Charge Order Lock-in by Electron-Phonon Coupling in La$_{1.675}$Eu$_{0.2}$Sr$_{0.125}$CuO$_4$
Qisi Wang, K. von Arx, M. Horio, D. John Mukkattukavil, J. Küspert, Y. Sassa, T. Schmitt, A. Nag, S. Pyon, T. Takayama, H. Takagi, M. Garcia-Fernandez, Ke-Jin Zhou, J. Chang
We report an ultrahigh resolution resonant inelastic x-ray scattering (RIXS) study of the in-plane bond-stretching phonon mode in stripe-ordered cuprate La$_{1.675}$Eu$_{0.2}$Sr$_{0.125}$CuO$_4$. Phonon softening and lifetime shortening are found around the charge ordering wave vector. In addition to these self-energy effects, the electron-phonon coupling is probed by its proportionality to the RIXS cross section. We find an enhancement of the electron-phonon coupling around the charge-stripe ordering wave vector upon cooling into the low-temperature tetragonal structure phase. These results suggest that in addition to electronic correlations, electron-phonon coupling contributes significantly to the emergence of long-range charge-stripe order in cuprates.
The dispersion of the Cu-O bond-stretching vibrations in overdoped La$_{1.7}$Sr$_{0.3}$CuO$_4$ (not superconducting) has been studied by high resolution inelastic neutron scattering. It was found that the doping-induced renormalization of the so-called breathing and the half-breathing modes is larger than in optimally doped La$_{1.85}$Sr$_{0.15}$CuO$_4$. On the other hand, the phonon linewidths are generally smaller in the overdoped sample. Features observed in optimally doped La$_{1.85}$Sr$_{0.15}$CuO$_4$ which suggest a tendency towards charge stripe formation are absent in overdoped La$_{1.…
To study the rare-earth doping effect on the phonon heat transport of La-based cuprates and shed light on the mechanism of phonon scattering, both $ab$-plane and c-axis thermal conductivities ($κ_{ab}$ and $κ_c$) are measured for La$_{2-y}$Eu$_y$CuO$_4$ ($y$ = 0, 0.02 and 0.2) and La$_{1.88-y}$Eu$_y$Sr$_{0.12}$CuO$_4$ ($y$ = 0 and 0.2) single crystals. It is found that the phonon peak (at 20 -- 25 K) in $κ_{ab}(T)$ of La$_{2-y}$Eu$_y$CuO$_4$ shows an anomalous Eu-doping dependence: it completely disappears for $y$ = 0.02, which is discussed to be due to the local lattice distortions around Eu …
The thermal conductivity of the antiferromagnet Nd$_2$CuO$_4$ was measured down to 50 mK. Using the spin-flop transition to switch on and off the acoustic Nd magnons, we can reliably separate the magnon and phonon contributions to heat transport. We find that magnons travel ballistically below 0.5 K, with a thermal conductivity growing as $T^3$, from which we extract their velocity. We show that the rate of scattering of acoustic magnons by phonons grows as $T^3$, and the scattering of phonons by magnons peaks at twice the average Nd magnon frequency.
In this Comment, we show that the experimental data reported by Li {\it et al.} (Phys. Rev. B {\bf 77}, 134501 (2008)) do not support the phonon specular reflection at low temperatures for high-T_c cuprates, because the phonon mean free path \ell calculated from their thermal conductivity data is much smaller than the averaged sample width above \sim 100 mK for both Nd_{2}CuO_{4} and YBa_{2}Cu_{3}O_{6.0} single crystals.
In their comment \cite{Sun} on our study of phonon heat transport in Nd$_2$CuO$_4$ \cite{Li}, Sun and Ando estimate that the phonon mean free path at low temperature is roughly half the width of the single crystal used in our study, from which they argue that phonon scattering cannot be dominated by sample boundaries. Here we show that their use of specific heat data on Nd$_2$CuO$_4$, which contains a large magnetic contribution at low temperature that is difficult to reliably extract, leads to an underestimate of the mean free path by a factor two compared to an estimate based on the specific…
This paper has been withdrawn by the authors, because we had probably observed some spurious intensity with x=0.29 sample (Fig.3(b)). This came out after further studies of the detailed x-dependence of the highest energy LO phonon branch in LSCO.
