“Relativistic” Nonlinear Electromagnetic Processes in Graphene

Abstract

As a condensed matter with unique nonlinear electromagnetic properties and, moreover, of “relativistic” nature of the interaction with strong electromagnetic radiation fields, in this chapter we will consider induced multiphoton coherent processes in graphene. The graphene—a single sheet of carbon atoms in a honeycomb lattice—possesses with such physical characteristics (quasiparticle states in graphene behave like massless “relativistic” Dirac fermions and in the interaction parameter instead of the light speed the much less Fermi velocity stands for) due to which the multiphoton effects at the interaction with external fields occur at incomparable small intensities than that are necessary in the common condensed matter with the bound–bound transitions, or free–free ones in case of charged particle beams. Thus, the nonlinear excitation of the Dirac sea and formation of multiphoton Rabi oscillations in graphene occur at billion time smaller intensities that are required for excitation of the electron–positron vacuum and, in general, for revealing of nonlinear effects in the ordinary materials. Owing to the mentioned unique property of graphene, the microscopic theory of such physical systems, in general, and specifically the description of electromagnetic processes in graphene-like nanostructures are succeeded on the basis of the “relativistic” Dirac theory, thereby connecting the microscopic theory of the condensed matter physics with the quantum electrodynamics. The significance of graphene nonlinear electromagnetic properties and, in general, the role of graphene in contemporary physics are difficult to exaggerate. Besides the various applications in nanoelectronics–nanooptics, the graphene physics opens wide research field unifying low-energy condensed matter physics and quantum electrodynamics. Many fundamental nonlinear QED processes, specifically, electron–positron pair production in superstrong laser fields of ultrarelativistic intensities, observation of which is problematic yet even in the current superintense laser fields, have their counterparts in graphene where considerably weaker electromagnetic fields are required for realization of production of the antimatter. In this connection one can note Klein paradox, Schwinger mechanism, and Zitterbewegung for particle-hole excitation, as well as diverse physical and applied effects based on Zitterbewegung, e.g., minimal conductivity at vanishing carrier concentration, etc. At the particle-hole annihilation from that induced by pump field coherent superposition states of quasiparticles in a graphene, the wave mixing and high harmonics generation processes occur with great efficiency. Due to the massless energy spectrum, the Compton wavelength for graphene quasiparticle tends to infinity. On the other hand, in the QED the Compton wavelength is characteristic length for particle–antiparticle pair creation and annihilation. So, at the interaction of an electromagnetic field with an intrinsic graphene, there is no quasiclassical limit, since no matter how weak the applied field is and how small the photon energy is, the particle-hole pairs will be created during the whole interaction process—at the arbitrary distances. One can change the topology of the Fermi surface in the low-energy region and many important features of a graphene using the multilayer graphene of diverse structure and geometry. The multilayer graphene is of great interest, since its electronic states are considerably richer than that of a monolayer graphene. For example, in case of a bilayer graphene, the interlayer coupling between the two graphene sheets changes the monolayer’s Dirac cone inducing a trigonal warping on the band dispersion and changing the topology of the Fermi surface. Thus, bilayer graphene (AB-stacked) may have better potential than a single-layer graphene for photonic applications due to its anisotropic band structure and widely tunable bandgap. For the intrinsic bilayer graphene trigonal warping effects in the energy spectrum are considerable for the low-energy excitations \( E\lesssim 10\) meV. Hence, one can expect essential enhancement of nonlinear electromagnetic response of a bilayer graphene compared with a monolayer one in the THz domain where high-power THz generators and frequency multipliers are of special interest for THz science.