Ultrafast X-Ray Absorption Spectroscopy of Strongly Correlated Systems: Core Hole Effect

In recent years, ultrafast pump-probe spectroscopy has provided insightful information about the nonequilibrium dynamics of excitations in materials. In a typical experiment of time-resolved x-ray absorption spectroscopy, the systems are excited by a femtosecond laser pulse (pump pulse) followed by an x-ray probe pulse after a time delay to measure the absorption spectra of the photoexcited systems. We present a theory for nonequilibrium x-ray absorption spectroscopy in one-dimensional strongly correlated systems. The core hole created by the x ray is modeled as an additional effective potential of the core hole site, which changes the spectrum qualitatively. In equilibrium, the spectrum reveals the charge gap at half-filling and the metal-insulator transition in the presence of the core hole effect. Furthermore, a pump-probe scheme is introduced to drive the system out of equilibrium before the x-ray probe. The effects of the pump pulse with varying frequencies, shapes, and fluences are discussed for the dynamics of strongly correlated systems in and out of resonance. The spectrum indicates that the driven insulating state has a metallic droplet around the core hole. The rich structures of the nonequilibrium x-ray absorption spectrum give more insight into the dynamics of electronic structures.

Figure 1

Static XAS under filling fraction: (a)–(b) ${\overline{n}}_f=1$, and (c) ${\overline{n}}_f=2/3$. In Fig. 1, the initial state is the Fermi sea state ($U=0$); and the different core hole potentials of $V_{\mathrm{ch}}/J=0$ (blue), 4 (red), and 12 (purple) are considered. The spectrum splits in the presence of nonzero core hole potential. In Figs. 1 and 1, with a shared legend, the initial state is the ground state with different $U$ and the core hole potential is set to $V_{\mathrm{ch}}=12J$. (d) Frequency difference versus core hole potential from Fermi sea state with different fillings. (e) Frequency difference versus interaction with different fillings, where the core hole potentials are set to $V_{\mathrm{ch}}=12J$ (filled) and $V_{\mathrm{ch}}=8J$ (open).

Figure 2

(a) XAS for different fillings under the same interaction ($U=2J$) and core hole potential ($V_{\mathrm{ch}}=12J$). Weights of XAS from singly (open symbols) and doubly (filled symbols) occupied states: (b) ${\overline{n}}_f=1$, and (c) ${\overline{n}}_f=1/3$ under different interactions and core hole potentials.

Figure 3

NE-XAS with core hole potential $V_{\mathrm{ch}}=12J$ and different time delays for (a) $U=2J$, (b) $4J$, (c) $6J$, and (d) $8J$ under pulse fluences of $\mathrm{\Omega }{t}_0=3$, $\tau =2t_0$, and $A_0=0.1$ in Figs. 3; and $A_0=0.3$ in Fig. 3. In Figs. 3 and 3, the peak around $\omega \sim -12J$ (magenta arrow) emerges as a singly occupied core hole signal from the metallic droplet. The system is at the half-filling.

Figure 4

(a) Changes of weight (filled symbols) and frequency (open symbols) of the doubly occupied state versus interaction under the intensity of $A_0=0.1$. (b) Frequency shift of the doubly occupied state versus different intensities under different interactions. In Figs. 4 and 4, the pump pulses have $\mathrm{\Omega }{t}_0=3$, $\tau =2t_0$, and $t_d=6t_0$. (c) Changes of weight (filled symbols) and frequency (open symbols) of the doubly occupied state versus interaction when systems at half-filling under fluence of $\mathrm{\Omega }{t}_0=6$, width of $\tau =3t_0$, time delay of $t_d=6t_0$, and $A_0=0.1$. (d) NE-XAS for systems at half-filling with different $U$ under single cycle terahertz pulse fluence of $\mathrm{\Omega }{t}_0=1$, width of $\tau =3t_0$, time delay of $t_d=6t_0$ and intensity of $A_0=1$. Inset shows the terahertz pulse profile. Core hole potential is set to $V_{\mathrm{ch}}=12J$ in all panels.