Collective nature of spin excitations in superconducting cuprates probed by resonant inelastic x-ray scattering
M. Minola, G. Dellea, H. Gretarsson, Y. Y. Peng, Y. Lu, J. Porras, T. Loew, F. Yakhou, N. B. Brookes, Y. B. Huang, J. Pelliciari, T. Schmitt, G. Ghiringhelli, B… 展开作者
M. Minola, G. Dellea, H. Gretarsson, Y. Y. Peng, Y. Lu, J. Porras, T. Loew, F. Yakhou, N. B. Brookes, Y. B. Huang, J. Pelliciari, T. Schmitt, G. Ghiringhelli, B. Keimer, L. Braicovich, M. Le Tacon
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Supplementary materials are available upon request
We used resonant inelastic x-ray scattering (RIXS) with and without analysis of the scattered photon polarization, to study dispersive spin excitations in the high temperature superconductor YBa2Cu3O6+x over a wide range of doping levels (0.1 < x < 1). The excitation profiles were carefully monitored as the incident photon energy was detuned from the resonant condition, and the spin excitation energy was found to be independent of detuning for all x. These findings demonstrate that the largest fraction of the spin-flip RIXS profiles in doped cuprates arises from magnetic collective modes, rather than from incoherent particle-hole excitations as recently suggested theoretically [Benjamin et al. Phys. Rev. Lett. 112, 247002(2014)]. Implications for the theoretical description of the electron system in the cuprates are discussed.
Tunneling and inelastic neutron scattering (INS) measurements in cuprates are discussed. There is a clear discrepancy among energy-gap values for different 90 K cuprates, inferred from tunneling measurements. By using the phase diagram of hole-doped cuprates we interpret tunneling measurements in 90 K cuprates and INS data in YBCO.
Inelastic Neutron Scattering (INS) data in LSCO, YBCO and Bi2212 are discussed. In the literature, the INS spectra remain far from being comprehensively understood. We show that local (Q-integrated) susceptibility data and the energy dependence of the spin susceptibility at antiferromagnetic vector, Q = (p,p), can be interpreted by using the phase diagram for hole-doped cuprates. We analyze also the origin of the resonant peak which relates to the order parameter for long-range phase coherence in hole-doped cuprates. Thus, we present an interpretation of neutron data in LSCO, YBCO and Bi2212 p…
The tunneling path between the CuO2-layers in cuprate superconductors and a scanning tunneling microscope tip passes through a barrier made from other oxide layers. This opens up the possibility that inelastic processes in the barrier contribute to the tunneling spectra. Such processes cause one or possibly more peaks in the second derivative current-voltage spectra displaced by phonon energies from the density of states singularity associated with superconductivity. Calculations of inelastic processes generated by apical O-phonons show good qualitative agreement with recent experiments report…
We present a low-energy muon-spin-rotation study of the magnetic and superconducting properties of YBa2Cu3O7/PrBa2Cu3O7 trilayer and bilayer heterostructures. By determining the magnetic-field profiles throughout these structures we show that a finite superfluid density can be induced in otherwise semiconducting PrBa2Cu3O7 layers when juxtaposed to YBa2Cu3O7 "electrodes" while the intrinsic antiferromagnetic order is unaffected.
We develop a formalism for calculating resonant inelastic x-ray scattering (RIXS) spectra in systems of itinerant electrons with arbitrary band structures, accounting for the effect of the positively-charged core hole exactly. We apply this formalism to the cuprate superconductors and obtain quantitative agreement with experimental data over a wide range of dopings. We reproduce the dispersing peaks and non-trivial polarization dependence found in RIXS experiments on several materials. Thus we demonstrate that features previously attributed to collective magnetic modes can be explained by band…
The resonant inelastic x-ray scattering spectrum in insulating cuprates is examined by using the exact diagonalization technique on small clusters in the two-dimensional Hubbard model with second and third neighbor hopping terms. When the incident photon energy is tuned near the Cu K absorption edges, we find that the features of the unoccupied upper Hubbard band can be extracted from the spectrum through an anisotropic momentum dependence. They provide an opportunity for the understanding of the different behavior of hole- and electron-doped superconductors.