The phonon dispersions of $\mathrm{Nd_{1.86}Ce_{0.14}CuO_{4+δ}}$ along the $[ξ,0,0]$ direction have been determined by inelastic x-ray scattering. Compared to the undoped parent compound, the two highest longitudinal phonon branches, associated with the Cu-O bond-stretching and out-of-plane oxygen vibration, are shifted to lower energies. Moreover, an anomalous softening of the bond-stretching band is observed around $\mathbf{q}=(0.2,0,0)$. These signatures provide evidence for strong electron-phonon coupling in this electron-doped high-temperature superconductor.
We present a comparative experimental and theoretical investigation of the two--dimensional charge-transfer gap in the strongly correlated material Sr$_2$CuO$_2$Cl$_2$. We observe an Urbach behaviour in the absorption profile over a surprisingly wide range of energies and temperatures. We present a model that accounts for phonon scattering to infinite order and which allows us to explain the data accurately by assuming coupling of the charge transfer gap exciton to lower energy electronic excitations.
Phonons in nearly optimally doped HgBa$_2$CuO$_{4+δ}$ were studied by inelastic X-ray scattering. The dispersion of the low energy modes is well described by a shell model, while the Cu-O bond stretching mode at high energy shows strong softening towards the zone boundary, which deviates strongly from the model. This seems to be common in the hole-doped high-$T_\mathrm{c}$ superconducting cuprates, and, based on this work, not related to a lattice distortion specific to each material.
The heat carriers responsible for the unexpectedly large thermal Hall conductivity of the cuprate Mott insulator La$_2$CuO$_4$ 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 - Nd$_2$CuO$_4$ and Sr$_2$CuO$_2$Cl$_2$ - and show that two potential mechanisms can be excluded - the scattering of phonons by rare-earth impurities and by structural domains. Ou…
We use inelastic neutron scattering to study the evolution of the generalized phonon density of states (GDOS) of the $n$-type high-$T_c$ superconductor Nd$_{2-x}$Ce$_x$CuO$_{4+δ}$ (NCCO), from the half-filled Mott-insulator ($x=0$) to the $T_c=24$ K superconductor ($x=0.15$). Upon doping the CuO$_2$ planes in Nd$_2$CuO$_{4+δ}$ (NCO) with electrons by Ce substitution, the most significant change in the GDOS is the softening of the highest phonon branches associated with the Cu-O bond stretching and out-of-plane oxygen vibration modes. However, the softening occurs within the first few percent o…
We investigate the hole and lattice dynamics in a prototypical high temperature superconducting system La{2-x}Sr{x}CuO{4} using infrared spectroscopy. By exploring the anisotropy in the electronic response of CuO2 planes we show that our results support the notion of stripes. Nevertheless, charge ordering effects are not apparent in the phonon spectra. All crystals show only the expected infrared active modes for orthorhombic phases without evidence for additional peaks that may be indicative of static charge ordering. Strong electron-phonon interaction manifests itself through the Fano linesh…
Although all superconducting cuprates display charge-ordering tendencies, their low-temperature properties are distinct, impeding efforts to understand the phenomena within a single conceptual framework. While some systems exhibit stripes of charge and spin, with a locked periodicity, others host charge density waves (CDWs) without any obviously related spin order. Here we use resonant inelastic x-ray scattering (RIXS) to follow the evolution of charge correlations in the canonical stripe ordered cuprate La$_{1.875}$Ba$_{0.125}$CuO$_{4}$ (LBCO~$1/8$) across its ordering transition. We find tha…
We reinterpret neutron scattering and Raman spectroscopy experiments in La(2-x)Sr(x)CuO(4), showing modulation of spin and lattice degrees of freedom both in the low-temperature orthorhombic and tetragonal phases, in terms of a magneto-elastic coupling between noncollinear configurations for the copper spins and the oxygen octahedra. The magneto-elastic coupling furthermore explains the recently discovered magnetic-field induced untwinning in La(2-x)Sr(x)CuO(4), for x<2%, and allows us to understand why in La(2-x-y)Sr(x)Nd(y)CuO(4) with y=0.4 and x=1/8, for example, when (1,0) and/or (0,1) sta…
