Dynamics of screening in photodoped Mott insulators

We use a nonequilibrium implementation of extended dynamical mean-field theory in combination with a noncrossing approximation impurity solver to study the effect of dynamical screening in photoexcited Mott insulators. The insertion of doublons and holes adds low-energy screening modes and leads to a reduction of the Mott gap. The coupling to low-energy bosonic modes furthermore opens new relaxation channels and significantly speeds up the thermalization process. We also investigate the effect of the energy distribution of the photo doped carriers on the screening.

Figure 1

(a) Vertices representing the coupling between pseudoparticle propagators (solid lines) and hybridization functions (dashed lines), or between pseudoparticle propagators and retarded interactions (wavy lines). (b) The lowest-order diagrams (in $\mathrm{\Delta }$ and $\mathcal{D}$) contributing to the Luttinger-Ward functional. (c) The pseudoparticle self-energy diagrams corresponding to the approximation (b) for the Luttinger-Ward functional.

Figure 2

(a) Comparison of the double occupancy in the Holstein-Hubbard model on the Bethe lattice for $\beta =5, U=10$, and ${\omega }_0=2$ obtained from the NCA and OCA approximation in combination with the weak-coupling expansion (W) and Lang-Firsov (L) transformation, and the numerically exact QMC results. (b) Comparison of the double occupancy for the extended Hubbard model for $\beta =5$ and $U=12$ obtained from the NCA approximation and the numerically exact QMC solver on the square lattice.

Figure 3

(a) Equilibrium spectral functions for $\beta =20$ and indicated values of $U$ and $V$. (b) Equilibrium phase diagram in the space of $U$ and $V$ at $\beta =20$. The dashed line roughly indicates the metal-insulator crossover defined by the appearance of a quasiparticle peak. (c) and (d) The equilibrium spectral function $A\left(\omega \right)$ for $U=12$ (c) and $U=7$ (d) for indicated values of the nearest-neighbor interaction $V$. The insets show the spectra on a logarithmic scale.

Figure 4

(a) and (b) Relaxation dynamics of the double occupancy $n_d$ for different values of $V$ after a pulse with frequency $\omega =10$ and pulse amplitude $E_0=5$. The on-site interaction is $U=10$ (a) and $U=7$ (b).

Figure 5

Relaxation time of the double occupancy as a function of the nearest-neighbor coupling $V$ for $U=10$ (a) and $U=7$ (c), pulse frequency $\omega =10$ and pulse amplitudes $E_0=2.5$ and 5. The dashed lines represent the relaxation time in the Hubbard model with an instantaneous interaction $U=\mathcal{U}(\omega =0)$ corresponding to the static interaction in a $U-V$ Hubbard model with a given $V$ (see discussion in the main text). (c) and (d) Scaling of the difference between the inverse relaxation times at $V=0$ and $V>0$ with $V^2$ for the same parameters as in (a) and (c).

Figure 6

(a) and (b) Partial Fourier transform of the spectral function $A(\omega ,t)$ with insets showing the difference from the initial value $A(\omega ,t)-A(\omega ,t=0)$ for $U=10,V=2,E_0=5.0$ (a) and $U=7,V=2,E_0=3.5$ (b). The dashed black lines represent the initial equilibrium spectral function. (c) and (d) Change in the gap size measured by the frequency ${\omega }^{*}$ at which the spectral function is equal to some fixed value, $A\left({\omega }^{*}\right)=A_0$, for $U=10$ (c) and $U=7$ (d). The dashed lines represent the ${\omega }^{*}$ for the same parameters but with coupling to an external bath with $\lambda =1,$ see also the discussion in the main text. For $U=7$, there is no intersection for $A_0=0.05$ in the case with coupling to an external bath. The corresponding cuts through the spectral function are shown by the dashed lines in (a) and (b). (e) and (f) Occupation function at fixed time delay $A^{<}(\omega ,t=10.0)$, for $U=10, V=2$ (e) and $U=7.3, V=2$ (f) at different pulse strength $E_0$.

Figure 7

Real [(a) and (b)] and imaginary [(c) and (d)] parts of the partial Fourier transform of the screened interaction $\text{Re}\left[W^R(\omega ,t)\right]-U$ for $U=10,E_0=5$ (left column), and $U=7,E_0=3.0$ (right column) at fixed $V=2,\omega =8.$ The insets in (a) and (b) show the evolution of the average boson frequency $\overline{\omega }\left(t\right)$. The black dashed lines represent the screened interaction in the initial equilibrium state. (e) and (f) Real part of the partial Fourier transform of the regular part of the partially screened on-site interaction $\text{Re}\left[{\mathcal{D}}^{\text{reg}}(t,\omega )\right]=\text{Re}\left[\mathcal{U}(t,\omega )\right]-U$ for $U=10,E_0=5$ (e) and $U=7,E_0=3.5$ (f).

Figure 8

Real (a) and the imaginary (b) parts of the partial Fourier transform of the screened interaction $W^R(t,\omega )$ for $U=6.9, V=2, E=0.25$, and $\omega =2.$ (c) Comparison of the dynamics of the partial Fourier transform of the spectral function $A(\omega ,t)$ for the $U-V$ (full lines) model and the Hubbard model (dashed lines) with a correspondingly reduced on-site interaction $U=6.425.$

Figure 9

Relaxation dynamics of the double occupancy $n_d$ for $U=7$ (a), 10 (b), and 14 (c) with different values of the coupling to the bath $\lambda$ during and after the pulse with frequency $\omega =8$ and pulse amplitude $E_0=5.$ The real part of the partial Fourier transform of the screened interaction $\text{Re}\left[W^{\text{reg}}(t,\omega )\right]=\text{Re}\left[W(t,\omega )\right]-U$ for $U=7$ (d), 10 (e), and 14 (f) at fixed $V=2.0,\lambda =1.0,E_0=5.$

Figure 10

Relaxation dynamics of the kinetic energy $E_{\text{kin}}$ (a) and the double occupancy $n_d$ (b) for $U=7.3$ and $U=7.1$ at $V=2.0$ for different values of the coupling with the bath $\lambda =0.5$, 1.0 during and after a pulse with $\omega =8$ and $E_0=1.0$. The partial Fourier transform of the spectral function $A(\omega ,t)$ for $U=7.3$ and $U=7.1$ is shown in (c) and (d). The dashed lines corresponds to the equilibrium spectral function. (e) and (f) plot the real part of the partial Fourier transform of the regular part of the partially screened on-site interaction $\text{Re}\left[\mathcal{D}\right(t,\omega \left)\right]=\text{Re}\left[\mathcal{U}\right(t,\omega \left)\right]-U$ for $U=7.3$ (e) and $U=7.1$ (f). The bottom panels shows the time evolution of the spectral function $A(\omega =0,t)$ for $U=7.3$ (g) and $U=7.1$ (h) for $\lambda =1$.

Figure 11

(a) and (b) Partial Fourier transform of the spectral function $A(\omega ,t)$ for $U=14,V=2,E_0=10.0,{\omega }_0=14$ (a) and $U=14,V=0,E_0=10.0,{\omega }_0=14$ (b) and coupling to a bath with $\lambda =1.0$. The dashed black lines represent the initial equilibrium spectral function. The bottom panels show the change in the gap size $\mathrm{\Delta }\overline{{\omega }^{*}}$ (see discussion in the main text) as a function of the change in the double occupancy $\mathrm{\Delta }{n}_d$ for $V=2$ (c) and $V=0$ (d).