Terahertz-induced high-order harmonic generation and nonlinear charge transport in graphene

We theoretically study the terahertz-induced high-order harmonic generation (HHG) and nonlinear electric transport in graphene based on the quantum master equation with the relaxation time approximation. To obtain microscopic insight into the phenomena, we compare the results of the fully dynamical calculations with those under a quasistatic approximation, where the electronic system is approximated as a nonequilibrium steady state. As a result, we find that the THz-induced electron dynamics in graphene can be accurately modeled with the nonequilibrium steady state at each instance. The population distribution analysis further clarifies that the THz-induced HHG in graphene originates from the reduction of effective conductivity due to a large displacement of electrons in the Brillouin zone. By comparing the present nonequilibrium picture with a thermodynamic picture, we explore the role of the nonequilibrium nature of electron dynamics on the extremely nonlinear optical and transport phenomena in graphene.

Figure 1

(a) Computed harmonic spectra $I_{\mathrm{HHG}}\left(\omega \right)$ with Eq. (9) for different chemical potentials, $\mu =0$, 70, and 170 meV. (b) Comparison of the HHG spectra computed with the fully dynamical simulations in Sec. 3a and the quasistatic approximation Sec. 3b. Here, the chemical potential is set to $\mu =170$ meV.

Figure 2

Nonlinear effective conductivities of graphene as a function of the static field strength $E_0$ evaluated with the total currents (solid lines) and intraband currents (dashed lines) for different values of the chemical potential, $\mu =0$, 70, and 170 meV.

Figure 3

(a) The equilibrium population distribution in the conduction band $f^{\mathrm{FD}}\left({\epsilon }_{c,\mathit{k}}\right)$. (b)–(d) The field-induced conduction population change for different field strengths, (b) 0.01 MV/m, (c) 3 MV/m, and (d) 10 MV/m. (e) The population distribution in the conduction band in the nonequilibrium steady state under a static field, $E_0=10$ MV/m.

Figure 4

Computed effective conductivities are shown as a function of the excess energy. The results for the nonequilibrium steady state (red solid), the thermodynamic model (green dashed), and the thermodynamic model plus the single-band approximation (blue dotted) are shown.

Figure 5

Electric current in graphene under a static electric field, $E_0=8.5$ MV/m.

Figure 6

Steady current ${\mathit{J}}_S\left(E_0\right)$ as a function of field strength $E_0$. The results of the fully dynamical calculation are shown as the red points, while the interpolated result is shown as the blue solid line.

Figure 7

Comparison of the THz-induced current computed with the fully dynamical calculation and the quasistatic approximation.