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R. Hackl

Publications and source records attributed to R. Hackl.

At least 37 records · Page 2Linked to original sources

Unravelling the glue and the competing order in superconducting cuprates

We present Raman scattering experiments in ${\rm La_{2-x}Sr_xCuO_4}$ single crystals at various doping levels x and compare the results with theoretical predictions obtained assuming an interaction mediated by spin and charge fluctuations. The light-scattering selection rules allow us to disentangle their respective contributions. We find that the glue spectral function is spin-dominated at low doping while the contribution of charge fluctuations becomes dominant around optimal doping. This indicates that the fluctuations of a nearly ordered state with coexisting spin and charge order support the superconducting pairing.

cond-mat.supr-con

Electron-boson glue function derived from electronic Raman scattering

Raman scattering cross sections depend on photon polarization. In the cuprates nodal and antinodal directions are weighted more strongly in $B_{2g}$ and $B_{1g}$ symmetry, respectively. On the other hand in angle-resolved photoemission spectroscopy (ARPES), electronic properties are measured along well-defined directions in momentum space rather than their weighted averages. In contrast, the optical conductivity involves a momentum average over the entire Brillouin zone. Newly measured Raman response data on high-quality Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ single crystals up to high energies have been inverted using a modified maximum entropy inversion technique to extract from $B_{1g}$ and $B_{2g}$ Raman data corresponding electron-boson spectral densities (glue) are compared to the results obtained with known ARPES and optical inversions. We find that the $B_{2g}$ spectrum agrees qualitatively with nodal direction ARPES while the $B_{1g}$ looks more like the optical spectrum. A large peak around $30 - 40\,$meV in $B_{1g}$, much less prominent in $B_{2g}$, is taken as support for the importance of $(π,π)$ scattering at this frequency.

cond-mat.supr-con

Quantitative comparison of single- and two-particle properties in the cuprates

We explore the strong variations of the electronic properties of copper-oxygen compounds across the doping phase diagram in a quantitative way. To this end we calculate the electronic Raman response on the basis of results from angle-resolved photoemission spectroscopy (ARPES). In the limits of our approximations we find agreement on the overdoped side and pronounced discrepancies at lower doping. In contrast to the successful approach for the transport properties at low energies, the Raman and the ARPES data cannot be reconciled by adding angle-dependent momentum scattering. We discuss possible routes towards an explanation of the suppression of spectral weight close to the $(π,0)$ points which sets in abruptly close to 21% doping.

cond-mat.supr-con

Electron interactions and charge ordering in La$_{2-x}$Sr$_x$CuO$_4$

We present results of inelastic light scattering experiments on single-crystalline La$_{2-x}$Sr$_{x}$CuO$_4$ in the doping range $0.00 \le x=p \le 0.30$ and Tl$_2$Ba$_2$CuO$_{6+δ}$ at $p=0.20$ and $p=0.24$. The main emphasis is placed on the response of electronic excitations in the antiferromagnetic phase, in the pseudogap range, in the superconducting state, and in the essentially normal metallic state at $x \ge 0.26$, where no superconductivity could be observed. In most of the cases we compare B$_{1g}$ and B$_{2g}$ spectra which project out electronic properties close to $(π,0)$ and $(π/2, π/2)$, respectively. In the channel of electron-hole excitations we find universal behavior in B$_{2g}$ symmetry as long as the material exhibits superconductivity at low temperature. In contrast, there is a strong doping dependence in B$_{1g}$ symmetry: (i) In the doping range $0.20 \le p \le 0.25$ we observe rapid changes of shape and temperature dependence of the spectra. (ii) In La$_{2-x}$Sr$_{x}$CuO$_4$ new structures appear for $x < 0.13$ which are superposed on the electron-hole continuum. The temperature dependence as well as model calculations support an interpretation in terms of charge-ordering fluctuations. For $x \le 0.05$ the response from fluctuations disappears at B$_{1g}$ and appears at B$_{2g}$ symmetry in full agreement with the orientation change of stripes found by neutron scattering. While, with a grain of salt, the particle-hole continuum is universal for all cuprates the response from fluctuating charge order in the range $0.05 \le p < 0.16$ is so far found only in La$_{2-x}$Sr$_{x}$CuO$_4$. We conclude that La$_{2-x}$Sr$_{x}$CuO$_4$ is close to static charge order and, for this reason, may have a suppressed $T_c$.