There are two commonly discussed points of view in theoretical description of cuprate superconductors, (i) Cuprates can be described by the modified t-J model. (ii) Overdoped cuprates are close to the regime of normal Fermi liquid (NFL). We argue that recent resonant inelastic X-ray scattering data challenge both points. While the modified t-J model describes well the strongly underdoped regime, it fails to describe high energy magnetic excitations when approaching optimal doping. This probably indicates failure of the Zhang-Rice singlet picture. In the overdoped regime the momentum-integrated…
We investigate resonant inelastic X-ray scattering (RIXS) at the O $K$-edge in insulating cuprates by means of three methods: cluster perturbation theory (CPT), Hartree--Fock approximation (HFA) and exact diagonalization (ED) method. We consider the three-band Hubbard model and show the overall momentum-dependence of the Zhang--Rice singlet (ZRS) excitation and charge-transfer excitation by the CPT combining with the perturbation scheme. A comparison of the RIXS spectra calculated using CPT and HFA reveals different momentum-dependencies through the changes in the properties of the upper Hubba…
Resonant inelastic x-ray scattering (RIXS) tuned for the Cu L edge is a possible tool to detect charge excitations in cuprate superconductors. We theoretically investigate the possibility for observing a collective charge excitation by the RIXS. The RIXS process via the intermediate state inevitably makes the spectral weight of charge excitation stronger in electron doping than in hole doping. Electron-hole asymmetry also appears in the dynamical charge structure factor, showing a new enhanced small-momentum low-energy mode in electron doping. These facts indicate a possibility of detecting th…
High Tc superconductors show a rich variety of phases associated with their charge degrees of freedom. Valence charges can give rise to charge ordering or acoustic plasmons in these layered cuprate superconductors. While charge ordering has been observed for both hole- and electron-doped cuprates, acoustic plasmons have only been found in electron-doped materials. Here, we use resonant inelastic X-ray scattering (RIXS) to observe the presence of acoustic plasmons in two families of hole-doped cuprate superconductors [La2-xSrxCuO4 (LSCO) and Bi2Sr1.6La0.4CuO6+d (Bi2201)], crucially completing t…
In underdoped cuprate superconductors, a rich competition occurs between superconductivity and charge density wave (CDW) order. Whether rotational symmetry breaking (nematicity) occurs intrinsically and generically or as a consequence of other orders is under debate. Here we employ resonant x-ray scattering in stripe-ordered (La,M)_2CuO_4 to probe the relationship between electronic nematicity of the Cu 3d orbitals, structure of the (La,M)_2O_2 layers, and CDW order. We find distinct temperature dependences for the structure of the (La,M)_2O_2 layers and the electronic nematicity of the CuO_2 …
We report measurements of the current noise generated by the optimally doped, x=0.15, ${\rm Au- La_{2-x}Sr_xCuO_4}$ junctions. For high transmission junctions on (110) surface, we observed split zero-bias conductance peak (ZBCP), accompanied by enhanced shot noise. We attribute the enhanced noise to the Cooper pair transport through the junction. The ZBCP disappears and the noise decreases to the one expected for the charge $e$ with heating at temperatures well below ${\rm T_c}$, and at voltages much smaller than the bulk superconducting gap, setting a new energy scale of 0.5 mV. We attribute …
We present a three-band Hubbard Hamiltonian and the associated Cu K-edge RIXS spectra for electron and hole doped cuprates over a wide range of energy and momentum transfers. By comparing computed spectra for the unfilled case with the corresponding results for 15% electron or hole doping at two different values of the effective Hubbard parameter U, generic signatures of the collapse of the magnetic gap and the characteristic momentum dependencies and evolution of the spectra with doping are identified. Available RIXS data support the gap collapse scenario for electron doped cuprates, but the …