The phonon densities-of-states of La(1.475)Nd(0.4)Sr(0.125)CuO(4) and La(1.9)Sr(0.1)CuO(4) were measured using inelastic neutron scattering. The ~70 meV phonon band which appears due to hole doping in La(1.9)Sr(0.1)CuO(4) is known to arise from strong electron-lattice coupling. This phonon band is strongly suppressed in the Nd-doped compound for which T_c is also suppressed, establishing a link between in-plane oxygen optical phonons and superconductivity. This suppression is attributed to hole localization which becomes strong near the stripe ordering condition of certain cuprates near x=1/8 …
Using resonant X-ray diffraction and Raman spectroscopy, we study charge correlations and lattice dynamics in two model cuprates, HgBa$_{2}$CuO$_{4+δ}$ and HgBa$_{2}$CaCu$_{2}$O$_{6+δ}$. We observe a maximum of the characteristic charge order temperature around the same hole concentration ($p \approx 0.09$) in both compounds, and concomitant pronounced anomalies in the lattice dynamics that involve the motion of atoms in and/or adjacent to the CuO$_2$ layers. These anomalies are already present at room temperature, and therefore precede the formation of the static charge correlations, and we a…
We present a comprehensive study of the phonon dispersion in an underdoped, superconducting Ca$_{2-x}$CuO$_2$Cl$_2$ crystal. We interpret the results using lattice dynamical calculations based on a shell model, and we compare the results, to other hole-doped cuprates, in particular to the ones isomorphic to La$_{2-x}$Sr$_x$CuO$_4$ (LSCO). We found that an anomalous dip in the Cu-O bond stretching dispersion develops in oxychlorides with a simultaneous marked broadening of the mode. The broadening is maximum at $\approx (π/ (2a) ~ 0 ~ 0)$ that corresponds to the charge-modulations propagation v…
The strength of the electron-phonon coupling parameter and its evolution throughout a solid's phase diagram often determines phenomena such as superconductivity, charge- and spin-density waves. Its experimental determination relies on the ability to distinguish thermally activated phonons from those emitted by conduction band electrons, which can be achieved in an elegant way by ultrafast techniques. Separating the electronic from the out-of-equilibrium lattice subsystems, we probed their re-equilibration by monitoring the transient lattice temperature through femtosecond X-ray diffraction in …
The cuprates exhibit a prominent charge-density-wave (CDW) instability with wavevector along [100], i.e., the Cu-O bond direction. Whereas CDW order is most prominent at moderate doping and low temperature, there exists increasing evidence for dynamic charge correlations throughout a large portion of the temperature-doping phase diagram. In particular, signatures of incipient charge order have been observed as phonon softening and/or broadening near the CDW wavevector approximately half-way through the Brillouin zone. Most of this work has focused on moderately-doped cuprates, for which the CD…
In superconducting copper oxides some Cu-O bond-stretching phonons around 70meV show anomalous giant softening and broadening of electronic origin and electronic dispersions have large renormalization kinks near the same energy. These observations suggest that phonon broadening originates from quasiparticle excitations across the Fermi surface and the electronic dispersion kinks originate from coupling to anomalous phonons. We measured the phonon anomaly in underdoped (x=0.05) and overdoped (x=0.20,0.25) La$_{2-x}$Sr$_x$CuO$_4$ by inelastic neutron and x-ray scattering with high resolution. Co…
Soft phonons and diffuse scattering in insulating La$_{2-x}$Sr$_{x}$CuO$_4$ ($x=0.05$) have been studied by the neutron scattering technique. The X-point phonon softens from high temperature towards the structural transition temperature $T_{s}=410$ K, and the Z-point phonon softens again below 200 K. The Z-point phonon softening persists to low temperature, in contrast to the behavior observed in the superconducting $x=0.15$ compound, in which the Z-point phonon hardens below $T_c$. The diffuse scattering associated with the structural phase transition at 410 K appears at commensurate position…
We use quantum Monte Carlo methods and single-mode approximation to study the magnon dispersion in the 2D half-filled Hubbard and phonon-coupled Heisenberg models. We find that in the Hubbard model with $U/t< 8$, high-energy magnon dispersion is similar to those observed in inelastic neutron scattering experiments in ${La}_2{CuO}_4$. On the other hand, our studies of a 2D Heisenberg model coupled to dynamic optical bond phonons, fails to reproduce the experimental dispersion. These results can be interpreted as evidence for intermediate $U/t$ and charge fluctuations in the cuprate materials.
