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The 40-70 meV band-structure renormalization (so-called kink) in high-temperature cuprate superconductors - which has been mainly interpreted in terms of electron-boson coupling - is observed to be strongly suppressed both above the superconducting transition temperature and under optical excitation. We employ equilibrium and time- and angle-resolved photoemission spectroscopy, in combination with Migdal-Eliashberg simulations, to investigate the suppression of the near-nodal kink in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. We show that the $\sim$30$\%$ decrease of the kink strength across the superconducting-to-normal-state phase transition can be entirely accounted for by the filling of the superconducting gap, without additional consideration of temperature-dependent electron-boson coupling. Our findings demonstrate that consideration of changes in the density of states is essential to quantitatively account for the band structure renormalization effects in cuprates.

FeSe$_{1-x}$S$_x$ remains one of the most enigmatic systems of Fe-based superconductors. While much is known about the orthorhombic parent compound, FeSe, the tetragonal samples, FeSe$_{1-x}$S$_x$ with x>0.17, remain relatively unexplored. Here, we provide an in-depth investigation of the electronic states of tetragonal FeSe$_{0.81}$S$_{0.19}$, using scanning tunneling microscopy and spectroscopy (STM/S) measurements, supported by angle-resolved photoemission spectroscopy (ARPES) and theoretical modeling. We demonstrate that by analyzing modulations of the local density of states (LDOS) near and away from Fe vacancy defects separately, we can identify quasiparticle interference (QPI) signals originating from multiple regions of the Brillouin zone, including the bands at the M and A points. We also observe that QPI signals coexist with a much stronger LDOS modulation for states near the Fermi level whose period is independent of energy. Our measurements further reveal that this strong pattern appears in the STS measurements as short range stripe patterns that are locally two-fold symmetric. Since these stripe patterns coexist with four-fold symmetric QPI around Fe-vacancies, the origin of their local two-fold symmetry must be distinct from that of nematic states in orthorhombic samples. To further understand these stripe patterns, we explore several aspects related to them, such as the role of S and Fe vacancy defects, and whether they can be explained by QPI. We consider the possibility that the observed stripe patterns may represent incipient charge order correlations, similar to those observed in the cuprates.

In the study of dynamic charge order correlations in the cuprates, most high energy-resolution resonant inelastic x-ray scattering (RIXS) measurements have focused on momenta along the high-symmetry directions of the copper oxide plane. However, electron scattering along other in-plane directions should not be neglected as they may contain information relevant, for example, to the origin of charge order correlations or to our understanding of the isotropic scattering responsible for strange metal behavior in cuprates. We report high-resolution resonant inelastic x-ray scattering (RIXS) experiments that reveal the presence of dynamic electron correlations over the $q_x$-$q_y$ scattering plane in underdoped $\textrm{Bi}_2\textrm{Sr}_2\textrm{Ca}\textrm{Cu}_2\textrm{O}_{8+\delta}$ with $T_c=54$ K. We use the softening of the RIXS-measured bond stretching phonon line as a marker for the presence of charge-order-related dynamic electron correlations. The experiments show that these dynamic correlations exist at energies below approximately $70$ meV and are centered around a quasi-circular manifold in the $q_x$-$q_y$ scattering plane with radius equal to the magnitude of the charge order wave vector, $q_{CO}$. We also demonstrate how this phonon-tracking procedure provides the necessary experimental precision to rule out fluctuations of short-range directional charge order (i.e. centered around $[q_x=\pm q_{CO}, q_y=0]$ and $[q_x=0, q_y=\pm q_{CO}]$) as the origin of the observed correlations., Comment: Submitted and under review

