Nonlinear cyclotron resonance of a massless quasiparticle in graphene

Abstract

We consider the classical motion of a massless quasi-particle in a magnetic field and under a weak electromagnetic radiation with the frequency ω. Due to the non-parabolic, linear energy dispersion, the particle responds not only at the frequency ω but generates a broad frequency spectrum around it. The linewidth of the cyclotron resonance turns out to be very broad even in a perfectly pure material which allows one to explain recent experimental data in graphene. It is concluded that the linear response theory does not work in graphene in finite magnetic fields.PACS numbers: 81.05. Uw, 73.50.Fq Graphene is a recently discovered two-dimensional (2D) material [1, 2] which has attracted much attention due to its non-trivial and very interesting physical properties, see reviews [3,4]. This is a monolayer of carbon atoms packed in a dense honeycomb lattice. The band structure of electrons in graphene consists of two bands (electron and hole) which touch each other at six corners of the hexagon-shaped Brillouin zone [5]. If graphene is undoped and the temperature is zero, the lower (hole) band is fully occupied while the upper (electron) band is empty. The Fermi level goes through these six, so called Dirac points. Near these points the states of electron and holes are described by the effective Dirac equation with the vanishing effective mass of the quasiparticles, and their energy spectrum is linear,Here p = (p x , p y ) is the electronic momentum, counted from the corresponding Dirac points and V ≈ 10 8 cm/s is the material parameter. It is the massless energy dispersion (1) and the Dirac nature of graphene quasiparticles that result in its amazing physical properties which attracted so much attention in the past years. If a charged massive particle (e.g. electron) is placed in a magnetic field B, it begins to rotate in the plane perpendicular to the field B with the frequency ω c = eB/mc, determined by its mass m and charge e. If such a rotating particle is irradiated by an external electromagnetic wave with the frequency ω, it absorbs the radiation energy if the frequency of the wave is close to the cyclotron frequency, ω ≃ ω c . The phenomenon is called the cyclotron resonance (CR) and is widely used in solid state physics for characterization of material properties such as the charge carrier effective mass and the Fermi surface cross-section in metals and semiconductors [6]. The linewidth of the CR absorption line δω is determined by the scattering rate of 2D electrons and by the radiative decay rate, i.e. by losses of energy of the rotating charged particle due to the re-radiation of electromagnetic waves, see e.g. [7]. In typical semiconductor 2D electron systems, e.g. in GaAs quantum well structures, the linewidth of the CR is small as compared to the CR frequency already in magnetic fields of order of 0

Giant Optical Nonlinearity of Graphene in a Strong Magnetic Field

“…Nonlinear cyclotron resonance in graphene was considered theoretically in [5], again in the classical limit, by solving the equation of motion F = dp/dt for a massless charge. Classical approximation can be applied to electrons in low magnetic field that are occupying highly excited Landau levels n 1, when energy and momentum quantization are neglected.…”

Circular polarization dependent cyclotron resonance in large-area graphene in ultrahigh magnetic fields

“…[1][2][3] While a number of electronic transport studies have revealed novel phenomena in the presence of a high magnetic field, including half-integer quantum Hall states observed at room temperature, 1,2,4 magneto-optical properties are expected to be equally unusual, [5][6][7][8][9][10][11][12][13][14][15] especially in the magnetic quantum limit 12 where the Fermi level resides in the lowest Landau level (LL). Even in conventional 2D electron systems such as found in GaAs quantum wells, studies of cyclotron resonance (CR) in the magnetic quantum limit have shown many-body effects, [16][17][18][19] such as spin splitting in the fractional quantum Hall regime, even though CR is not expected to be sensitive to electron-electron interactions due to Kohn's theorem.…”

Magnetoabsorption of elliptically polarized electromagnetic radiation by graphene: The relaxation-time approximation and Monte Carlo method

“…This fact was theoretically discussed in [31], where it was shown that the EM response linear theory is inapplicable to describe cyclotron absorption in zero band gap graphene.…”