Simulation the response of graphene to far-infrared pulses

Background and Objectives: The emergence of sources of ultrashort high-intensity laser pulses has made it possible to subject various materials to a strong electric field without the risk of irreversible damage. Nonlinear effects observed under these conditions, such as the generation of high-frequency harmonics, have great potential for practical application. Graphene is considered one of the most promising materials due to the specificity of its band structure. The aim of the work is to demonstrate the applicability of the model based on the quantum kinetic equation in describing the results of the action of an external electric field with frequencies close to the lower limit of the IR range on the electronic subsystem of a material. Comparison of the model behavior at different values of temperature, relaxation time of nonequilibrium population and decoherence time with experimental data will allow us to estimate possible values of these parameters. Materials and Method: The work uses a quantum kinetic equation for the charge carrier distribution function in the state space. It allows one to reproduce the behavior of the electron subsystem of the material in an external classical electric field with an arbitrary time dependence. The spectrum of single-electron states is determined using the tight-binding approximation of nearest neighbors. The model parameters are the sample temperature, which determines the initial equilibrium distribution, the relaxation time of the nonequilibrium population of excited states, and the decoherence time. The implemented efficient computational procedure allows one to reproduce the characteristics of radiation induced by the action of an external field and analyze its spectral composition. The subject of comparison was the published results of experiments on the generation of high-frequency harmonics by far-infrared pulses at the TELBE facility. Results: The results presented in the work confirm the applicability of the used model for the frequency range near the lower boundary of the IR. It has been shown that under such conditions the external electric field forms a strongly anisotropic distribution in the conduction band with the population of states with high, up to several eV, energy values. In this case, the initial population of the conduction band, determined by the temperature of the sample at zero chemical potential, is much smaller than that created by the external field and does not significantly affect the observed results of the external field action. On the contrary, the relaxation time of the nonequilibrium population turns out to be the most important parameter determining the achieved values of the carrier density and conduction current. This is due to the fact that its value is small compared to the duration of the half-period of the external field. The estimate of this parameter made on the basis of the comparison with the experimental data is in good agreement with the expected values. Due to the insignificant role of the polarization current reflecting the dynamics of interband transitions, a comparison of the model behavior with the available experimental data does not provide criteria for estimating the decoherence time. Conclusion: The results of the work have shown the promise of new tools for modeling, studying, and qualitatively and quantitatively reproducing the characteristics of nonlinear effects under the action of an external electric field on graphene with frequencies close to the lower limit of the IR range. It has been shown that the distinguished role of the conduction current in this frequency range allows one to obtain an independent estimate of the relaxation time of the nonequilibrium population of excited states by comparing the behavior of the model with the experimental results.

graphene, quantum kinetic equation, tight-binding model, high frequency harmonic generation