Third order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature
J. L. Cheng, N. Vermeulen, J. E. Sipe
备注：
23+ pages, 10 figures. In this version we correct a sign typo in Eq. (25), for which we thank the discussion in the work http://arxiv.org/abs/1506.00534v3
We investigate the effect of phenomenological relaxation parameters on the third order optical nonlinearity of doped graphene by perturbatively solving the semiconductor Bloch equation around the Dirac points. An analytic expression for the nonlinear conductivity at zero temperature is obtained under the linear dispersion approximation. With this analytic formula as starting point, we construct the conductivity at finite temperature and study the optical response to a laser pulse of finite duration. We illustrate the dependence of several nonlinear optical effects, such as third harmonic generation, Kerr effects and two photon absorption, parametric frequency conversion, and two color coherent current injection, on the relaxation parameters, temperature, and pulse duration. In the special case where one of the electric fields is taken as a dc field, we investigate the dc-current and dc-field induced second order nonlinearities, including dc-current induced second harmonic generation and difference frequency generation.
Numerically solving the semiconductor Bloch equations within a phenomenological relaxation time approximation, we extract both the linear and nonlinear optical conductivities of doped graphene and gapped graphene under excitation by a laser pulse. We discuss in detail the dependence of second harmonic generation, third harmonic generation, and the Kerr effects on the doping level, the gap, and the electric field amplitude. The numerical results for weak electric fields agree with those calculated from available analytic perturbation formulas. For strong electric fields when saturation effects …
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We present the first experimental investigation of nonlinear optical properties of graphene flakes. We find that at near infrared frequencies a graphene monolayer exhibits a remarkably high third-order optical nonlinearity which is practically independent of the wavelengths of incident light. The nonlinear optical response can be utilized for imaging purposes, with image contrasts of graphene which are orders of magnitude higher than those obtained using linear microscopy.
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Graphene is a rising star in nonlinear optics due to its saturable absorption and giant Kerr nonlinearity, these properties are useful in digital optics based on optical nonlinear devices. However, practical applications require large optical nonlinearities and these are inherently limited by the interaction length of atomically thin graphene. Here, we demonstrate optical bistability in a Fabry Perot cavity containing monolayer and bilayer graphene which have been restructured to form nanobubbles. We find that graphene nanobubble can act as a new type of optical nonlinear media due to its vert…
Third-order nonlinear absorption and refraction coefficients of a few-layer boron carbon nitride (BCN) and reduced graphene oxide (RGO) suspensions have been measured at 3.2 eV in the femtosecond regime. Optical limiting behavior is exhibited by BCN as compared to saturable absorption in RGO. Nondegenerate time-resolved differential transmissions from BCN and RGO show different relaxation times. These differences in the optical nonlinearity and carrier dynamics are discussed in the light of semiconducting electronic band structure of BCN vis-à-vis the Dirac linear band structure of graphene.
The understanding of the structural and thermal properties of membranes, low-dimensional flexible systems in a space of higher dimension, is pursued in many fields from string theory to chemistry and biology. The case of a two-dimensional (2D) membrane in three dimensions is the relevant one for dealing with real materials. Traditionally, membranes are primarily discussed in the context of biological membranes and soft matter in general. The complexity of these systems hindered a realistic description of their interatomic structures based on a truly microscopic approach. Therefore, theories of…
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We have experimentally studied the nonlinear nature of electrical conduction in monolayer graphene devices on silica substrates. This nonlinearity manifests itself as a nonmonotonic dependence of the differential resistance on applied DC voltage bias across the sample. At temperatures below ~70K, the differential resistance exhibits a peak near zero bias that can be attributed to self-heating of the charge carriers. We show that the shape of this peak arises from a combination of different energy dissipation mechanisms of the carriers. The energy dissipation at higher carrier temperatures depe…
Most mechanical resonators are treated as simple linear oscillators. Nonlinearity in the resonance behavior of nanoelectromechanical systems (NEMS) has only lately attracted significant interest. Most recently, cubic-order nonlinearity has been used to explain anomalies in the resonance frequency behaviors in the frequency domain. Particularly, such nonlinearities were explained using cubic nonlinearity in the restoring force (Duffing nonlinearity) or damping (van der Pol nonlinearity). Understanding the limits of linear resonant behavior is particularly important in NEMS, as they are frequent…
We solve a nonlinear integral equation for the electrostatic potential in doped graphene due to an external charge, arising from a Thomas-Fermi (TF) model for screening by graphene's $π$ electron bands. In particular, we study the effects of a finite equilibrium charge carrier density in graphene, non-zero temperature, non-zero gap between graphene and a dielectric substrate, as well as the nonlinearity in the band density of states. Effects of the exchange and correlation interactions are also briefly discussed for undoped graphene at zero temperature. Nonlinear results are compared with both…
