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Register a new userTemperature-dependent electron-phonon coupling in La$_{2-x}$Sr$_x$CuO$_4$ probed by femtosecond X-ray diffraction
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The strength of the electron-phonon coupling parameter and its evolution throughout a solids 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 La$_{2-x}$Sr$_x$CuO$_4$ single crystals with $x$=0.1 and 0.21. The temperature dependence of the electron-phonon coupling is obtained experimentally and shows similar trends to what is expected from the textit{ab-initio} calculated shape of the electronic density-of-states near the Fermi energy. This study evidences the important role of band effects in the electron-lattice interaction in solids, in particular in superconductors.
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Strong electron correlations are responsible both for the insulator ground state of undoped La$_2$CuO$_4$ and strong antiferromagnetic coupling $J$ between neighbouring spins. We consider magnetic mechanism of superconducting pairing in the effective low energy $t - t - t - J^*$ model with all parameters calculated {it ab initio}. Interaction of strongly correlated electrons with different phonon modes is also incorporated. In a BCS type theory the $d_{x^2 - y^2}$ gap is given by a sum of magnetic and phonon contributions. The phonon coupling parameter $lambda = f(x)G$, where $G$ is a combination of bare electron-phonon couplings for all modes and the function $f$ depends on the hole concentration $x$ due to strong electron correlations. The main contribution to the only fitting parameter $G$ is determined by a competition of the breathing and buckling modes. Fitting the parameter $G$ from the isotope effect we obtain that magnetic and phonon contributions to the critical temperature $T_c $ work together and are of the same order of magnitude.
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$_{6+delta}$ 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 $(pi,0)$ and $(pi/2, pi/2)$, 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 $T_c$.
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.
Interlayer transport in high-$T_C$ cuprates is mediated by superconducting tunneling across the CuO$_2$ planes. For this reason, the terahertz frequency optical response is dominated by one or more Josephson plasma resonances and becomes highly nonlinear at fields for which the tunneling supercurrents approach their critical value, $I_C$. These large terahertz nonlinearities are in fact a hallmark of superconducting transport. Surprisingly, however, they have been documented in La$_{2-x}$Ba$_x$CuO$_4$ also above $T_C$ for doping values near $x=1/8$, and interpreted as an indication of superfluidity in the stripe phase. Here, Electric Field Induced Second Harmonic (EFISH) is used to study the dynamics of time-dependent interlayer voltages when La$_{2-x}$Ba$_x$CuO$_4$ is driven with large-amplitude terahertz pulses, in search of other characteristic signatures of Josephson tunnelling in the normal state. We show that this method is sensitive to the voltage anomalies associated with 2$pi$ Josephson phase slips, which near $x=1/8$ are observed both below and above $T_C$. These results document a new regime of nonlinear transport that shares features of sliding charge-density-waves and superconducting phase dynamics.
The specific heat $C$ of the cuprate superconductors La$_{2-x}$Sr$_x$CuO$_4$ and Bi$_{2+y}$Sr$_{2-x-y}$La$_x$CuO$_{6+delta}$ was measured at low temperature (down to $0.5~{rm K}$), for dopings $p$ close to $p^star$, the critical doping for the onset of the pseudogap phase. A magnetic field up to $35~{rm T}$ was applied to suppress superconductivity, giving direct access to the normal state at low temperature, and enabling a determination of $C_e$, the electronic contribution to the normal-state specific heat, at $T to 0$. In La$_{2-x}$Sr$_x$CuO$_4$ at $x=p = 0.22$, $0.24$ and $0.25$, $C_e / T = 15-16~{rm mJmol}^{-1}{rm K}^{-2}$ at $T = 2~{rm K}$, values that are twice as large as those measured at higher doping ($p > 0.3$) and lower doping ($p < 0.15$). This confirms the presence of a broad peak in the doping dependence of $C_e$ at $p^starsimeq 0.19$, as previously reported for samples in which superconductivity was destroyed by Zn impurities. Moreover, at those three dopings, we find a logarithmic growth as $T to 0$, such that $C_e / T sim {rm B}ln(T_0/T)$. The peak vs $p$ and the logarithmic dependence vs $T$ are the two typical thermodynamic signatures of quantum criticality. In the very different cuprate Bi$_{2+y}$Sr$_{2-x-y}$La$_x$CuO$_{6+delta}$, we again find that $C_e / T sim {rm B}ln(T_0/T$) at $p simeq p^star$, strong evidence that this $ln(1/T)$ dependence - first discovered in the cuprates La$_{1.8-x}$Eu$_{0.2}$Sr$_x$CuO$_4$ and La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ - is a universal property of the pseudogap critical point. All four materials display similar values of the $rm B$ coefficient, indicating that they all belong to the same universality class.
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