Bond stretching phonon softening and kinks in the angle-resolved photoemission spectra of optimally doped Bi2Sr1.6La0.4Cu2O6+delta superconductors

Magnetic excitations in strained infinite-layer nickelate PrNiO2 films

Strongly correlated materials respond sensitively to external perturbations such as strain, pressure, and doping. In the recently discovered superconducting infinite-layer nickelates, the superconducting transition temperature can be enhanced via only ~ 1% compressive strain-tuning with the root of such enhancement still being elusive. Using resonant inelastic x-ray scattering (RIXS), we investigate the magnetic excitations in infinite-layer PrNiO2 thin films grown on two different substrates, namely SrTiO3 (STO) and (LaAlO3)0.3(Sr2TaAlO6)0.7 (LSAT) enforcing different strain on the nickelates films. The magnon bandwidth of PrNiO2 shows only marginal response to strain-tuning, in sharp contrast to the enhancement of the superconducting transition temperature Tc in the doped superconducting samples. These results suggest the bandwidth of spin excitations of the parent compounds is similar under strain while Tc in the doped ones is not, and thus provide important empirics for the understanding of superconductivity in infinite-layer nickelates.

Anharmonic theory of superconductivity and its applications to emerging quantum materials

The role of anharmonicity on superconductivity has often been disregarded in the past. Recently, it has been recognized that anharmonic decoherence could play a fundamental role in determining the superconducting properties (electron-phonon coupling, critical temperature, etc) of a large class of materials, including systems close to structural soft-mode instabilities, amorphous solids and metals under extreme high-pressure conditions. Here, we review recent theoretical progress on the role of anharmonic effects, and in particular certain universal properties of anharmonic damping, on superconductivity. Our focus regards the combination of microscopic-agnostic effective theories for bosonic mediators with the well-established BCS theory and Migdal-Eliashberg theory for superconductivity. We discuss in detail the theoretical frameworks, their possible implementation within first-principles methods, and the experimental probes for anharmonic decoherence. Finally, we present several concrete applications to emerging quantum materials, including hydrides, ferroelectrics and systems with charge density wave instabilities.

Signature of quantum criticality in cuprates by charge density fluctuations

The universality of the strange metal phase in many quantum materials is often attributed to the presence of a quantum critical point (QCP), a zero-temperature phase transition ruled by quantum fluctuations. In cuprates, where superconductivity hinders direct QCP observation, indirect evidence comes from the identification of fluctuations compatible with the strange metal phase. Here we show that the recently discovered charge density fluctuations (CDF) possess the right properties to be associated to a quantum phase transition. Using resonant x-ray scattering, we studied the CDF in two families of cuprate superconductors across a wide doping range (up to p = 0.22). At p* ≈ 0.19, the putative QCP, the CDF intensity peaks, and the characteristic energy Δ is minimum, marking a wedge-shaped region in the phase diagram indicative of a quantum critical behavior, albeit with anomalies. These findings strengthen the role of charge order in explaining strange metal phenomenology and provide insights into high-temperature superconductivity.

Possible enhancement of the superconductingTcdue to sharp Kohn-like soft phonon anomalies

Phonon softening is a ubiquitous phenomenon in condensed matter systems which is often associated with charge density wave (CDW) instabilities and anharmonicity. The interplay between phonon softening, CDW and superconductivity is a topic of intense debate. In this work, the effects of anomalous soft phonon instabilities on superconductivity are studied based on a recently developed theoretical framework that accounts for phonon damping and softening within the Migdal-Eliashberg theory. Model calculations show that the phonon softening in the form of a sharp dip in the phonon dispersion relation, either acoustic or optical (including the case of Kohn-type anomalies typically associated with CDW), can cause a manifold increase of the electron-phonon coupling constantλ. This, under certain conditions, which are consistent with the concept of optimal frequency introduced by Bergmann and Rainer, can produce a large increase of the superconducting transition temperatureTc. In summary, our results suggest the possibility of reaching high-temperature superconductivity by exploiting soft phonon anomalies restricted in momentum space.

Multiorbital charge-density wave excitations and concomitant phonon anomalies in Bi2Sr2LaCuO6+δ

Charge-density waves (CDWs) are a ubiquitous form of electron density modulation in cuprate superconductors. Unveiling the nature of quasistatic CDWs and their dynamical excitations is crucial for understanding their origin––similar to the study of antiferromagnetism in cuprates. However, dynamical CDW excitations remain largely unexplored due to the limited availability of suitable experimental probes. Here, using resonant inelastic X-ray scattering, we observe dynamical CDW excitations in Bi₂Sr₂LaCuO_6+δ (Bi2201) superconductors through its interference with the lattice. The distinct anomalies of the bond-buckling and the bond-stretching phonons allow us to draw a clear picture of funnel-shaped dynamical CDW excitations in Bi2201. Our results of the interplay between CDWs and the phonon anomalies shed light on the nature of CDWs in cuprates.