cond-mat.supr-con

Pinpointing Gap Minima in Ba(Fe$_{0.94}$Co$_{0.06})_{2}$As$_2$ \textit{via} Band Structure Calculations and Electronic Raman Scattering

A detailed knowledge of the gap structure for the Fe-pnictide superconductors is still rather rudimentary, with several conflicting reports of either nodes, deep gap minima, or fully isotropic gaps on the Fermi surface sheets, both in the $k_{x}-k_{y}$ plane and along the c-axis. In this paper we present considerations for electronic Raman scattering which can help clarify the gap structure and topology using different light scattering geometries. Using density functional calculations for the Raman vertices, it is shown that the location of the gap minima may occur on loops stretching over a portion of the c-axis in Ba(Fe$_{0.94}$Co$_{0.06})_{2}$As$_2$.

cond-mat.supr-con

Femtosecond Quasiparticle and Phonon Dynamics in Superconducting YBa2Cu3O7 Studied by Wideband Terahertz Spectroscopy

We measure the anisotropic mid-infrared response of electrons and phonons in bulk YBa2Cu3O7 after femtosecond photoexcitation. A line shape analysis of specific lattice modes reveals their transient occupation and coupling to the superconducting condensate. The apex oxygen vibration is strongly excited within 150 fs demonstrating that the lattice absorbs a major portion of the pump energy before the quasiparticles are thermalized. Our results attest to substantial electron-phonon scattering and introduce a powerful concept probing electron-lattice interactions in a variety of complex materials.

cond-mat.supr-con

Band and momentum dependent electron dynamics in superconducting ${\rm Ba(Fe_{1-x}Co_{x})_2As_2}$ as seen via electronic Raman scattering

We present details of carrier properties in high quality ${\rm Ba(Fe_{1-x}Co_{x})_2As_2}$ single crystals obtained from electronic Raman scattering. The experiments indicate a strong band and momentum anisotropy of the electron dynamics above and below the superconducting transition highlighting the importance of complex band-dependent interactions. The presence of low energy spectral weight deep in the superconducting state suggests a gap with accidental nodes which may be lifted by doping and/or impurity scattering. When combined with other measurements, our observation of band and momentum dependent carrier dynamics indicate that the iron arsenides may have several competing superconducting ground states.

cond-mat.supr-con

Raman scattering evidence for a cascade-like evolution of the charge-density-wave collective amplitude mode

The two-dimensional rare-earth tri-tellurides undergo a unidirectional charge-density-wave (CDW) transition at high temperature and, for the heaviest members of the series, a bidirectional one at low temperature. Raman scattering experiments as a function of temperature on DyTe$_3$ and on LaTe$_3$ at 6 GPa provide a clear-cut evidence for the emergence of the respective collective CDW amplitude excitations. In the unidirectional CDW phase, we surprisingly discover that the amplitude mode develops as a succession of two mean-field, BCS-like transitions in different temperature ranges.

cond-mat.str-el

Spectral signatures of critical charge and spin fluctuations in cuprates

We discuss how Raman spectra of high temperature superconducting cuprates are affected by nearly-critical spin and charge collective modes, which are coupled to charge carriers near a stripe quantum critical point. We find that specific fingerprints of nearly-critical collective modes can be observed and that the selectivity of Raman spectroscopy in momentum space may be exploited to distinguish the spin and charge contribution. We apply our results to discuss the spectra of high-T_c superconducting cuprates finding that the collective modes should have masses with substantial temperature dependence in agreement with their nearly critical character. Moreover spin modes have larger masses and are more diffusive than charge modes indicating that in stripes the charge is nearly ordered, while spin modes are strongly overdamped and fluctuating with high frequency.

