With a combination of numerical methods, including quantum Monte Carlo, exact diagonalization, and a simplified dynamical mean-field model, we consider the attosecond charge dynamics of electrons induced by strong-field laser pulses in two-dimensional Mott insulators. The necessity to go beyond single-particle approaches in these strongly correlated systems has made the simulation of two-dimensional extended materials challenging, and we contrast their resulting high-harmonic emission with more widely studied one-dimensional analogues. As well as considering the photo-induced breakdown of the Mott insulating state and magnetic order, we also resolve the time and ultra-high frequency domains of emission, which are used to characterize both the photo-transition, and the sub-cycle structure of the electron dynamics. This extends simulation capabilities and understanding of the photo-melting of these Mott insulators in two-dimensions, at the frontier of attosecond non-equilibrium science of correlated materials.
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