Temperature-dependent electron-phonon coupling in La${}_{2-x}$Sr${}_x$CuO${}_4$ probed by femtosecond x-ray diffraction

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 reequilibration 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 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.

Figure 1

Rocking curves obtained for the La${}_{2-x}$Sr${}_x$CuO${}_4$ samples with the core beam of the Micro-XAS-FEMTO beamline.

Figure 2

Rocking curve of the (400) peak in La${}_{2-x}$Sr${}_x$CuO${}_4$, $x=0.1$, for different time delays after excitation. Light blue triangles are the unpumped curve, dark blue circles the pumped one, and the difference between them is shown as red crosses.

Figure 3

Rocking curve of the (400) peak in La${}_{2-x}$Sr${}_x$CuO${}_4$, $x=0.21$, for different time delays after excitation. Light blue triangles are the unpumped curve, dark blue the pumped one, and the difference between them is shown as red crosses.

Figure 4

Delay scans at different angles of the rocking curve of the (400) peak in La${}_{2-x}$Sr${}_x$CuO${}_4$, $x=0.1$.

Figure 5

Delay scans at different angles of the rocking curve of the (400) peak in La${}_{2-x}$Sr${}_x$CuO${}_4$, $x=0.21$.

Figure 6

Diffraction intensity as a function of time delay for the (400) peak in La${}_{2-x}$Sr${}_x$CuO${}_4$: (a) $x=0.1$ and (b) $x=0.21$. The diffraction angles are set at $-26.{35}^{\circ }$ ($x=0.1$) and 56.21${}^{\circ }$ ($x=0.21$), i.e., in the center of the Bragg peak.

Figure 7

Transient lattice temperature obtained from the (400) diffraction peak intensity of LSCO: (a) $x=0.1$ and (b) $x=0.21$. Markers represent experimental data and solid lines the corresponding three-temperature model (3TM) simulations, from which we plot the effective average lattice temperature as $T_L=\alpha T_h+(1-\alpha )T_c$.

Figure 8

Specific heat measurements in La${}_{2-x}$Sr${}_x$CuO${}_4$, $x=0.1$ and $0.21$.

Figure 9

Density of states for La${}_2$CuO${}_4$ self-consistently calculated at two different electronic temperatures.

Figure 10

The $T$ dependence of the effective DOS at the chemical potential, $N_T$, in LSCO owing to the effect of Fermi-Dirac occupation for dopings $x$ indicated in the frame. Thermal disorder or disorder from lattice defects are neglected. Inset: The bare DOS of La${}_2$CuO${}_4$ near $E_F$. The vertical dashed lines indicate the rigid-band positions of $E_F$ for hole dopings 0.1 (red) and 0.21 (light blue).

Figure 11

Electron-phonon coupling constant histograms for the 21 modes at the $\Gamma$ point of La${}_{2-x}$Sr${}_x$CuO${}_4$, $x=0.1$ and $x=0.21$.

Figure 12

Atomic motions corresponding to the most coupled modes in La${}_{2-x}$Sr${}_x$CuO${}_4$, from Ref. 28. Displacements smaller than $25\%$ of the maximum are not shown.

Figure 13

Electron-phonon coupling constant obtained from 3TM simulations of time-resolved x-ray diffraction of the (400) peak in LSCO (solid symbols, left), and density of states at the Fermi level obtained by LDA calculations (open symbols, right).