cond-mat.supr-con

Pair breaking versus symmetry breaking: Origin of the Raman modes in superconducting cuprates

We performed Raman experiments on superconducting ${\rm Bi_2 Sr_2 (Ca_{1-x} Y_x) Cu_2 O_{8+δ}}$ (Bi-2212) and ${\rm YBa_{2} Cu_{3}O_{6+x}}$ (Y-123) single crystals. These results in combination with earlier ones enable us to analyze systematically the spectral features in the doping range $0.07 \le p \le 0.23$. In $B_{2g}$ ($xy$) symmetry we find universal spectra and the maximal gap energy $Δ_0$ to follow the superconducting transition temperature $T_c$. The $B_{1g}$ ($x^2-y^2$) spectra in Bi-2212 show an anomalous increase of the intensity towards overdoping, indicating that the corresponding energy scale is neither related to the pairing energy nor to the pseudogap, but possibly stems from a symmetry breaking transition at the onset point of superconductivity at $p_{\rm sc2} \simeq 0.27$.

cond-mat.supr-con

First-Order Type Effects in YBa$_2$Cu$_3$O$_{6+x}$ at the Onset of Superconductivity

We present results of Raman scattering experiments on tetragonal ${\rm (Y_{1-y}Ca_{y})Ba_{2}Cu_{3}O_{6+x}}$ for doping levels $p(x,y)$ between 0 and 0.07 holes/CuO$_2$. Below the onset of superconductivity at $p_{\rm sc1} \approx 0.06$, we find evidence of a diagonal superstructure. At $p_{\rm sc1}$, lattice and electron dynamics change discontinuously with the charge and spin properties being renormalized at all energy scales. The results indicate that charge ordering is intimately related to the transition at $p_{\rm sc1}$ and that the maximal transition temperature to superconductivity at optimal doping $T_{c}^{\rm max}$ depends on the type of ordering at $p>p_{\rm sc1}$.

cond-mat.supr-con

Vibrational spectra of C60C8H8 and C70C8H8 in the rotor-stator and polymer phases

C60-C8H8 and C70-C8H8 are prototypes of rotor-stator cocrystals. We present infrared and Raman spectra of these materials and show how the rotor-stator nature is reflected in their vibrational properties. We measured the vibrational spectra of the polymer phases poly(C60C8H8) and poly(C70C8H8) resulting from a solid state reaction occurring on heating. Based on the spectra we propose a connection pattern for the fullerene in poly(C60C8H8), where the symmetry of the C60 is D2h. On illuminating the C60-C8H8 cocrystal with green or blue light a photochemical reaction was observed leading to a similar product to that of the thermal polymerization.

cond-mat.mtrl-sci

Inelastic Light Scattering From Correlated Electrons

Inelastic light scattering is an intensively used tool in the study of electronic properties of solids. Triggered by the discovery of high temperature superconductivity in the cuprates and by new developments in instrumentation, light scattering both in the visible (Raman effect) and the X-ray part of the electromagnetic spectrum has become a method complementary to optical (infrared) spectroscopy while providing additional and relevant information. The main purpose of the review is to position Raman scattering with regard to single-particle methods like angle-resolved photoemission spectroscopy (ARPES), and other transport and thermodynamic measurements in correlated materials. Particular focus will be placed on photon polarizations and the role of symmetry to elucidate the dynamics of electrons in different regions of the Brillouin zone. This advantage over conventional transport (usually measuring averaged properties) indeed provides new insights into anisotropic and complex many-body behavior of electrons in various systems. We review recent developments in the theory of electronic Raman scattering in correlated systems and experimental results in paradigmatic materials such as the A15 superconductors, magnetic and paramagnetic insulators, compounds with competing orders, as well as the cuprates with high superconducting transition temperatures. We present an overview of the manifestations of complexity in the Raman response due to the impact of correlations and developing competing orders. In a variety of materials we discuss which observations may be understood and summarize important open questions that pave the way to a detailed understanding of correlated electron systems.