Charge-density waves (CDWs) are ubiquitous in underdoped cuprate superconductors. As a modulation of the valence electron density, CDWs in hole-doped cuprates possess both Cu-3d and O-2p orbital character owing to the strong hybridization of these orbitals near the Fermi level. Here, we investigate underdoped Bi₂Sr_1.4La_0.6CuO_6+δ using resonant inelastic X-ray scattering (RIXS) and find that a short-range CDW exists at both Cu and O sublattices in the copper-oxide (CuO₂) planes with a comparable periodicity and correlation length. Furthermore, we uncover bond-stretching and bond-buckling phonon anomalies concomitant to the CDWs. Comparing to slightly overdoped Bi₂Sr_1.8La_0.2CuO_6+δ, where neither CDWs nor phonon anomalies appear, we highlight that a sharp intensity anomaly is induced in the proximity of the CDW wavevector (Q_CDW) for the bond-buckling phonon, in concert with the diffused intensity enhancement of the bond-stretching phonon at wavevectors much greater than Q_CDW. Our results provide a comprehensive picture of the quasistatic CDWs, their dispersive excitations, and associated electron-phonon anomalies, which are key for understanding the competing electronic instabilities in cuprates.

High-energy-resolution inelastic X-ray scattering spectrometer at beamline 30-ID of the Advanced Photon Source

Inelastic X-ray scattering is a powerful and versatile technique for studying lattice dynamics in materials of scientific and technological importance. In this article, the design and capabilities of the momentum-resolved high-energy-resolution inelastic X-ray spectrometer (HERIX) at beamline 30-ID of the Advanced Photon Source are reported. The instrument operates at 23.724 keV and has an energy resolution of 1.3-1.7 meV. It can accommodate momentum transfers of up to 72  nm-1, at a typical X-ray flux of 4.5 × 109 photons s-1 meV-1 at the sample. A suite of in situ sample environments are provided, including high pressure, static magnetic fields and uniaxial strains, all at high or cryogenic temperatures.

Phonon Driven Floquet Matter

The effect of electron-phonon coupling in materials can be interpreted as a dressing of the electronic structure by the lattice vibration, leading to vibrational replicas and hybridization of electronic states. In solids, a resonantly excited coherent phonon leads to a periodic oscillation of the atomic lattice in a crystal structure bringing the material into a nonequilibrium electronic configuration. Periodically oscillating quantum systems can be understood in terms of Floquet theory, which has a long tradition in the study of semiclassical light-matter interaction. Here, we show that the concepts of Floquet analysis can be applied to coherent lattice vibrations. This coupling leads to phonon-dressed quasi-particles imprinting specific signatures in the spectrum of the electronic structure. Such dressed electronic states can be detected by time- and angular-resolved photoelectron spectroscopy (ARPES) manifesting as sidebands to the equilibrium band structure. Taking graphene as a paradigmatic material with strong electron-phonon interaction and nontrivial topology, we show how the phonon-dressed states display an intricate sideband structure revealing the electron-phonon coupling at the Brillouin zone center and topological ordering of the Dirac bands. We demonstrate that if time-reversal symmetry is broken by the coherent lattice perturbations a topological phase transition can be induced. This work establishes that the recently demonstrated concept of light-induced nonequilibrium Floquet phases can also be applied when using coherent phonon modes for the dynamical control of material properties.

Highly anisotropic anomaly in the dispersion of the copper-oxygen bond-bending phonon in superconducting YBa2Cu3O7 from inelastic neutron scattering

Motivated by predictions of a substantial contribution of the "buckling" vibration of the CuO(2) layers to d-wave superconductivity in the cuprates, we have performed an inelastic neutron scattering study of this phonon in an array of untwinned crystals of YBa(2)Cu(3)O(7). The data reveal a pronounced softening of the phonon at the in-plane wave vector q=(0,0.3) upon cooling below ~105 K, but no corresponding anomaly at q=(0.3,0). Based on the observed in-plane anisotropy, we argue that the electron-phonon interaction responsible for this anomaly supports an electronic instability associated with a uniaxial charge-density modulation and does not mediate d-wave superconductivity.

Direct determination of the electron-phonon coupling matrix element in a correlated system

High-resolution electron energy loss spectroscopy measurements have been carried out on an optimally doped cuprate Bi(2)Sr(2)CaCu(2)O(8+δ). The momentum-dependent energy and linewidth of an A1 optical phonon were obtained. Based on these data as well as detailed knowledge of the electronic structure, we developed a scheme to determine the electron-phonon coupling (EPC) matrix element related to a specific phonon mode. Such an approach is general and applicable to elucidating the full structure of EPC in a system with anisotropic electronic structure.