The nature of the pseudogap phase of cuprates remains a major puzzle. One of its new signatures is a large negative thermal Hall conductivity $κ_{\rm xy}$, which appears for dopings $p$ below the pseudogap critical doping $p^*$, but whose origin is as yet unknown. Because this large $κ_{\rm xy}$ is observed even in the undoped Mott insulator La$_2$CuO$_4$, it cannot come from charge carriers, these being localized at $p = 0$. Here we show that the thermal Hall conductivity of La$_2$CuO$_4$ is roughly isotropic, being nearly the same for heat transport parallel and normal to the CuO$_2$ planes,…
Inelastic neutron scattering has been used to study the in-plane Cu-O bond-stretching mode in oxygen doped La$_{1.94}$Sr$_{0.06}$CuO$_{4.035}$ ($T_c = 38\,\text{K}$) and La$_2$CuO$_{4+δ}$ ($T_c = 43\,\text{K}$). Similar to results from optimally doped La$_{1.85}$Sr$_{0.15}$CuO$_4$ ($T_c = 35\,\text{K}$), we observe anomalous features in the dispersion of this half-breathing mode in the form of a softening halfway through the Brillouin Zone. Considering the differences in electronic structure and local environment between the oxygen- and strontium-doped compounds with similar $T_\text{c}$, we r…
We measure the dispersion of the Cu-O bond-stretching phonon mode in the high-temperature superconducting parent compound Ca$_2$CuO$_2$Cl$_2$. Our density functional theory calculations predict a cosine-shaped bending of the dispersion along both the ($ξ$00) and ($ξξ$0) directions, while comparison with previous results on Ca$_{1.84}$CuO$_2$Cl$_2$ show it only along ($ξ$00), suggesting an anisotropic effect which is not reproduced in calculation at optimal doping. Comparison with isostructural La$_{2-x}$Sr$_x$CuO$_4$ suggests that these calculations reproduce well the overdoped regime, however…
The magnetic-field (H) dependence of the thermal conductivity κof Pr_{1.3}La_{0.7}CuO_4 is found to show a pronounced minimum for in-plane fields at low temperature, which is best attributed to the scattering of phonons by free spins that are seen by a Schottky-type specific heat and a Curie-Weiss susceptibility. Besides pointing to a strong spin-phonon coupling in cuprates, the present result demonstrates that the H-dependence of the phonon heat transport should not be naively neglected when discussing the κ(H) behavior of cuprates, since the Schottky anomaly is ubiquitously found in cuprates…
Both ab-plane and c-axis thermal conductivities ($κ_{ab}$ and $κ_c$) of lightly doped La$_{2-x}$Sr$_x$CuO$_4$ and La$_2$Cu$_{1-y}$Zn$_y$O$_4$ single crystals ($x$ or $y$ = 0 -- 0.04) are measured from 2 to 300 K. It is found that the low-temperature phonon peak (at 20 -- 25 K) is significantly suppressed upon Sr or Zn doping even at very low doping, though its precise doping dependences show interesting differences between the Sr and Zn dopants, or between the $ab$ plane and the c axis. Most notably, the phonon peak in $κ_c$ decreases much more quickly with Sr doping than with Zn doping, while…
We report high-resolution inelastic x-ray scattering measurements of the acoustic phonons in the single-layer cuprate $Bi_{2}Sr_{2-x)La_{x}CuO_{6+δ}$. These measurements reveal anomalous broadening of the longitudinal acoustic phonon near the (1/4,1/4,0) wavevector. The observed wavevector and its doping dependence indicate the coupling of the phonons to an underlying electronic density wave state. In addition, a comparison of the scattered intensities for x-ray energy-gain and x-ray energy-loss indicates that both time-reversal and inversion symmetries are broken in the material. Upon cooling…
The microscopic understanding of high-temperature superconductivity in cuprates has been hindered by the apparent complexity of crystal structures in these materials. We used scanning tunneling microscopy and spectroscopy to study an electron-doped copper oxide compound Sr$_{1-x}$Nd$_x$CuO$_2$ that has only bare cations separating the CuO$_2$ planes and thus the simplest infinite-layer structure among all cuprate superconductors. Tunneling conductance spectra of the major CuO$_2$ planes in the superconducting state revealed direct evidence for a nodeless pairing gap, regardless of variation of…
