Nonlinear magneto-optic effects in doped graphene and in gapped graphene: A perturbative treatment

Abstract

The nonlinear magneto-optic responses are investigated for gapped graphene and doped graphene in a perpendicular magnetic field. The electronic states are described by Landau levels, and the electron dynamics in an optical field is obtained by solving the density matrix in the equation of motion. In the linear dispersion approximation around the Dirac points, both linear conductivity and third order nonlinear conductivities are numerically evaluated for infrared frequencies. The nonlinear phenomena, including third harmonic generation, Kerr effects and two photon absorption, and four wave mixing, are studied. All optical conductivities show strong dependence on the magnetic field. At weak magnetic fields, our results for doped graphene agree with those in the literature. We also present the spectra of the conductivities of gapped graphene. At strong magnetic fields, the third order conductivities show peaks with varying the magnetic field and the photon energy. These peaks are induced by the resonant transitions between different Landau levels. The resonant channels, the positions, and the divergences of peaks are analyzed. The conductivities can be greatly modified, up to orders of magnitude. The dependence of the conductivities on the gap parameter and the chemical potential is studied.

Third order optical nonlinearity of three dimensional massless Dirac fermions

“…As ∆ → ∞, From Eqs (22). and(23) we have σ(1);xx gg (∆ → ∞) → −4iσ 0 ω/(3π)∆ −1 and σ (3);xxyy gg (∆ → ∞) ∼ ∆ −5 . It is obvious that I (1);xx (A → ∞) diverges as ln A and I (3);xxyy (A → ∞) converges.The ∆ dependence in the conductivities of gapped graphene appears in ∆ or ∆ n G(E c ; w) for n = 0, 2, 4.…”

“…investigated various nonlinear effects both by numerically solving the equations of motion 13 and by approximation from the results of gapped graphene under a perpendicular magnetic field. 23 Recently, we derived analytic expressions for the third order conductivities of gapped graphene 24 at general frequencies, following earlier work on graphene. 12 There have also been a host of recent studies focused on the prediction and discovery of three dimensional (3D) Dirac and Weyl semimetals, [25][26][27][28][29][30][31][32] where the low energy excitations can be described by DFs with a three dimensional wave vector.…”

Radiation-induced magnetoresistance oscillations with massive Dirac fermions

“…An important point of the gapped monolayer graphene eigenstates is that at low lying energies in the conduction band, the amplitude of the wave function at the A site is predominant [55][56][57] for Φ n,K ′ . Thus, close to the conduction band bottom in the gapped monolayer graphene the Dirac fermions are A-sublatticepolarised.…”

Monolayer transition metal dichalcogenides in strong magnetic fields: Validating the Wannier model using a microscopic calculation

“…The eigenvalues and eigenfunctions of ĤB can be found by expressing ĤB in terms of creation and annihilation operators, 8,32 and then expanding the eigenfunctions in a basis of harmonic oscillator eigenfunctions. We find that the eigenvalues and the normalized eigenfunctions are given by…”