Probing the electron-phonon interaction in correlated systems with coherent lattice fluctuation spectroscopy

Tailoring the properties of correlated oxides is accomplished by chemical doping, pressure, temperature, or magnetic field. Photoexcitation is a valid alternative to reach out-of-equilibrium states otherwise inaccessible. Here, we quantitatively estimate the coupling between a lattice distortion and the charge-transfer excitation in ${\mathrm{La}}_2{\mathrm{CuO}}_{4+\delta }$. We photoinduce a coherent La ion vibration and monitor the response of the optical constants in a broad energy range, providing quantitative information on the electron-phonon matrix element that can be compared to theoretical models. We propose the same methodology to probe electron-phonon and electron-electron interactions in other materials.

Figure 1

(a) Real and (b) imaginary parts of the dielectric function $\varepsilon$ from spectroscopic ellipsometry measurements. The dashed vertical line indicates the pump energy, the shaded area denotes the probe spectrum. The dashed blue lines are fits to the data with the model of Ref. [26].

Figure 2

(a) In-plane reflectivity change of ${\mathrm{La}}_2{\mathrm{CuO}}_{4+\delta }$, shown in color coding. (b) Time-dependent reflectivity change for selected probe energies. Traces are integrated over 0.15 eV wide slices centered on the horizontal lines in (a). The pump light is polarized parallel to the $c$ axis. (c) Oscillatory contribution ${\left(\frac{\mathrm{\Delta }R}{R}\right)}^{\mathrm{osc}}$ of our data for $E=2.1$ eV. (d) Eigenvector of the La $A_{1g}$ phonon mode identified as the oscillation in our data, after Ref. [30].

Figure 3

Canonical time traces (a) $u_1\left(t\right)$ and (b) $u_2\left(t\right)$ obtained from the singular value decomposition. The traces have been fitted with a sum of two exponentials and a damped oscillation.

Figure 4

(a) and (b) Physical traces $U_i\left(t\right), V_i\left(E\right)$ extracted from the singular value decomposition. The relaxation is included in $U_1$ to $U_4$, while the oscillation is represented by $U_5$. The energy vectors $V_i$ have been smoothed using a sliding average.

Figure 5

Reconstruction of the data using the SVD results up to second rank: (a) reconstructed data, compare to Fig. 2. (b) and (c) Relaxation and oscillatory contributions according to Eq. (7).

Figure 6

(a) Differential reflectivity energy profile of the coherent oscillation at $t=t_M$ for out-of-plane and in-plane excitation, and fit. The data with the pump $\parallel c$ were rescaled to match the intensity of the data with the pump $\perp$ c. (b) Differential dielectric function $\mathrm{\Delta }{\varepsilon }_1$ corresponding to in-plane pump and probe polarizations at $t=t_M$ (left scale). The absolute right scale was obtained as explained in the text.