Two-dimensional Keldysh theory for non-resonant strong-field ionization of monolayer 2D materials

The Keldysh theory of photoionization for bulk dielectrics is generalized to atomically thin two-dimensional semiconductors. We derive closed-form formulas and their multiphoton and tunneling limiting forms for a two-band model with a Kane dispersion, without (KLD) and with (cKLD) the interference of two saddle points. Compared to the 3D KLD rates, the 2D KLD rates are enhanced except in the tunneling limit and exhibit more abrupt channel closure events, and their ratioshows strong edge enhancement as it approaches the channel closures. These phenomena are consistent with the scaling of the electronic density of states in the reduced dimensionality. Additionally, with the interference of the saddle points, the edge enhancement of the 2D/3D cKLD rate ratio is modulated periodically beyond the multiphoton regime, exhibiting additional enhancement and significant suppression at even-to-odd and odd-to-even edges, respectively. Moreover, we also derive the selection rules related to the parity of 2D multiphoton orders, which are characteristically different compared to the bulk. Furthermore, our theory provides a better match to published experimental results without any fitting; it simultaneously reproduces the general trends of 2PA and 3PA absorption spectra and bridges the gap in the HHG efficiency ratio between a monolayer and a single layer in bulk material. Lastly, even though their approaches are drastically different in nature, the predictions of our multiphoton theory match well with that of 2D perturbation theory. Considering the tremendous success of the original Keldysh theory in describing strong-field optical phenomena in atoms and solids, our 2D Keldysh theory is expected to find a wide range of applications in intense light-2D material interaction.