The recent development of x-ray scattering techniques revealed the charge-excitation spectrum in high-$T_c$ cuprate superconductors. While the presence of a dispersive signal in the high-energy charge-excitation spectrum is well accepted in the electron-doped cuprates, its interpretation and universality are controversial. Since charge fluctuations are observed ubiquitously in cuprate superconductors, the understanding of its origin is a pivotal issue. Here, we employ the layered $t$-$J$ model with the long-range Coulomb interaction and show that an acoustic-like plasmon mode with a gap at in-…
The ladder compound Sr$_{14}$Cu$_{24}$O$_{41}$ is of interest both as a quasi-one-dimensional analog of the superconducting cuprates and as a superconductor in its own right when Sr is substituted by Ca. In order to model resonant inelastic x-ray scattering (RIXS) spectra for this compound, we investigate the simpler SrCu$_{2}$O$_{3}$ system in which the crystal structure contains very similar ladder planes. We approximate the LDA dispersion of SrCu$_{2}$O$_{3}$ by a Cu only two-band tight-binding model. Strong correlation effects are incorporated by assuming an anti-ferromagnetic ground state…
We report a Cu K-edge resonant inelastic x-ray scattering (RIXS) study of high-Tc cuprates. Momentum-resolved charge excitations in the CuO2 plane are examined from parent Mott insulators to carrier-doped superconductors. The Mott gap excitation in undoped insulators is found to commonly show a larger dispersion along the [pi,pi] direction than the [pi,0] direction. On the other hand, the resonance condition displays material dependence. Upon hole doping, the dispersion of the Mott gap excitation becomes weaker and an intraband excitation appears as a continuum intensity below the gap at the s…
The spin dynamics of high temperature superconductors measured by inelastic neutron scattering is reviewed. The spin susceptibility evolves a lot with increasing doping from the undoped insulating state to the overdoped metallic state. In the superconducting state, a strong magnetic resonance peak occurs in the spin excitation spectrum whose energy is proportional to the superconducting temperature. In underdoped and optimally doped regimes, normal state antiferromagnetic fluctuations are observed, proving the existence of strong electronic correlations in cuprates. They are characterized by a…
Assuming the exchange of antiferromagnetic spin fluctuations as the Cooper pairing mechanism we calculate the doping dependence of the resonance peak seen in inelastic neutron scattering and the magnetic coherence effect. Most importantly, we find that the resonance peak in the magnetic susceptibility, ${Im}χ({\bf q},ω)$, appears {\it only} in the superconducting state, that it scales with $T_c$, and that magnetic coherence is a result of a d-wave order parameter. We further analyze the structure of ${Im}χ$ below $T_c$, the position of the peak at $ω_{res}$ and the consequences for photoemissi…
Using resonant inelastic x-ray scattering (RIXS) at the Cu $L$-absorption edge, we have observed intense, dispersive spin excitations in highly overdoped Tl$_2$Ba$_2$CuO$_{6+δ}$ (superconducting $T_c =6$ K), a compound whose normal-state charge transport and thermodynamic properties have been studied extensively and shown to exhibit canonical Fermi-liquid behavior. Complementary RIXS experiments on slightly overdoped Tl$_2$Ba$_2$CuO$_{6+δ}$ ($T_c =89$ K) and on Y$_{1-x}$Ca$_{x}$Ba$_2$Cu$_3$O$_{6+δ}$ compounds spanning a wide range of doping levels indicate that these excitations exhibit energi…
Coherence factors are a hallmark of superconductivity as a pair-condensation phenomenon. When electrons pair, quasi-particles develop an acute sensitivity to different types of scattering potential, described by the appearance of coherence factors in the scattering amplitudes. While the effects of coherence factors are well established in isotropic superconductors, they are much harder to detect in their anisotropic counterparts, such as high-Tc cuprates. Here we demonstrate a new approach which highlights the momentum-dependent coherence factors in Ca2-xNaxCuO2Cl2. Using Fourier-transform sca…
