Knee structure in the laser intensity dependence of high-order harmonic generations for graphene

TL;DR

This study reveals a universal knee structure in high-order harmonic generation in graphene across a wide laser intensity range, explained by interference effects and tunable via Fermi energy, confirmed by multiple theoretical approaches.

Contribution

It uncovers the universal knee structure in HHG intensity dependence in graphene and explains its mechanisms using two-band models and ab initio calculations, with experimental relevance.

Findings

Knee structure appears in HHG intensity dependence over wide laser intensities.

Fermi energy tuning can modify the knee structure.

The knee structure is confirmed by both density-matrix and ab initio calculations.

Abstract

We investigate the high-order harmonic generations (HHGs) of graphene irradiated by linearly polarized lasers with intensities in a wide range from $10^{8}$ W/cm$^2$ to $10^{13}$ W/cm$^2$. We find a striking knee structure in the laser intensity dependence of HHGs, which consists of a linear growth regime, followed by a plateau of the saturated HHGs, and then a transition to a nonlinear growth. The knee structure is rather universal for the varied harmonic orders and has been certificated by the calculations of two-band density-matrix equations as well as the \textit{ab initio} calculations of time-dependent density functional theory. Based on the two-band model, we reveal the underlying mechanisms: The behavior of linear growth can be depicted analytically by the perturbative theory of optical conductivity; While, the plateau of saturated HHGs and the transition to a nonlinear growth are caused by the quantum destructive interference and constructive interference of harmonics generated by the electrons corresponding to the lattice momentums around Dirac points and M points in Brillouin zone, respectively. In particular, we find that tuning Fermi energy can effectively alter the knee structure while the profile of the knee structure is not sensitive to the temperature. Our calculations of the third-order harmonic vs. tuning Fermi energy are compared with recent experiment showing a good agreement. Our predicted knee structure and its associated properties are observable with the current experimental techniques.