, as tests of fundamental symmetries, are driving a vibrant programme of research. In this regard, a limiting factor in most experiments is the availability of large numbers of cold ground state antihydrogen atoms. Here, we describe how an improved synthesis process results in a maximum rate of 10.5 ± 0.6 atoms trapped and detected per cycle, corresponding to more than an order of magnitude improvement over previous work. Additionally, we demonstrate how detailed control of electron, positron and antiproton plasmas enables repeated formation and trapping of antihydrogen atoms, with the simultaneous retention of atoms produced in previous cycles. We report a record of 54 detected annihilation events from a single release of the trapped anti-atoms accumulated from five consecutive cycles.Antihydrogen studies are important in testing the fundamental principles of physics but producing antihydrogen in large amounts is challenging. Here the authors demonstrate an efficient and high-precision method for trapping and stacking antihydrogen by using controlled plasma.

Observation of the hyperfine spectrum of antihydrogen.

The observation of hyperfine structure in atomic hydrogen by Rabi and co-workers and the measurement of the zero-field ground-state splitting at the level of seven parts in 1013 are important achievements of mid-twentieth-century physics. The work that led to these achievements also provided the first evidence for the anomalous magnetic moment of the electron, inspired Schwinger's relativistic theory of quantum electrodynamics and gave rise to the hydrogen maser, which is a critical component of modern navigation, geo-positioning and very-long-baseline interferometry systems. Research at the Antiproton Decelerator at CERN by the ALPHA collaboration extends these enquiries into the antimatter sector. Recently, tools have been developed that enable studies of the hyperfine structure of antihydrogen-the antimatter counterpart of hydrogen. The goal of such studies is to search for any differences that might exist between this archetypal pair of atoms, and thereby to test the fundamental principles on which quantum field theory is constructed. Magnetic trapping of antihydrogen atoms provides a means of studying them by combining electromagnetic interaction with detection techniques that are unique to antimatter. Here we report the results of a microwave spectroscopy experiment in which we probe the response of antihydrogen over a controlled range of frequencies. The data reveal clear and distinct signatures of two allowed transitions, from which we obtain a direct, magnetic-field-independent measurement of the hyperfine splitting. From a set of trials involving 194 detected atoms, we determine a splitting of 1,420.4 ± 0.5 megahertz, consistent with expectations for atomic hydrogen at the level of four parts in 104. This observation of the detailed behaviour of a quantum transition in an atom of antihydrogen exemplifies tests of fundamental symmetries such as charge-parity-time in antimatter, and the techniques developed here will enable more-precise such tests.

Imaging the real space structure of the spin fluctuations in an iron-based superconductor.

Spin fluctuations are a leading candidate for the pairing mechanism in high temperature superconductors, supported by the common appearance of a distinct resonance in the spin susceptibility across the cuprates, iron-based superconductors and many heavy fermion materials. The information we have about the spin resonance comes almost exclusively from neutron scattering. Here we demonstrate that by using low-temperature scanning tunnelling microscopy and spectroscopy we can characterize the spin resonance in real space. We show that inelastic tunnelling leads to the characteristic dip-hump feature seen in tunnelling spectra in high temperature superconductors and that this feature arises from excitations of the spin fluctuations. Spatial mapping of this feature near defects allows us to probe non-local properties of the spin susceptibility and to image its real space structure.

Anomalous thermal diffusivity in underdoped YBa2Cu3O6+x.

The thermal diffusivity in the [Formula: see text] plane of underdoped YBCO crystals is measured by means of a local optical technique in the temperature range of 25-300 K. The phase delay between a point heat source and a set of detection points around it allows for high-resolution measurement of the thermal diffusivity and its in-plane anisotropy. Although the magnitude of the diffusivity may suggest that it originates from phonons, its anisotropy is comparable with reported values of the electrical resistivity anisotropy. Furthermore, the anisotropy drops sharply below the charge order transition, again similar to the electrical resistivity anisotropy. Both of these observations suggest that the thermal diffusivity has pronounced electronic as well as phononic character. At the same time, the small electrical and thermal conductivities at high temperatures imply that neither well-defined electron nor phonon quasiparticles are present in this material. We interpret our results through a strongly interacting incoherent electron-phonon "soup" picture characterized by a diffusion constant [Formula: see text], where [Formula: see text] is the soup velocity, and scattering of both electrons and phonons saturates a quantum thermal relaxation time [Formula: see text].