By means of resonant inelastic x-ray scattering at the Cu L$_3$ edge, we measured the spin wave dispersion along $\langle$100$\rangle$ and $\langle$110$\rangle$ in the undoped cuprate Ca$_2$CuO$_2$Cl$_2$. The data yields a reliable estimate of the superexchange parameter $J$ = 135 $\pm$ 4 meV using a classical spin-1/2 2D Heisenberg model with nearest-neighbor interactions and including quantum fluctuations. Including further exchange interactions increases the estimate to $J$ = 141 meV. The 40 meV dispersion between the magnetic Brillouin zone boundary points (1/2,\,0) and (1/4,\,1/4) indicat…
We present RIXS data at O K edge from La2-xSrxCuO4 vs. doping between x=0.10 and x=0.22 with attention to the magnetic excitations in the Mid-Infrared region. The sampling done by RIXS is the same as in the undoped cuprates provided the excitation is at the first pre-peak induced by doping. Note that this excitation energy is about 1.5 eV lower than that needed to see bimagnons in the parent compound. This approach allows the study of the upper region of the bimagnon continuum around 450 meV within about one third of the Brilluoin Zone around Γ. The results show the presence of damped bimagnon…
We study the $τ_1$-impurity induced $\mathbf{q}$-space pattern of the energy derivative local density of states (LDOS) in a d-wave superconductor. We are motivated in part by the recent scanning tunneling microscopy (STM) observation of strong gap inhomogeneity with weak charge density variation in Bi$_{2}$Sr$_2$CaCu$_2$O$_{8+δ}$ (BSCCO). The hypothesis is that the gap inhomogeneity might be triggered by the disorder in pair potential. We focus on the effects of electron coupling to various bosonic modes, at the mode energy shifted by the d-wave superconducting gap. The pattern due to a highly…
The recent findings about two distinct quasiparticle inelastic scattering rates in angle-dependent magnetoresistance (ADMR) experiments in overdoped high-$T_c$ cuprates superconductors have motivated many discussions related to the link between superconductivity, pseudogap, and transport properties in these materials. After computing dynamical self-energy corrections in the framework of the $t-J$ model the inelastic scattering rate was introduced as usual. Two distinct scattering rates were obtained showing the main features observed in ADMR experiments. Predictions for underdoped cuprates are…
Recent improvements in instrumentation have established resonant inelastic x-ray scattering (RIXS) as a valuable new probe of the magnetic excitations in the cuprates. This article introduces RIXS, focusing on the Cu $L_3$ resonance, and reviews recent experiments using this technique. These are discussed in light of other experimental probes such as inelastic neutron scattering and Raman scattering. The success of these studies has motivated the development of several new RIXS spectrometers at synchrotrons around the world that promise, among other improvements, 5-10 times better energy resol…
Calculations are presented for electronic Raman scattering and infrared conductivity in a $d_{x^{2}-y^{2}}$ superconductor including the effects of elastic scattering via anisotropic impurities and inelastic spin-fluctuation scattering. A consistent description of experiments on optimally doped Bi-2212 is made possible by considering the effects of correlations on both inelastic and elastic scattering.
Explaining the mechanism of superconductivity in the high-$T_c$ cuprates requires an understanding of what causes electrons to form Cooper pairs. Pairing can be mediated by phonons, the screened Coulomb force, spin or charge fluctuations, excitons, or by a combination of these. An excitonic pairing mechanism has been postulated, but experimental evidence for coupling between conduction electrons and excitons in the cuprates is sporadic. Here we use resonant inelastic x-ray scattering (RIXS) to monitor the temperature dependence of the $\underline{d}d$ exciton spectrum of Bi$_2$Sr$_2$CaCu$_2$O$…
Starting from the generalized t-J-G model Hamiltonian, we analyze the spin response in the superconducting cuprates taking into account both local and itinerant spin components which are coupled to each other self-consistently. Derived expression reproduces the basic observations of neutron scattering data in YBa2Cu3O6+y compounds near the optimal doping level.