In strongly correlated systems the strength of Coulomb interactions between electrons, relative to their kinetic energy, plays a central role in determining their emergent quantum mechanical phases. We perform resonant x-ray scattering on Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, a prototypical cuprate superconductor, to probe electronic correlations within the CuO$_2$ plane. We discover a dynamic quasi-circular pattern in the $x$-$y$ scattering plane with a radius that matches the wave vector magnitude of the well-known static charge order. Along with doping- and temperature-dependent measurements, our experiments reveal a picture of charge order competing with superconductivity where short-range domains along $x$ and $y$ can dynamically rotate into any other in-plane direction. This quasi-circular spectrum, a hallmark of Brazovskii-type fluctuations, has immediate consequences to our understanding of rotational and translational symmetry breaking in the cuprates. We discuss how the combination of short- and long-range Coulomb interactions results in an effective non-monotonic potential that may determine the quasi-circular pattern., Comment: This is a post-peer-review, pre-copyedit version of an article published in Nature Communications. The final authenticated version is available online at: https://doi.org/10.1038/s41467-020-20824-7. Supplementary materials are available through the published version in Nature Communications

The La-based '214' cuprates host several symmetry breaking phases including superconductivity, charge and spin order in the form of stripes, and a structural othorhombic-to-tetragonal phase transition. Therefore, these materials are an ideal system to study the effects of uniaxial stress onto the various correlations that pervade the cuprate phase diagram. We report resonant x-ray scattering experiments on $\textrm{La}_{1.475}\textrm{Nd}_{0.4}\textrm{Sr}_{0.125}\textrm{Cu}\textrm{O}_{4}$ (LNSCO-125) that reveal a significant response of charge stripes to uniaxial tensile-stress of $\sim$ 0.1 GPa. These effects include a reduction of the onset temperature of stripes by $\sim$ 50 K, a 29 K reduction of the low-temperature orthorhombic-to-tetragonal transition, competition between charge order and superconductivity, and a preference for stripes to form along the direction of applied stress. Altogether, we observe a dramatic response of the electronic properties of LNSCO-125 to a modest amount of uniaxial stress., Comment: 6 pages, 3 figures, Supplemental material available upon request

Superconductivity and charge density waves (CDW) are competitive, yet coexisting orders in cuprate superconductors. To understand their microscopic interdependence, a probe capable of discerning their interaction on its natural length and time scales is necessary. We use ultrafast resonant soft x-ray scattering to track the transient evolution of CDW correlations in YBa$_{2}$Cu$_{3}$O$_{6+x}$ following the quench of superconductivity by an infrared laser pulse. We observe a non-thermal response of the CDW order characterized by a near doubling of the correlation length within $\approx$ 1 picosecond of the superconducting quench. Our results are consistent with a model in which the interaction between superconductivity and CDW manifests inhomogeneously through disruption of spatial coherence, with superconductivity playing the dominant role in stabilizing CDW topological defects, such as discommensurations., Comment: Accepted version. 34 pages, 11 figures, Main text and Supplementary Materials

We report a detailed experimental study of the band structure of the recently discovered topological material $\textrm{Hf}_{2}\textrm{Te}_2\textrm{P}$. Using the combination of scanning tunneling spectroscopy and angle-resolved photo-emission spectroscopy with surface K-doping, we probe the band structure of $\textrm{Hf}_{2}\textrm{Te}_2\textrm{P}$ with energy and momentum resolution above the Fermi level. Our experiments show the presence of multiple surface states with a linear Dirac-like dispersion, consistent with the predictions from previously reported band structure calculations. In particular, scanning tunneling spectroscopy measurements provide the first experimental evidence for the strong topological surface state predicted at 460 meV, which stems from the band inversion between Hf-d and Te-p orbitals. This band inversion comprised of more localized d-states could result in a better surface-to-bulk conductance ratio relative to more traditional topological insulators., Comment: Supplementary materials available upon request

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 YBa$_2$Cu$_3$O$_{6+x}$ (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., Comment: 17 pages, 4 figures + supplementary information

