Two-Dimensional Graphene: Theoretical Study of Multi-photon Non-linear Absorption Coefficient of a Strong Electromagnetic Wave by Using Quantum Kinetic Equation

TL;DR

This paper presents a theoretical analysis of multi-photon non-linear absorption in 2D graphene under strong electromagnetic waves, considering different scattering mechanisms and magnetic fields, with results aligning with experimental data.

Contribution

It provides the first analytical expressions for multi-photon absorption coefficients in graphene considering magnetic fields and temperature effects, extending classical models.

Findings

Absence of absorption peak without magnetic field contrasts previous 2D systems.

Magnetic fields induce spectral lines consistent with magneto-phonon resonance.

Multi-photon absorption is stronger than mono-photon absorption.

Abstract

Based on the quantum kinetic equation for electrons, we theoretically study the quantum multi-photon non-linear absorption of a strong electromagnetic wave (EMW) in two-dimensional graphene. Two cases of the electron scattering mechanism are considered: Electron-optical phonon scattering and electron-acoustic phonon scattering. The general multi-photon absorption coefficient is presented as a function of the temperature, the external magnetic field, the photon energy and the amplitude of external EMW. These analytical expressions for multi-photon non-linear absorption coefficient (MNAC) are numerically calculated and the results are discussed in both the absence and presence of a magnetic field perpendicular to the graphene sheet. The results show that there is no absorption peak in the absence of the magnetic field, which contrasts with previous results in 2D systems such as quantum wells or superlattices. However, when there is a strong magnetic field along the direction perpendicular to the 2D graphene, absorption spectral lines appear consistent with the magneto-phonon resonance conditions. Our calculations show that the MPA's effect is stronger than mono-photon absorption. Besides, the quantum multi-photon non-linear absorption phenomenon has been studied from low to high temperatures. This transcends the limits of the classical BKE which is studied in the high-temperature domain. The computational results show that the dependence of MNAC on the above quantities is consistent with the previous theoretical investigation. Another novel feature of this work is that the general analytic expression for MNAC shows the Half Width at Half Maximum dependence on the magnetic field which is in good agreement with the previous experimental observations. Thus, our estimation might give a critical prediction for future experimental observations in 2D graphene.