Reflectance measurements in properly selected samples of Nd$_{1.96}$Ce$_{0.04}$CuO$_{4+y}$ with different carrier concentrations provide a firm evidence of Fano antiresonances for the four transverse optical $E_u$ phonons in the $a-b$ plane. Fits performed without any previous subtraction of the electronic background, as well as the dependence on temperature of the renormalized phonon frequencies, show that the electronic continuum repsonsible for the Fano effect is the polaron band found in all parent compounds of high-T$_c$ superconductors.
We find excitations lower in energy than known phonon modes in underdoped La$\_{2-x}$Sr$\_x$CuO$\_{4+δ}$ (x=0.08), with both inelastic X-Ray scattering (IXS) and inelastic neutron scattering (INS). A non dispersive excitation at 9 meV is identified and is also seen by INS in (La,Nd)$\_{2-x}$Sr$\_x$CuO$\_{4+δ}$, with 40$\%$ Nd substitution. INS also identifies a still lower energy dispersive mode at low q in the Nd free sample. These modes are clearly distinct from the longitudinal acoustic phonon and correspond in energy to the Zone Centre modes measured by optical spectroscopy and associated …
Soft phonon behavior associated with a structural phase transition from the low-temperature-orthorhombic (LTO) phase ($Bmab$ symmetry) to the low-temperature-tetragonal (LTT) phase ($P4_{2}/ncm$ symmetry) was investigated in La$_{1.875}$Ba$_{0.125}$CuO$_{4}$ using neutron scattering. As temperature decreases, the TO-mode at $Z$-point softens and approaches to zero energy around $T_{\rm d2}=62$ K, where the LTO -- LTT transition occurs. Below $T_{\rm d2}$, the phonon hardens quite rapidly and it's energy almost saturates below 50 K. At $T_{\rm d2}$, the energy dispersion of the soft phonon alon…
We have identifies the otical phonon modes of the superconducting infinite-layer compounds Sr$_{0.9}Ln_{0.1}$CuO$_2$ ($Ln$ = La, Gd, Sm; $T_c$ = 43 K for all) from their infrared reflectivity spectra obtained with a Fourier-transform infrared spectrometer on high-quality high-purity samples synthesized under high pressure. The La- and the Gd-doped compounds exhibited only four (2$A_{\rm 2u}$+2$E_{\rm u}$) out of the five (2$A_{\rm 2u}$+3$E_{\rm u}$) infrared-active phonon modes predicted by a group theoretical analysis whereas the Sm-doped compound exhibited all five modes. We propose the atom…
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 phononanomalies 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 characteristi…
We present time-of-fight neutron-scattering measurements on single crystals of $La_{2-x}Ba_{x}CuO_{4}$ (LBCO) with 0 $\leq$ x $\leq$ 0.095 and $La_{2-x}Sr_{x}CuO_{4}$ (LSCO) with x = 0.08 and 0.11. This range of dopings spans much of the phase diagram relevant to high temperature cuprate superconductivity, ranging from insulating, three dimensional (3D) commensurate long range antiferromagnetic order, for x $\leq$ 0.02, to two dimensional (2D) incommensurate antiferromagnetism co-existing with superconductivity for x $\geq$ 0.05. Previous work on lightly doped LBCO with x = 0.035 showed a clea…
We present time-of-flight inelastic neutron scattering measurements of $La_{1.965}Ba_{0.035}CuO_{4}$ (LBCO), a lightly doped member of the high temperature superconducting La-based cuprate family. By using time-of-flight neutron instrumentation coupled with single crystal sample rotation we obtain a four-dimensional data set (three {\bf Q} and one energy) that is both comprehensive and spans a large region of reciprocal space. Our measurements identify rich structure in the energy dependence of the highly dispersive spin excitations, which are centered at equivalent ($\frac{1}{2},\frac{1}{2}, …
The representative cuprate, La$_{2-x}$M$_x$CuO$_4$, with M = Sr and $x = 1/8$ is studied via first-principles calculations in the high-temperature tetragonal (HTT), low-temperature orthorhombic (LTO), and low-temperature less-orthorhombic (LTLO) structures. By suppressing the magnetism and superconductivity, the LTLO phase, which has rarely been observed in La$_{2-x}$Sr$_x$CuO$_4$, is found to be the ground state, where the structural phase transitions, HTT$\rightarrow$LTO$\rightarrow$LTLO, can be understood via phonon instability. While the La-O composition is identified to be responsible for…