Electron interactions are pivotal for defining the electronic structure of quantum materials. In particular, the strong electron Coulomb repulsion is considered the keystone for describing the emergence of exotic and/or ordered phases of quantum matter as disparate as high-temperature superconductivity and charge- or magnetic-order. However, a comprehensive understanding of fundamental electronic properties of quantum materials is often complicated by the appearance of an enigmatic partial suppression of low-energy electronic states, known as the pseudogap. Here we take advantage of ultrafast angle-resolved photoemission spectroscopy to unveil the temperature evolution of the low-energy density of states in the electron-doped cuprate Nd$_{\text{2-x}}$Ce$_{\text{x}}$CuO$_{\text{4}}$, an emblematic system where the pseudogap intertwines with magnetic degrees of freedom. By photoexciting the electronic system across the pseudogap onset temperature T*, we report the direct relation between the momentum-resolved pseudogap spectral features and the spin-correlation length with an unprecedented sensitivity. This transient approach, corroborated by mean field model calculations, allows us to establish the pseudogap in electron-doped cuprates as a precursor to the incipient antiferromagnetic order even when long-range antiferromagnetic correlations are not established, as in the case of optimal doping., Comment: 17 pages, 3 figures

Time- and angle-resolved photoemission spectroscopy accesses the ultrafast evolution of quasiparticles and many-body interactions in solid-state systems. However, the momentum- and energy-resolved transient photoemission intensity may not be unambiguously related to the intrinsic relaxation dynamics of photoexcited electrons. In fact, interpretation of the time-dependent photoemission signal can be affected by the transient evolution of both the one-electron removal spectral function as well as the photoemission dipole matrix elements. Here we investigate the topological insulator Bi$_{1.1}$Sb$_{0.9}$Te$_2$S to demonstrate, by means of a careful probe-polarization study, the transient contribution of matrix elements to the time-resolved photoemission signal., Comment: 7 pages, 3 figures

Incommensurate charge order (CO) has been identified as the leading competitor of high-temperature superconductivity in all major families of layered copper oxides, but the perplexing variety of CO states in different cuprates has confounded investigations of its impact on the transport and thermodynamic properties. The three-dimensional (3D) CO observed in YBa$_2$Cu$_3$O$_{6+x}$ in high magnetic fields is of particular interest, because quantum transport measurements have revealed detailed information about the corresponding Fermi surface. Here we use resonant X-ray scattering to demonstrate 3D-CO in underdoped YBa$_2$Cu$_3$O$_{6+x}$ films grown epitaxially on SrTiO$_3$ in the absence of magnetic fields. The resonance profiles indicate that Cu sites in the charge-reservoir layers participate in the CO state, and thus efficiently transmit CO correlations between adjacent CuO$_2$ bilayer units. The results offer fresh perspectives for experiments elucidating the influence of 3D-CO on the electronic properties of cuprates without the need to apply high magnetic fields.

Charge order has now been observed in several cuprate high-temperature superconductors. We report a resonant inelastic x-ray scattering experiment on the electron-doped cuprate Nd$_{2-x}$Ce$_{x}$CuO$_4$ that demonstrates the existence of dynamic correlations at the charge order wave vector. Upon cooling we observe a softening in the electronic response, which has been predicted to occur for a d-wave charge order in electron-doped cuprates. At low temperatures, the energy range of these excitations coincides with that of the dispersive magnetic modes known as paramagnons. Furthermore, measurements where the polarization of the scattered photon is resolved indicate that the dynamic response at the charge order wave vector primarily involves spin-flip excitations. Overall, our findings indicate a coupling between dynamic magnetic and charge-order correlations in the cuprates., Comment: Supplementary information available upon request

