Ultrafast Modification of Hubbard $U$ in a Strongly Correlated Material: Ab initio High-Harmonic Generation in NiO

Engineering effective electronic parameters is a major focus in condensed matter physics. Their dynamical modulation opens the possibility of creating and controlling physical properties in systems driven out of equilibrium. In this Letter, we demonstrate that the Hubbard $U$, the widely used on-site Coulomb repulsion in strongly correlated materials, can be modified on femtosecond timescales by a strong nonresonant laser pulse excitation in the prototypical charge-transfer insulator NiO. Using our recently developed time-dependent density-functional theory plus self-consistent $U$ method, we demonstrate the importance of a dynamically modulated $U$ in the description of the high-harmonic generation of NiO. Our study opens the door to novel ways of modifying effective interactions in strongly correlated materials via laser driving, which may lead to new control paradigms for field-induced phase transitions and perhaps laser-induced Mott insulation in charge-transfer materials.

Figure 1

Self-consistent dynamics of Hubbard $U$ for the Ni $3d$ orbitals (middle) and the oxygen $2p$ orbitals (bottom) for pump intensities as indicated. (Top) Represents the time-dependent vector potential, and the vertical dashed lines indicate the extrema of the vector potential, i.e., the minima of the driving electric field.

Figure 2

Calculated change of $U$ at the end of the laser pulse versus the peak driving field strength, for the Ni $3d$ orbitals (red curve) and the O $2p$ orbitals (blue curve). The dashed lines indicate a linear scaling in electric field strength, as expected from linear response theory. The calculated ground-state value of $U_{\mathrm{eff}}$ is 6.93 eV.

Figure 3

Time evolution of the magnetization integrated around the Ni atoms for different driving intensities. We only report the magnetization computed around one of the Ni atoms, as the two atoms are found to have exactly opposite magnetization, as expected for the antiferromagnetic phase considered here. The magnetization is calculated by averaging over a sphere of radius 1.97 bohr around the Ni atom.

Figure 4

Effect of the time evolution of $U$ (from Fig. 1) on the HHG spectrum of NiO. The HHG spectrum obtained from the full time evolution is shown in black, whereas the spectrum obtained for frozen $U$ is shown in red. The red vertical line indicates the calculated ground-state band gap of NiO. The intensity is taken here as $I_0={10}^{12}W{\mathrm{cm}}^{-2}$.