Nematicity is ubiquitous in electronic phases of high-$T_c$ superconductors, particularly in the Fe-based systems. We used inelastic x-ray scattering to extract the temperature-dependent nematic correlation length $ξ$ from the anomalous softening of acoustic phonon modes in FeSe, underdoped Ba(Fe$_{0.97}$Co$_{0.03}$)$_2$As$_2$ and optimally doped Ba(Fe$_{0.94}$Co$_{0.06}$)$_2$As$_2$. In all cases, we find that $ξ$ is well described by a power law $(T-T_0)^{-1/2}$ extending over a wide temperature range. We attributed this mean-field behavior and the extended fluctuation regime to a sizable nem…
We investigate the low energy acoustical and optical modes in $\mathrm{HgBa_2CuO_{4+δ}}$ using inelastic x-ray scattering (IXS). The experimental phonon dispersion and the dynamical structure factor are compared with an atomic shell model, and the set of the atomic potentials obtained are discussed. Our results are also compared with those obtained by Raman spectroscopy and with density-of-state data measured by inelastic neutron scattering.
The $t-U-V-J$ model is used to describe the positions of the experimental peaks associated with commensurate and incommensurate structure of the magnetic susceptibility probed by neutron scattering in cuprate compounds. Assuming that the tight-binding form of the mean-field electron energy and the maximum gap can be obtained by fitting the angle-resolved photoemission spectroscopy (ARPES) data, we have determined the strengths of the on-site repulsive interaction $U$, the spin-independent attractive interaction $V$ and the spin-dependent antiferromagnetic interaction $J$ from the positions of …
Inelastic x-ray scattering (IXS) with very high (meV) energy resolution has become a valuable spectroscopic tool, complementing the well established coherent inelastic neutron scattering (INS) technique for phonon dispersion investigations. In the study of crystalline systems IXS is a viable alternative to INS, especially in cases where only small samples are available. Using IXS, we have measured the phonon dispersion of Nd_{1.86}Ce_{0.14}CuO_{4+δ} along the [x,0,0] and [x,x,0] in-plane directions. Compared to the undoped parent compound, the two highest longitudinal optical (LO) phonon branc…
We present calculations for resonant inelastic x-ray scattering (RIXS) in edge-shared copper oxide systems, such as CuGeO$_{3}$ and Li$_{2}$CuO$_{2}$, appropriate for hard x-ray scattering where the photoexcited electron lies above oxygen 2p and copper 3d orbital energies. We perform exact diagonalizations of the multi-band Hubbard and determine the energies, orbital character and resonance profiles of excitations which can be probed via RIXS. We find excellent agreement with recent results on Li$_{2}$CuO$_{2}$ and CuGeO$_{3}$ in the 2-7 eV photon energy loss range.