cond-mat.str-el

Dynamical Properties of Charged Stripes in La_{2-x}Sr_xCuO_4

Inelastic light-scattering spectra of underdoped ${\rm La_{2-x}Sr_xCuO_4}$ (LSCO) single crystals are presented which provide direct evidence of the formation of quasi one-dimensional charged structures in the two-dimensional $\rm CuO_2$ planes. The ``stripes'' manifest themselves in a Drude-like peak at low energies and temperatures. The selection rules allow us to determine the orientation to be along the diagonals at $x=0.02$ and along the principal axes at $x=0.10$. The electron-lattice interaction determines the correlation length which turns out to be larger in compound classes with lower superconducting transition temperatures. Temperature is the only scale of the response at different doping levels demonstrating the importance of quantum critical behavior.

cond-mat.str-el

Comment on: Nonmonotonic $d_{x^{2}-y^{2}}$ Superconducting Order Parameter in Nd$_{2-x}$Ce$_x$CuO$_4$

In a recent letter Blumberg and collaborators claim that a non-monotonic $d_{x^2-y^2}$ form for the superconducting order parameter is required to explain their Raman scattering measurements in Nd$_{2-x}$Ce$_x$CuO$_4$ . In this comment we show with a simple model calculation that the basis for this conclusion is insufficient. The proposed functional dependence of the gap is neither consistent with their measured spectra nor compatible with other experimental results. Therefore the issue of the superconduing gap in electron-doped systems cannot be considered solved by now.

cond-mat.supr-con

Raman Scattering versus Infrared Conductivity: Evidence for one-dimensional Conduction in La_{2-x}Sr_{x}CuO_{4}

Raman and Infrared (IR) spectra of an underdoped La_{1.90}Sr_{0.10}CuO_{4} single crystal have been measured as a function of temperature. Both techniques provide unconventional low-energy spectra. The IR conductivity exhibits features peaked at finite frequencies which do not have a counterpart in the Raman response. Below approximately 100 K a transfer of both Raman and IR spectral weight towards lower energies is found and a new component in the Raman response builds up being characterized by a very long lifetime of electrons propagating along the Cu-O bonds.

cond-mat.supr-con

Observation of an unconventional metal-insulator transition in overdoped CuO_2 compounds

The electron dynamics in the normal state of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ is studied by inelastic light scattering over a wide range of doping. A strong anisotropy of the electron relaxation is found which cannot be explained by single-particle properties alone. The results strongly indicate the presence of an unconventional quantum-critical metal-insulator transition where "hot" (antinodal) quasiparticles become insulating while "cold" (nodal) quasiparticles remain metallic. A phenomenology is developed which allows a quantitative understanding of the Raman results and provides a scenario which links single- and many-particle properties.

cond-mat.supr-con

Doping dependence of the electronic Raman spectra in cuprates

We report electronic Raman scattering measurements on Bi$_2$Sr$_2$(Y$_{1-x}$Ca$_x$)Cu$_2$O$_{8+δ}$ single crystals at different doping levels. The dependence of the spectra on doping and on incoming photon energy is analyzed for different polarization geometries, in the superconducting and in the normal state. We find the scaling behavior of the superconductivity pair-breaking peak with the carrier concentration to be very different in B$_{1g}$ and B$_{2g}$ geometries. Also, we do not find evidence of any significant variation of the lineshape of the spectra in the overdoped region in both symmetries, while we observe a reduction of the intensity in B$_{2g}$ upon decreasing photon energies. The normal state data are analyzed in terms of the memory-function approach. The quasiparticle relaxation rates in the two symmetries display a dependence on energy and temperature which varies with the doping level.

cond-mat.supr-con