Despite the intensive efforts for determining the mechanism that causes high-temperature superconductivity in copper oxide materials, no consensus on the pairing mechanism has been reached. Recent advances in high resolution angle-resolved photoemission spectroscopies have suggested that a sizeable electron-phonon coupling exists as the principal cause for kinks in the dispersion relations (energy versus wave vector) of the electronic states. Here, we report on a systematic study about the influence of the electron-phonon coupling parameter "$λ$" in the electronic quasiparticle dispersions alo…
Measurements of the thermal Hall conductivity in hole-doped cuprates have shown that phonons acquire chirality in a magnetic field, both in the pseudogap phase and in the Mott insulator state. The microscopic mechanism at play is still unclear. A number of theoretical proposals are being considered, including skew scattering of phonons by various defects, the coupling of phonons to spins, and a state of loop-current order with the appropriate symmetries, but more experimental information is required to constrain theoretical scenarios. Here we present our study of the thermal Hall conductivity …
New surprises continue to be revealed about La$_2$CuO$_4$, the parent compound of the original cuprate superconductor. Here we present neutron scattering evidence that the structural symmetry is lower than commonly assumed. The static distortion results in anisotropic Cu-O bonds within the CuO$_2$ planes; such anisotropy is relevant to pinning charge stripes in hole-doped samples. Associated with the extra structural modulation is a soft phonon mode. If this phonon were to soften completely, the resulting change in CuO$_6$ octahedral tilts would lead to weak ferromagnetism. Hence, we suggest t…
Band calculations on HgBa$_2$CuO$_4$ and La$_{(2-x)}$Sr$_x$CuO$_4$ with phonon and spin-waves within the CuO planes show that partial gaps are created at various energies depending on wavelengths. Spin and phonon gaps appear at different energies when the modulations are along [1,1,0], while they are at the same energy for modulations along [1,0,0]. It is shown that the ability to form gaps and antiferromagnetic waves is correlated with the strength of the interaction parameter $λ_{sf}$ for spin fluctuations. Many unusual properties of the high-T$_C$ oxides can be understood from spin-phonon c…
It is shown theoretically that the buckling of the CuO$_{2}$ planes in certain cuprate systems can be explained in terms of an electric field across the planes which originates from different valences of atoms above and below the plane. This field results also in a strong coupling of the Raman-active out-of-phase vibration of the oxygen atoms ($B_{1g}$ mode) to the electronic charge transfer between the two oxygens in the CuO$_{2}$ plane. Consequently, the electric field can be deduced from the Fano-type line shape of the $B_{1g}$ phonon. Using the electric field estimated from the electron-ph…
Cuprate superconductors host a multitude of low-energy optical phonons. Using time- and angle-resolved photoemission spectroscopy, we study coherent phonons in Bi$_{2}$Sr$_{2}$Ca$_{0.92}$Y$_{0.08}$Cu$_{2}$O$_{8+δ}$. Sub-meV modulations of the electronic band structure are observed at frequencies of $3.94\pm 0.01$ and $5.59\pm 0.06$ THz. For the dominant mode at 3.94 THz, the amplitude of the band energy oscillation weakly increases as a function of momentum away from the node. Theoretical calculations allow identifying the observed modes as CuO$_{2}$-derived $A_{1g}$ phonons. The Bi- and Sr-de…
Charge density wave (CDW) correlations are prevalent in all copper-oxide superconductors. While CDWs in conventional metals are driven by coupling between lattice vibrations and electrons, the role of the electron-phonon coupling (EPC) in cuprate CDWs is strongly debated. Using Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS), we study the CDW and Cu-O bond-stretching phonons in the stripe-ordered cuprate La$_{1.8-x}$Eu$_{0.2}$Sr$_{x}$CuO$_{4+δ}$. We investigate the interplay between charge order and EPC as a function of doping and temperature, and find that the EPC is enhanced in a na…