The possibility of driving phase transitions in low-density condensates through the loss of phase coherence alone has far-reaching implications for the study of quantum phases of matter. This has inspired the development of tools to control and explore the collective properties of condensate phases via phase fluctuations. Electrically-gated oxide interfaces, ultracold Fermi atoms, and cuprate superconductors, which are characterized by an intrinsically small phase-stiffness, are paradigmatic examples where these tools are having a dramatic impact. Here we use light pulses shorter than the internal thermalization time to drive and probe the phase fragility of the Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ cuprate superconductor, completely melting the superconducting condensate without affecting the pairing strength. The resulting ultrafast dynamics of phase fluctuations and charge excitations are captured and disentangled by time-resolved photoemission spectroscopy. This work demonstrates the dominant role of phase coherence in the superconductor-to-normal state phase transition and offers a benchmark for non-equilibrium spectroscopic investigations of the cuprate phase diagram., Comment: 24 pages, 9 figures, Main Text and Supplementary Information

Understanding the interplay between charge order (CO) and other phenomena (e.g. pseudogap, antiferromagnetism, and superconductivity) is one of the central questions in the cuprate high-temperature superconductors. The discovery that similar forms of CO exist in both hole- and electron-doped cuprates opened a path to determine what subset of the CO phenomenology is universal to all the cuprates. Here, we use resonant x-ray scattering to measure the charge order correlations in electron-doped cuprates (La2-xCexCuO4 and Nd2-xCexCuO4) and their relationship to antiferromagnetism, pseudogap, and superconductivity. Detailed measurements of Nd2-xCexCuO4 show that CO is present in the x = 0.059 to 0.166 range, and that its doping dependent wavevector is consistent with the separation between straight segments of the Fermi surface. The CO onset temperature is highest between x = 0.106 and 0.166, but decreases at lower doping levels, indicating that it is not tied to the appearance of antiferromagnetic correlations or the pseudogap. Near optimal doping, where the CO wavevector is also consistent with a previously observed phonon anomaly, measurements of the CO below and above the superconducting transition temperature, or in a magnetic field, show that the CO is insensitive to superconductivity. Overall these findings indicate that, while verified in the electron-doped cuprates, material-dependent details determine whether the CO correlations acquire sufficient strength to compete for the ground state of the cuprates., Comment: Supplementary information available upon request

Fine questions our interpretation of unidirectional-stripes over bidirectional-checkerboard, and illustrates his criticism by simulating a momentum space structure consistent with our data and corresponding to a checkerboard-looking real space density. Here we use a local rotational-symmetry analysis to demonstrate that the simulated image is in actuality composed of locally unidirectional modulations of the charge density, consistent with our original conclusions., Comment: Response to original comment: B.V. Fine, Science 351, 235 (2016) (arxiv version at http://arxiv.org/abs/1602.00888)

Following the early discovery of stripe-like order in La-based copper-oxide superconductors, charge ordering instabilities were observed in all cuprate families. However, it has proven difficult to distinguish between uni- (stripes) and bi-directional (checkerboard) charge order in Y- and Bi-based materials. Here we use resonant x-ray scattering (RXS) to measure the two-dimensional structure factor in YBCO, in reciprocal space. Our data reveal the presence of charge stripe order, i.e. locally unidirectional density waves, suggesting it as the true microscopic nature of charge modulations in cuprates. At the same time, we find that the well-established competition between charge order and superconductivity is stronger for charge correlations across than along the stripes, which provides additional evidence for the intrinsic unidirectional nature of the charge order.

We study the magnetic relaxation rate Gamma of the single-molecule magnet Mn_{12}-tBuAc as a function of magnetic field component H_T transverse to the molecule's easy axis. When the spin is near a magnetic quantum tunneling resonance, we find that Gamma increases abruptly at certain values of H_T. These increases are observed just beyond values of H_T at which a geometric-phase interference effect suppresses tunneling between two excited energy levels. The effect is washed out by rotating H_T away from the spin's hard axis, thereby suppressing the interference effect. Detailed numerical calculations of Gamma using the known spin Hamiltonian accurately reproduce the observed behavior. These results are the first experimental evidence for geometric-phase interference in a single-molecule magnet with true four-fold symmetry., Comment: version accepted by PRL; added inset to Fig. 1, added three references and a footnote; other minor changes; 5 pages, 4 figures