We assess the capabilities of magnetic Resonant Inelastic X-ray Scattering (RIXS) at the O $K$ edge in undoped cuprates by taking La_{2}CuO_{4} as a benchmark case, based on a series of RIXS measurements that we present here. By combining the experimental results with basic theory we point out the fingerprints of bimagnon in the O $K$ edge RIXS spectra. These are a dominant peak around 450 meV, the almost complete absence of dispersion both with $π$ and $σ$ polarization and the almost constant intensity vs. the transferred momentum with $σ$ polarization. This behavior is quite different from C…
This article summarizes and extends the recent developments in the microscopic modeling of the magnetic excitations in cuprate two-leg ladder systems. The microscopic Hamiltonian comprises dominant Heisenberg exchange terms plus an additional four-spin interaction which is about five times smaller. We give an overview over the relevant energies like the one-triplon dispersion, the energies of two-triplon bound states and the positions of multi-triplon continua and over relevant spectral properties like spectral weights and spectral densities in the parameter regime appropriate for cuprate syst…
We present GW based self-energy calculations for the state of coexisting spin-density wave and d-wave superconductivity in a series of cuprate superconductors. In these systems, the spin resonance spectrum exhibits the typical `hour-glass' form, whose upward and downward dispersion branches come from the gapped spin-wave and magnetic scattering of Cooper pairs, respectively. We show that the crossover between these two different dispersion features leads to an abrupt change in slope in the quasiparticle self-energy, and hence the low-energy kink commences in the single-particle quasiparticle s…
The Cu K-edge resonant inelastic x-ray scattering (RIXS) spectrum in one-dimensional insulating cuprates is theoretically examined by using the exact diagonalization technique for the extended one-dimensional Hubbard model with nearest neighbor Coulomb interaction. We find the following characteristic features that can be detectable by RIXS experiments: (i) The spectrum with large momentum transfer indicates the formation of excitons, i.e., bound states of holon and doublon. (ii) The spectrum with small momentum transfer depends on the incident photon energy. We propose that the RIXS provides …
We report on the phase diagram of antiferromagnetism (AFM) and superconductivity (SC) in three-layered Ba_2Ca_2Cu_3O_6(F,O)_2 by means of Cu-NMR measurements. It is demonstrated that AFM and SC uniformly coexist in three-layered compounds as well as in four- and five-layered ones. The critical hole density p_c for the long range AFM order is determined as p_c ~ 0.075, which is larger than p_c ~ 0.02 and 0.055 in single- and bi-layered compounds, and smaller than p_c ~ 0.08-0.09 and 0.10-0.11 in four- and five-layered compounds, respectively. This variation of p_c is attributed to the magnetic …
In the present work we address a long standing problem of the magnetic ground state and magnetic excitations in underdoped cuprates. Modelling cuprates by the extended $t-J$ model we show that there is a hidden dimensionless parameter $λ$ which drives magnetic criticality at low doping $x$. Hence we derive the zero temperature $λ-x$ phase diagram of the model. It is argued that all underdoped cuprates are close to the quantum tricritical point $x=0$, $λ=1$. The three phases "meet" at the tricritical point: (i) Néel antiferromagnet, (ii) spin spiral with antinodal direction of the spiral wave v…
We report thermopower measurements under hydrostatic pressure on the cuprate superconductor La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ (Nd-LSCO), at low-temperature in the normal state accessed by suppressing superconductivity with a magnetic field up to $H = 31$ T. Using a newly developed AC thermopower measurement technique suitable for high pressure and high field, we track the pressure evolution of the Seebeck coefficient $S$. At ambient pressure and low temperature, $S/T$ was recently found to suddenly increase in Nd-LSCO at the pseudogap critical doping $p^{\star} = 0.23$, consistent with a dro…
The discovery of infinite-layer nickelate superconductors has spurred enormous interest. While the Ni$^{1+}$ cations possess nominally the same 3$d^9$ configuration as Cu$^{2+}$ in cuprates, the electronic structure variances remain elusive. Here, we present a soft x-ray photoemission spectroscopy study on parent and doped infinite-layer Pr-nickelate thin films with a doped perovskite reference. By identifying the Ni character with resonant photoemission and comparison to density functional theory + U (on-site Coulomb repulsion energy) calculations, we estimate U ~5 eV, smaller than the charge…
The relevance of magnetism for the mechanism responsible for high-temperature superconductivity remains an open and still interesting issue. The observation by inelastic neutron scattering of strong antiferromagnetic dynamical correlations in superconducting cuprates is discussed in relation to the unusual physical properties of the cuprates as well as in relation to the superconducting pairing.