Quasiparticle Scattering off Defects and Possible Bound States in Charge-Ordered YBa_{2}Cu_{3}O_{y}.

We report the NMR observation of a skewed distribution of ^{17}O Knight shifts when a magnetic field quenches superconductivity and induces long-range charge-density-wave (CDW) order in YBa_{2}Cu_{3}O_{y}. This distribution is explained by an inhomogeneous pattern of the local density of states N(E_{F}) arising from quasiparticle scattering off, yet unidentified, defects in the CDW state. We argue that the effect is most likely related to the formation of quasiparticle bound states, as is known to occur, under specific circumstances, in some metals and superconductors (but not in the CDW state, in general, except for very few cases in 1D materials). These observations should provide insight into the microscopic nature of the CDW, especially regarding the reconstructed band structure and the sensitivity to disorder.

Observation of the 1S-2S transition in trapped antihydrogen.

The spectrum of the hydrogen atom has played a central part in fundamental physics over the past 200 years. Historical examples of its importance include the wavelength measurements of absorption lines in the solar spectrum by Fraunhofer, the identification of transition lines by Balmer, Lyman and others, the empirical description of allowed wavelengths by Rydberg, the quantum model of Bohr, the capability of quantum electrodynamics to precisely predict transition frequencies, and modern measurements of the 1S-2S transition by Hänsch to a precision of a few parts in 1015. Recent technological advances have allowed us to focus on antihydrogen-the antimatter equivalent of hydrogen. The Standard Model predicts that there should have been equal amounts of matter and antimatter in the primordial Universe after the Big Bang, but today's Universe is observed to consist almost entirely of ordinary matter. This motivates the study of antimatter, to see if there is a small asymmetry in the laws of physics that govern the two types of matter. In particular, the CPT (charge conjugation, parity reversal and time reversal) theorem, a cornerstone of the Standard Model, requires that hydrogen and antihydrogen have the same spectrum. Here we report the observation of the 1S-2S transition in magnetically trapped atoms of antihydrogen. We determine that the frequency of the transition, which is driven by two photons from a laser at 243 nanometres, is consistent with that expected for hydrogen in the same environment. This laser excitation of a quantum state of an atom of antimatter represents the most precise measurement performed on an anti-atom. Our result is consistent with CPT invariance at a relative precision of about 2 × 10-10.

Ideal charge-density-wave order in the high-field state of superconducting YBCO.

The existence of charge-density-wave (CDW) correlations in cuprate superconductors has now been established. However, the nature of the CDW ground state has remained uncertain because disorder and the presence of superconductivity typically limit the CDW correlation lengths to only a dozen unit cells or less. Here we explore the field-induced 3D CDW correlations in extremely pure detwinned crystals of YBa2Cu3O2 (YBCO) ortho-II and ortho-VIII at magnetic fields in excess of the resistive upper critical field ([Formula: see text]) where superconductivity is heavily suppressed. We observe that the 3D CDW is unidirectional and possesses a long in-plane correlation length as well as significant correlations between neighboring CuO2 planes. It is significant that we observe only a single sharply defined transition at a critical field proportional to [Formula: see text], given that the field range used in this investigation overlaps with other high-field experiments including quantum oscillation measurements. The correlation volume is at least two to three orders of magnitude larger than that of the zero-field CDW. This is by far the largest CDW correlation volume observed in any cuprate crystal and so is presumably representative of the high-field ground state of an "ideal" disorder-free cuprate.