The phonon dynamics of the low-temperature superconductor Sr$_{2}$RuO$_{4}$ is calculated quantitatively in linear response theory and compared with the structurally isomorphic high-temperature superconductor La$_{2}$CuO$_{4}$. Our calculation corrects for a typical deficit of LDA-based calculations which always predict a too large electronic $k_{z}$-dispersion insufficient to describe the c-axis response in the 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…
The Raman spectra on the cleaved surface of La$_{2-x}$Sr$_x$CuO$_4$ is found to be different from those on the mechanically polished or chemically etched surface. On the cleaved surface, the step-like increase of the scattering intensity below 700 cm$^{-1}$ is washed away and the two-phonon peaks are preserved clearly even at the optimum doping. The difference is demonstrated on the optimally doped crystal at x=0.15 and the stripe phase crystal at x=0.115. The stripe phase is stabilized by defects induced by mechanical polishing.
Cuprates are promising candidates for study in developing higher temperature superconductors. A thorough understanding of a material's phonon modes enables further investigation of its emergent properties, however, no complete reference of the phonon modes exists. Here, using density functional theory, we evaluate the phonon frequencies and atomic displacements for $\text{La}_2\text{CuO}_4$, $\text{Bi}_2\text{Sr}_2\text{CuO}_6$, and $\text{Bi}_2\text{Sr}_2\text{CaCu}_2\text{O}_8$ in their tetragonal structures. The phonon modes for all materials agree with those expected from space group symme…
We present a detailed temperature-dependent Raman light scattering study of optical phonons in molecular-beam-epitaxy-grown films of the electron-doped superconductor La_{2-x}Ce_{x}CuO_{4} close to optimal doping (x ~ 0.08, T_c = 29 K and x ~ 0.1, T_c = 27 K). The main focus of this work is a detailed characterization and microstructural analysis of the films. Based on micro-Raman spectroscopy in combination with x-ray diffraction, energy-dispersive x-ray analysis, and scanning electron microscopy, some of the observed phonon modes can be attributed to micron-sized inclusions of Cu_{2}O. In th…
We report a doping dependent study of the quasiparticles dynamics in HgBa$_2$CuO$_{4+δ}$ via Electronic Raman Scattering. A well-defined energy scale is found in the normal state dynamics of the quasiparticles over a broad doping range. It is interpreted as evidence for coupling between the quasiparticles and a collective bosonic mode whose energy scale depend only weakly with doping. We contrast this behavior with that of the superconducting gap whose amplitude near the node continuously decreases towards the underdoped regime. We discuss the implications of our findings on the nature of the …
The mechanism of spin-phonon coupling in high-T$_C$ copper oxides is explored from band calculations on La$_{(2-x)}$Sr$_x$CuO$_4$ and HgBa$_2$CuO$_4$ systems. The LMTO band calculations, based on the local density approximation, are made for cells containing frozen phonon displacements and/or spin waves within the CuO plane. The virtual crystal approximation is used for studies of hole doped systems. The main result is that phonons are favorable for spin waves and vice-versa, and that pseudogaps appear naturally in the band structures of striped materials with strong SPC. The qualitative resul…
The strong, electronically induced anomaly in the spectrum of the longitudinal optical (LO) phonons propagating along the main axes of the CuO$_2$ plane is tentatively attributed to the oxygen-oxygen charge transfer between the two oxygens in the plane. It is argued that this charge transfer can be large and that it is strongly coupled to the zone boundary LO phonons. The corresponding negative contribution to the free energy is quartic in the LO phonon amplitude, making the LO phonon unstable through the first order phase transition, with a concomitant domain structure.