The magnetic excitations in the superconducting electron-doped cuprates are studied in the framework of spin-density-wave description. The superconducting resonance is a natural product of the superconductivity due to the opening of d-wave gap. Its resonance energy exhibits well linear scaling with superconducting gap as $E_{res}/2Δ\sim 0.6$, quantitatively consisting with the experimental discovery. This ratio is insensitive to the selected parameters, manifesting its universality. Another lower-energy peak below resonance energy is predicted when the hole pocket emerges due to suppression of…
Quantum critical behavior of cuprate superconductors observed by inelastic X-ray scattering
National Synchrotron Radiation Research Center（国家同步辐射研究中心）；Center for Quantum Science and Technology and Department of Physics, National Tsing Hua University（国立清华大学量子科学与技术中心及物理系）；Central Research Institute of Electric Power Industry（电力研究院）；Institute of Physics, Academia Sinica（中央研究院物理研究所）；Department of Physics, National Tsing Hua University（国立清华大学物理系）；Department of Physics, University of Tokyo（东京大学物理系）；Department of Electrophysics, National Yang Ming Chiao Tung University（国立阳明交通大学电子物理系）
We report the first measurement of collective charge modes of insulating Sr14Cu24O41 using inelastic resonant x-ray scattering over the complete Brillouin zone. Our results show that the intense excitation modes at the charge gap edge predominantly originate from the ladder-containing planar substructures. The observed ladder modes (E vs. Q) are found to be dispersive for momentum transfers along the "legs" but nearly localized along the "rungs". Dispersion and peakwidth characteristics are similar to the charge spectrum of 1D Mott insulators, and we show that our results can be understood in …
Measurements of spin excitations are essential for an understanding of spin-mediated pairing for superconductivity; and resonant inelastic X-ray scattering (RIXS) provides a considerable opportunity to probe high-energy spin excitations. However, whether RIXS correctly measures the collective spin excitations of doped superconducting cuprates remains under debate. Here we demonstrate distinct Raman- and fluorescence-like RIXS excitations of Bi$_{1.5}$Pb$_{0.6}$Sr$_{1.54}$CaCu$_{2}$O$_{8+δ}$ in the mid-infrared energy region. Combining photon-energy and momentum dependent RIXS measurements with…
We identify a new kind of elementary excitations, spin-rotons, in the doped Mott insulator. They play a central role in deciding the superconducting transition temperature Tc, resulting in a simple Tc formula,Tc=Eg/6, with Eg as the characteristic energy scale of the spin rotons. We show that the degenerate S=1 and S=0 rotons can be probed by neutron scattering and Raman scattering measurements, respectively, in good agreement with the magnetic resonancelike mode and the Raman A1g mode observed in the high-Tc cuprates.
Polarized neutron scattering experiments on the slightly overdoped superconductor Ba$_{0.5}$K$_{0.5}$Fe$_2$As$_2$ reveal broad magnetic resonance scattering peaking at approximately 15 meV. In spite of doping far beyond the suppression of magnetic order, this compound exhibits dispersive and anisotropic magnetic excitations. At energies below the resonance maximum, magnetic correlations polarized parallel to the layers but perpendicular to the propagation vector are reduced by a factor two compared to those in the two orthogonal directions; in contrast correlations at the peak maximum are isot…
The coupling between lattice vibration quanta and valence electrons can induce charge density modulations and decisively influence the transport properties of materials, e.g. leading to conventional superconductivity. In high critical temperature superconductors, where electronic correlation is the main actor, the actual role of electron-phonon coupling (EPC) is being intensely debated theoretically and investigated experimentally. We present an in-depth study of how the EPC strength can be obtained directly from resonant inelastic x-ray scattering (RIXS) data through the theoretical approach …
A new generation of angular-resolved photoemission spectroscopy (ARPES) measurements on the cuprate superconductors offer the promise of enhanced momentum and energy resolution. In particular, the energy and temperature dependence of the on-shell nodal (k_x=k_y) quasiparticle scattering rate can be studied. In the superconducting state, low temperature transport measurements suggest that one can describe nodal quasiparticles within the framework of a BCS d-wave model by including forward elastic scattering and spin-fluctuation inelastic scattering. Here, using this model, we calculate the temp…