Dynamic charge inhomogeneity in cuprate superconductors

The inelastic x-ray scattering spectrum for phonons of Δ(1) symmetry, including the CuO bond-stretching phonon dispersion, is analyzed by means of Lorentz fitting for HgBa(2)CuO(4) and Bi(2)Sr(2)CuO(6), using recently calculated phonon frequencies as input parameters. The resulting mode frequencies of the fit are almost all in good agreement with the calculated data. An exception is the case for the second-highest Δ(1) branch compromising the bond-stretching modes, which disagrees for both compounds with the calculations. This branch shows an anomalous softening with a minimum around the wavevector [Formula: see text], at variance with the calculation predictions. Such a disparity with the calculated results, that are based on the assumption of an undisturbed translation and point group invariant electronic structure of the CuO plane, indicates some static charge inhomogeneities in the measured probes. Most likely these will be charge stripes along the CuO bonds which have the strongest coupling to certain longitudinal bond-stretching modes, that in turn self-consistently induce corresponding dynamic charge inhomogeneities. The symmetry breaking by the mix of dynamic and static charge inhomogeneities can lead to a reconstruction of the Fermi surface into small pockets.

Phonon dispersion and anomalies in one-layer high-temperature superconductors

Phonon dynamics, charge response and the phonon density of states are calculated for the high-temperature superconductors HgBa(2)CuO(4) and Bi(2)Sr(2)CuO(6) within a microscopic model for the electronic density response. The results are compared with previous calculations for La(2)CuO(4) and Nd(2)CuO(4). Our main focus is on the phonon anomalies which are connected with the high-frequency oxygen bond-stretching modes (OBSM) found before in our calculations for p-doped La(2)CuO(4) and n-doped Nd(2)CuO(4). We investigate the question if the characteristic softening of the OBSM and the related strong coupling to the electrons is also present in HgBa(2)CuO(4) and Bi(2)Sr(2)CuO(6). In particular, the importance of the contribution of the more delocalized Cu 4s state besides the localized Cu 3d state on the softening is investigated and the different anticrossing behavior due to the presence of several phonon modes with the same symmetry as the OBSM is studied. This makes the identification of the anomalies quite complicated. Furthermore, the influence of electronic polarization processes at ions out of the CuO plane in the ionic layers on the phonon dynamics is calculated. In this context the qualitative type of charge response, i.e. the presence or not of possible metallic charge fluctuations at the Hg or Bi ion, respectively, linked via the apex oxygen to the CuO plane, proves to be very sensitive for certain phonon modes. All the calculations are compared to the experimental results available so far. The latter, however, are rather incomplete for the Hg and Bi compounds.

The phonon dynamics of Sr(2)RuO(4): microscopic calculation and comparison with that of La(2)CuO(4)

The phonon dynamics of the low-temperature superconductor Sr(2)RuO(4) is calculated quantitatively in linear response theory and compared with that of the structurally isomorphic high-temperature superconductor La(2)CuO(4). Our calculation corrects for a typical deficiency of local density approximation-based calculations, which always predict too large an electronic k(z)-dispersion insufficient for describing the c-axis response of real materials. With a more realistic computation of the electronic band structure, the frequency and wavevector dependent irreducible polarization part of the density response function is determined and used for adiabatic and nonadiabatic phonon calculations. Our analysis for Sr(2)RuO(4) reveals important differences from the lattice dynamics of p- and n-doped cuprates. Consistently with experimental evidence from inelastic neutron scattering, the anomalous doping related softening of the strongly coupling high-frequency oxygen bond-stretching modes which is generic for the cuprate superconductors is largely suppressed or completely absent, respectively, depending on the actual value of the on-site Coulomb repulsion of the Ru 4d orbitals. Also the presence of a characteristic Λ(1) mode in La(2)CuO(4) with a very steep dispersion coupled strongly to the electrons is not found for Sr(2)RuO(4). Moreover, we evaluate the possibility of a phonon-plasmon scenario for Sr(2)RuO(4), which has been shown recently to be realistic for La(2)CuO(4). In contrast to the case for La(2)CuO(4), in Sr(2)RuO(4) the plasmons that are very low lying are overdamped along the c-axis.

Angle-resolved photoemission spectroscopy of electron-doped cuprate superconductors: isotropic electron-phonon coupling

We have performed high resolution angle-resolved photoemission (ARPES) studies on electron-doped cuprate superconductors Sm2-xCexCuO4 (x=0.10, 0.15, 0.18), Nd2-xCexCuO4 (x=0.15), and Eu2-xCexCuO4 (x=0.15). Imaginary parts of the electron removal self energy show steplike features due to an electron-bosonic mode coupling. The steplike feature is seen along both nodal and antinodal directions but at energies of 50 and 70 meV, respectively, independent of the doping and rare earth element. Such energy scales can be understood as being due to preferential coupling to half- and full-breathing mode phonons, revealing the phononic origin of the kink structures. Estimated electron-phonon coupling constant lambda from the self energy is roughly independent of the doping and momentum. The isotropic nature of lambda is discussed in comparison with the hole-doped case where a strong anisotropy exists.