Abstract
A transverse magnetic field in graphene, together with the high speed of Dirac electrons moving with Fermi velocity, gives rise to a set of collective modes, viz., kinetic magnetoplasmonic modes, two-dimensional equivalent of Bernstein modes, with frequencies in between the harmonics of electron cyclotron frequency. We develop a Vlasov theory of these modes in a moderate magnetic field, including finite gyroradius effects, and study their excitation by laser through linear mode conversion, facilitated by grating or periodic ribbons. At kρ→0 (where k is the wave number and ρ is the gyroradius of electrons), the magnetoplasmonic modes have frequencies near the harmonics of electron cyclotron frequency. The frequencies rise with wave number, attain maxima in the vicinity of the next cyclotron harmonic, and then fall off. In high-mobility graphene, with ribbons or grating of appropriate ripple wave number, a normally impinged laser coverts a significant fraction of its power into magnetoplasmons, reducing the laser transmissivity as observed in experiments.
Highlights
One important property of graphene[1,2,3,4,5,6,7,8] is that all its Dirac electrons, irrespective of their energy, have the same speed; vF 1⁄4 108 cm∕s as energy versus momentum relation is linear
A transverse magnetic field opens up a variety of magnetoplasmonic modes in graphene
The lowest frequency mode, at wavelengths longer than the electron gyroradius, is sort of an upper hybrid mode; its frequency variation with wave number and electron density is very different from plasmas
Summary
One important property of graphene[1,2,3,4,5,6,7,8] is that all its Dirac electrons, irrespective of their energy, have the same speed; vF 1⁄4 108 cm∕s as energy versus momentum relation is linear. We develop Vlasov formalism of magnetoplasmons in graphene mounted on a dielectric placed in a transverse static magnetic field and study their excitation via linear mode conversion. One may mention that though the electron dynamics in graphene is strongly correlated and one normally uses Dirac theory to deduce optical conductivity, Boltzmann’s equation reasonably describes transport properties.[2,18] we may add that graphene plasmons can be excited by electron beams.[19,20] Batrakov and Maksimenkov[20] have studied theoretically the excitation of terahertz surface wave over a system of unmagnetized graphene layers by a nonrelativistic electron beam They obtain spatial growth rate of the order of 0.2 cm−1 at 30 THz in eight layered graphene, using a 10-keV electron beam.
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