Spin excitations in the overdoped high temperature superconductors Tl$_2$Ba$_2$CuO$_{6+δ}$ and (Bi,Pb)$_2$(Sr,La)$_{2}$CuO$_{6+δ}$ were investigated by resonant inelastic x-ray scattering (RIXS) as functions of doping and detuning of the incoming photon energy above the Cu-$L_3$ absorption peak. The RIXS spectra at optimal doping are dominated by a paramagnon feature with peak energy independent of photon energy, similar to prior results on underdoped cuprates. Beyond optimal doping, the RIXS data indicate a sharp crossover to a regime with a strong contribution from incoherent particle/hole e…
We examine the influence of coupling between particle-hole and particle-particle spin fluctuations on the inelastic neutron scattering resonance (INSR) in cuprate superconductors in both weak and strong interaction limits. For weak-interactions in the particle-hole channel, we find that the interchannel coupling can eliminate the resonance. For strong interactions which drive the system close to a $\bm{Q}=(π,π)$ magnetic instablity, the resonance frequency always approaches zero but its value is influenced by the interchannel coupling. We comment on constraints imposed on cuprate physics by th…
The memory function approach to spin dynamics in doped antiferromagnetic insulator combined with the assumption of temperature independent static spin correlations and constant collective mode damping leads to omega/T scaling in a broad range. The theory involving a non universal scaling parameter is used to analyze recent inelastic neutron scattering results for underdoped cuprates. Adopting modified damping function also the emerging central peak in low-doped cuprates at low temperatures can be explained within the same framework.
Probing d-wave superconducting gap of high-$T_\mathrm{c}$ cuprate $\mathrm{Bi}_2\mathrm{Sr}_2\mathrm{Ca}_2\mathrm{Cu}_3\mathrm{O}_{10+δ}$ by resonant inelastic X-ray scattering
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；Diamond Light Source（英国钻石光源）；Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理北京实验室）；Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）；School of Nuclear Science and Technology, University of Science and Technology of China（中国科学技术大学核科学技术学院）
We explore the combined pressure and finite-size effects on the in-plane penetration depth λ_{ab} in YBa_2Cu_4O_8. Even though this cuprate is stoichiometric the finite-size scaling analysis of λ_{ab}^{-2}(T) uncovers the granular nature and reveals domains with nanoscale size L_{c} along the c-axis. L_{c} ranges from 33.2 Angstrom to 28.9 Angstrom at pressures from 0.5 to 11.5 kbar. These observations raise serious doubts on the existence of a phase coherent macroscopic superconducting state in cuprate superconductors.
We measured high resolution Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS) of the undoped cuprates La$_2$CuO$_4$, Sr$_2$CuO$_2$Cl$_2$, CaCuO$_2$ and NdBa$_2$Cu$_3$O$_6$. The dominant spectral features were assigned to $dd$ excitations and we extensively studied their polarization and scattering geometry dependence. In a pure ionic picture, we calculated the theoretical cross sections for those excitations and used them to fit the experimental data with excellent agreement. By doing so, we were able to determine the energy and symmetry of Cu-3$d$ states for the four systems with unpre…
Results of resonant inelastic X-ray scattering (RIXS) measurements at Fe L-edges and electronic structure calculations of LiFeAs and NaFeAs are presented. Both experiment and theory show that in the vicinity of the Fermi energy, the density of states is dominated by contributions from Fe 3d-states. The comparison of Fe L2,3 non-resonant and resonant (excited at L2-threshold) X-ray emission spectra with spectra of LaOFeAs and CaFe2As2 show a great similarity in energy and I(L2)/I(L3) intensity ratio. The I(L2)/I(L3) intensity ratio of all FeAs-based superconductors is found to be more similar t…
Within a model that supports stripe spin and charge order coexisting with a d$_{x^2-y^2}$-wave superconducting phase, we study the self-consistently obtained electronic structure and the associated transverse dynamical spin susceptibility. In the coexisting phase of superconducting and static stripe order, the resulting particle-hole continuum can strongly damp parts of the low-energy spin wave branches. This provides insight into recent inelastic neutron scattering data revealing the dispersion of the low-energy collective magnetic modes of lanthanum based cuprate superconductors.