We report on theoretical study of second harmonic generation in graphene. Phenomenological analysis based on symmetry arguments is carried out. It is demontrated, that in ideal graphene samples second harmonic generation is possible only if the radiation wave vector or its magnetic field is taken into account. Microscopic theory is developed for the classical regime of radiation interaction with electrons, where photon energy is much smaller than the charge carriers characteristic energy. It is demonstrated, that the emitted radiation can be strongly circularly polarized for the linearly polar…
The long-wavelength physics of monolayer graphene in the presence of periodic strain fields has a natural chiral scattering network description. When the strain field varies slowly compared to the graphene lattice and the effective magnetic length of the induced valley pseudomagnetic field, the low-energy physics can be understood in terms of valley-polarized percolating domain-wall modes. Inspired by a recent experiment, we consider a strain field with threefold rotation and mirror symmetries but without twofold rotation symmetry, resulting in a system with the connectivity of the oriented ka…
Significant excitonic effects were observed in graphene by measuring its optical conductivity in a broad spectral range including the two-dimensional π-band saddle-point singularities in the electronic structure. The strong electron-hole interactions manifest themselves in an asymmetric resonance peaked at 4.62 eV, which is red-shifted by nearly 600 meV from the value predicted by ab-initio GW calculations for the band-to-band transitions. The observed excitonic resonance is explained within a phenomenological model as a Fano interference of a strongly coupled excitonic state and a band contin…
The nonlinear optical and optoelectronic properties of graphene with the emphasis on the processes of harmonic generation, frequency mixing, photon drag and photogalvanic effects as well as generation of photocurrents due to coherent interference effects, are reviewed. The article presents the state-of-the-art of this subject, including both recent advances and well-established results. Various physical mechanisms controlling transport are described in depth including phenomenological description based on symmetry arguments, models visualizing physics of nonlinear responses, and microscopic th…
Recent optical conductivity experiments of doped graphene in the infrared regime reveal a strong background in the energy region between the intra and interband transitions difficult to explain within conventional pictures. We propose a phenomenological model taking into account the marginal Fermi liquid nature of the quasiparticles in graphene near the neutrality point that can explain qualitatively the observed features. We also study the electronic Raman signal and suggest that it will also be anomalous.
Nonlinear optics is an increasingly important field for scientific and technological applications, owing to its relevance and potential for optical and optoelectronic technologies. Currently, there is an active search for suitable nonlinear material systems with efficient conversion and small material footprint. Ideally, the material system should allow for chip-integration and room-temperature operation. Two-dimensional materials are highly interesting in this regard. Particularly promising is graphene, which has demonstrated an exceptionally large nonlinearity in the terahertz regime. Yet, t…
This work explores a nontrivial temperature behavior of the carriers concentration, which governs graphene channel conductance in the nano-structure "graphene channel on ferroelectric substrate" that is a basic element for FETs in non-volatile memory units of new generation. We revealed the transition from a single to double antiferroelectric-like hysteresis loop of the concentration voltage dependence that happens with the temperature increase and then exist in a wide temperature range (from 350 to 500 K). Unexpectedly we revealed the double loops of polarization and concentration can have ir…
We develop a hydrodynamic description of transport properties in graphene-based systems which we derive from the quantum kinetic equation. In the interaction-dominated regime, the collinear scattering singularity in the collision integral leads to fast unidirectional thermalization and allows us to describe the system in terms of three macroscopic currents carrying electric charge, energy, and quasiparticle imbalance. Within this "three-mode" approximation we evaluate transport coeffcients in monolayer graphene as well as in double-layer graphene-based structures. The resulting classical magne…
Graphene exhibits extremely strong optical nonlinearity when a strong perpendicular magnetic field is applied, the response current shows strong field dependence even for moderate light intensity, and the perturbation theory fails. We nonperturbatively calculate full optical conductivities induced by a periodic field in an equation-of-motion framework based on the Floquet theorem, with the scattering described phenomenologically. The nonlinear response at high fields is understood in terms of the dressed electronic states, or Floquet states, which is further characterized by the optical conduc…
The complete theory of electrical conductivity of graphene at arbitrary temperature is developed with taken into account mass-gap parameter and chemical potential. Both the in-plane and out-of-plane conductivities of graphene are expressed via the components of the polarization tensor in (2+1)-dimensional space-time analytically continued to the real frequency axis. Simple analytic expressions for both the real and imaginary parts of the conductivity of graphene are obtained at zero and nonzero temperature. They demonstrate an interesting interplay depending on the values of mass gap and chemi…
We analyze nonlinear optics schemes for generating pairs of quantum entangled plasmons in the terahertz-infrared range in graphene. We predict that high plasmonic field concentration and strong optical nonlinearity of monolayer graphene enables pair-generation rates much higher than those of conventional photonic sources. The first scheme we study is spontaneous parametric down conversion in a graphene nanoribbon. In this second-order nonlinear process a plasmon excited by an external pump splits into a pair of plasmons, of half the original frequency each, emitted in opposite directions. The …
