Anomalous optical saturation of low-energy Dirac states in graphene and its implication for nonlinear optics

Abstract

We reveal that optical saturation of the low-energy states takes place in graphene for arbitrarily weak electromagnetic fields. This effect originates from the diverging field-induced interband coupling at the Dirac point. Using semiconductor Bloch equations to model the electronic dynamics of graphene, we argue that the charge carriers undergo ultrafast Rabi oscillations leading to the anomalous saturation effect. The theory is complemented by a many-body study of the carrier relaxations dynamics in graphene. It will be demonstrated that the carrier relaxation dynamics is slow around the Dirac point, which in turn leads to a more pronounced saturation. The implications of this effect for the nonlinear optics of graphene are then discussed. Our analysis shows that the conventional perturbative treatment of the nonlinear optics, i.e., expanding the polarization field in a Taylor series of the electric field, is problematic for graphene, in particular at small Fermi levels and large field amplitudes.Graphene is a two-dimensional material made of carbon atoms in a honeycomb structure. Its reduced dimensionality and the symmetries of its crystalline structure render graphene a gapless semiconductor [1]. Graphene exhibits a wealth of exceptional properties, including a remarkably high mobility at room temperature [2], Klein tunneling and Zitterbewegung [3,4], existence of a nonzero Berry phase, anomalous quantum Hall effect [5-7], quantum-limited intrinsic conductivity [8], and a unique Landau level structure [9,10]. Underlying these peculiar electronic properties are its pseudo-relativistic quasiparticles that obey the massless Dirac equation [1]. As a direct consequence of their massless nature, the Dirac fermions have definite chiralities [11,12]. Owing to the specific symmetries of the crystalline structure of graphene, the dynamics of the massless Dirac quasiparticles and their chiral character are topologically preserved-i.e., many-body induced band renormalizations as well as any moderate perturbations of the lattice will not open a gap in graphene's band structure [13]. A large number of the unusual properties of graphene are associated with the topologically protected band-crossing and the chiral dynamics of the charge carriers [3].One major consequence of the topologically protected chirality of the charge carriers is the anomalous structure of the interband coupling mediated by an electromagnetic field. Its dipole matrix element obtained in the length gauge [14] exhibits a singularity at the degeneracy points, in contrast to ordinary (and even other gapless) semiconductors [15,16]. This has raised some controversy regarding the treatment of the optical response of graphene [15,17,18]. Specifically, the perturbative treatment of the nonlinear optical response has been questioned [17,19]. The nonlinear optical coeffi-cients of graphene obtained by means of perturbation theory suffer from a nonresolvable singularity [15,17]. Although substantial effort has been spent on developing comprehensive models for the ...

Terahertz shifted optical sideband generation in graphene

“…A more involved modelling of the damping constants, as done in Ref. [38], also yields a very similar results for the population inversion and the interband coherence.…”

Experimental Characterization of the Ultrafast, Tunable and Broadband Optical Kerr Nonlinearity in Graphene

“…However, if the pulse duration is longer than τ 1 then carriers continuously undergo excitation and relaxation as the pulse passes with the carrier population difference continuously evolving, and therefore the optical nonlinearity becomes dependent on the duration of the pulse. The saturability in graphene deviates from saturability in other 2D materials due to the presence of its unique gapless band structure which facilitates spontaneous saturation near the Dirac point even when there is no field 23 . Therefore, it is apt that we refer to the Kerr-type nonlinearity characterised using the Z-scan method as n 2, eff due to the presence of this contributing mechanism.…”

“…SBEs can be combined and recast in the form of a damp-driven harmonic oscillator equation. The distinctive nonlinear process can be then obtained using an iterative technique 23 .…”

“…Several theoretical works have attempted to provide a cohesive theory for the third order nonlinearity in graphene, addressing the magnitude 3,16–18 of the nonlinear refractive index (), the spectral 3,4,16 and temporal 19,20 dependence, and effects of Fermi energy modulation 3,17,18,21,22 . Although topological anomalies in graphene hinder the adaption of perturbation theory in the treatment of the optical response of graphene 3,23 , fortunately, over the optical wavelength range, nonlinear response coefficients can still describe interactions of photons. Perturbative treatment of the nonlinear optical response of graphene yields explicit expressions for the higher orders conductivity tensors.…”

Third order optical nonlinearity of three dimensional massless Dirac fermions

“…1,2 Their attractive optical properties 3 include broadband linear optical absorption and the ability to use the chemical potential to tune both plasmon resonances and an extremely strong nonlinear optical response. 4 The strong nonlinear response makes graphene a potential candidate for integration in photonic devices [5][6][7] as a source of nonlinear functionality, and it has been the focus of a large number of experimental 8,9 and theoretical [10][11][12][13][14][15][16][17][18] studies over the past decade. Experiments have explored different nonlinear phenomena including third harmonic generation (THG), the Kerr effect and two photon carrier injection, parametric frequency conversion (PFC), and two-color coherent current injection (CCI); the corresponding nonlinear coefficients have been extracted for different photon energies and chemical potentials.…”