We have obtained mid-infrared optical absorption spectra of the S=1/2 quasi one-dimensional CuO using polarized transmission measurement and interpreted the spectra in terms of phonon assisted magnetic excitations. When the electric field is parallel to the main antiferromagnetic direction a Delta shaped peak is observed with the maximum at 0.23eV which is attributed to spinons along Cu-O chains. At low temperatures in the antiferromagnetic phase another peak appears at 0.16eV which is attributed to two-magnon absorption but the spinon peak remains. This behavior is interpreted as due to a dim…
Electrical characteristics $(I(eV), dV/dI(eV), d^{2}V/dI^{2}(eV))$ are studied comprehensively for pressed submicron point contacts between fresh fractures of LaSrCuO ceramic pellets and a normal metal (Cu). Point contacts (PC) with the direct-type conductivity are investigated, which are characterized by a considerable excess current due to Andreev reflection of quasiparticles at an NS boundary of high transparency. Basic requirements for point contacts suitable for PC measurements are formulated. The models of investigated point contacts permitting the interpretation of the observed characte…
The t-t'-t''-J model of electrons interacting with three phonon modes (breathing, apical breathing, and buckling) is considered. The wave-vector dependence of the matrix elements of the electron-phonon interaction leads to opposite contributions to the pairing potential with the d-symmetry: the buckling mode facilitates electron pairing, while the breathing mode suppresses it. As a result, the critical temperature of La{2 - x}Sr{x}CuO{4} that is associated with the magnetic mechanism is lowered when phonons are taken into account.
Effects of coupling between phonon distortions and stripe-like spin waves in the CuO plane of HgBa$_2$CuO$_4$ are studied by band calculations. Local exchange enhancements depend sensitively on the local structure around Cu sites. Interactions where spin waves have twice as long wave length as phonon waves can lead to a 'dip' in the density of states (DOS) below the Fermi energy, $E_F$. This type of interaction is compatible with several seemingly contradictory observations among high-$T_C$ cuprates, like the isotope effect, anti-ferromagnetic fluctuations, stripes and pseudogaps. It can also …
We reported two-magnon Raman scattering from La_{1.9}Sr_{0.1}CuO_4, which has a suppressed Tc=12 K, as the temperature is lowered below 37 K and an ordered spin phase is formed. The two-magnon Raman intensity increases with decreasing temperature. The magnetic scattering in La_{1.9}Sr_{0.1}CuO_4 is totally different from that reported in the parent compound La_2CuO_4. We analyze the line shape of the two-magnon scattering within the traditional Loudon-Fleury theory and find the superexchange constant J=1052 cm^{-1}. The calculation of the frequency moment suggests that the quantum fluctuations…
We investigate the structural modulations induced by optical excitation of a polar phonon mode in YBa$_2$Cu$_3$O$_7$, using first-principles calculations based on density functional theory. We focus on the intense-excitation regime in which we expect that fourth-order phonon-phonon coupling terms dominate, and model the structural modulations induced by pulses of such intensity. Our calculations of the phonon-phonon anharmonicities confirm that the cubic coupling between modes, shown in earlier work to cause a quasi-static change in the apical O - Cu distance and a buckling of the CuO$_2$ plan…
