Evidence for photoinduced sliding of the charge-order condensate in ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_4$

We use femtosecond resonant soft x-ray scattering to measure the ultrafast optical melting of charge-order correlations in ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_4$. By analyzing both the energy-resolved and the energy-integrated order-parameter dynamics, we find evidence of a short-lived nonequilibrium state, the features of which are compatible with a sliding charge-density wave coherently set in motion by the pump. This transient state exhibits shifts in both the quasielastic line energy and its wave vector, as expected from a classical Doppler effect. The wave-vector change is indeed found to directly follow the pump propagation direction. These results demonstrate the existence of sliding charge-order behavior in an unconventional charge-density wave system and underscore the power of ultrafast optical excitation as a tool to coherently manipulate electronic condensates.

Figure 1

Sketch of the experiment. The LBCO charge order is perturbed by 1.55-eV pump pulses and then probed by scattering of copropagating soft x-ray FEL pulses resonantly tuned to the Cu $L_{3/2}$ edge. Both pump and probe pulses are p polarized in the scattering plane.

Figure 2

tr-RIXS spectra as a function of momentum transfer along the $(H,0,1.5)$ r.l.u. direction (a) before and (b) after the pump arrival. (c) Momentum dependence of the integrated elastic line (between $-1.2$ and 0.9 eV) before and after the pump arrival. Black dashed lines are pseudo-Voigt fits to the data. Error bars represent Poisson counting uncertainties.

Figure 3

(a) tr-RIXS spectra at $Q_{\text{CO}}=(0.23,0.00,1.50)$ r.l.u. as a function of pump-probe time delay. The data are binned in 400-fs time steps to improve statistics. (b) Fit components of the tr-RIXS spectra at $Q_{\text{CO}}=(0.23,0.00,1.50)$ r.l.u. The shaded red area is the Gaussian used to model the quasielastic scattering, while the two shaded blue areas are the two Lorentzians capturing the $dd$ and CT excitations, respectively. (c) Zoom of the quasielastic scattering before (red) and after (blue) the pump arrival. Data are shown as filled circles, while the red and blue dashed lines are fits to the data. The solid black lines are the Gaussian components of the fit, and the black dashed line is the Lorentzian fit to the $dd$ excitations. Error bars are Poisson counting uncertainties.

Figure 4

Fit parameters for the RIXS spectra at $Q_{\text{CO}}=(0.23,0.00,1.50)$ r.l.u. as a function of pump-probe time delay. Panels (a)–(c), respectively, show the integrated intensity, energy, and HWHM of the CO elastic line. Panels (d)–(f) report the same parameters for the peak associated to the $dd$ excitation/${\mathrm{Cu}}^{2+}$ fluorescence line. Panels (g)–(i) describe instead the spectral feature associated to the charge-transfer excitations. Error bars represent fit uncertainties.

Figure 5

Transverse momentum scan of the charge-order peak along the $(H,0.00,1.50)$ r.l.u. direction for a selection of time delays. Dashed lines are fits using Eq. (1). Dashed vertical lines mark the position of the peak at equilibrium and the maximum observed shift. Panel (a) shows data acquired at $\varphi =0$, while panel (b) shows data acquired at $\varphi \sim \pi$. Note that the change in momentum reverses sign between the two configurations. (c) Transverse momentum scan along the $(H,0,1)$ direction of the structural (0,0,1) Bragg peak before and after the pump arrival. The vertical dashed line marks the peak position before and after the pump.

Figure 6

Azimuthal rotation of the LBCO crystal. The $Q_{\text{CO}}=(0.23,0.00,1.50)$ r.l.u. diffraction peak has been measured in two configurations: (a) $\varphi =0$, with the pump propagating from positive to negative H, and (b) $\varphi =\pi$, from negative to positive H. (c) Observed Doppler recoil of the condensate from the equilibrium diffraction peak (gray) to the $\mathrm{\Delta }q$-shifted reflection (red, blue). (d) Diffraction peak shift due to a change of the charge-density periodicity (deformation). Red and blue arrows indicate the direction of the shift for $\varphi =0\text{and}\pi$, respectively.

Figure 7

Time-dependent CO peak fit parameters at $\varphi =0$ (red symbols) and $\varphi \sim \pi$ (blue symbols). (a) Pseudo-Voigt amplitude A, (b) CO peak position along the $(H_{\text{CO}},0.00,1.50)$ direction, (c) CO peak HWHM g, and (d) Pseudo-Voigt mixing parameter f.

Figure 8

Correlation plots of the elastic line energy $E_{\text{el}}$ with the intensity $I$, center energy E, and HWHM of the $dd/{\text{Cu}}^{2+}$ and CT lines for all the sampled time delays (red symbols). Blue symbols identify the time delays corresponding to the maximum quasielastic energy shift.

Figure 9

Fit parameters of the quasielastic line for free (red) and fixed (gray) parameters of both $dd/{\text{Cu}}^{2+}$ and CT lines.