Transport of Dirac quasiparticles in graphene: Hall and optical conductivities

Abstract

The analytical expressions for both diagonal and off-diagonal ac and dc conductivities of graphene placed in an external magnetic field are derived. These conductivities exhibit rather unusual behavior as functions of frequency, chemical potential, and applied field which is caused by the fact that the quasiparticle excitations in graphene are Dirac-like. One of the most striking effects observed in graphene is the odd integer quantum Hall effect. We argue that it is caused by the anomalous properties of the Dirac quasiparticles from the lowest Landau level. Other quantities such as Hall angle and Nernst signal also exhibit rather unusual behavior, in particular when there is an excitonic gap in the spectrum of the Dirac quasiparticle excitations.

Dirac charge dynamics in graphene by infrared spectroscopy

“…2, and yet we registered significant conductivity below 2E F (see the Supplementary Information). This result has not been anticipated by theories developed for Dirac fermions [6][7][8] . Both extrinsic and intrinsic effects may give rise to the residual conductivity in Fig.…”

Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids

“…(39)] partially overlap at high frequency, with the effect that the real part of σ xx (ω) displays the so-called Shubnikov-de Haas oscillations around the universal ac optical conductivity of graphene, σ g (the imaginary part, in turn, oscillates around zero). [8][9][10][11][12][13][14][15] The semi-classical conductivity is null, on the other hand, thus failing to describe the magneto-transport in neutral graphene.…”

“…7 In the absence of disorder and other relaxation mechanisms (such as electron-phonon scattering), the conductivity of graphene (at zero magnetic field) would be exclusively determined by interband transitions. In the limit of no disorder, the optical conductivity of doped graphene, in the infrared region of the spectrum and at zero magnetic field, is given by [8][9][10][11][12][13][14][15] σ xx = σ g n F ( ω − 2E F ) ,…”

“…We note in passing that, when the external magnetic field is absent, a dynamic Hall effect can still be induced by using circularly polarized light impinging on graphene at a finite angle with the normal to the graphene surface. 23 In the theoretical side, the magneto-optical transport properties of graphene have been investigated with the Green's function method 8,10 , and by means of numerical implementations of the Kubo formula, us-ing exact diagonalization 19 and Chebyshev polynomial expansions. 24 These approaches come with pros and cons: numerical studies allow to explore general scenarios, whereas Green's functions allows to obtain analytic results, but many times at the expense of a lengthy calculations.…”

Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects

“…The unusual, linear dispersion of graphene quasiparticles near the Fermi level leads to a number of interesting and so far not fully understood transport phenomena, such as the minimal electrical conductivity 7,8,14,15,16,17,18,19,20,21,22,23,24,25 , absense of the weak localization 26 , unconventional quantum Hall effect 7,8,15,27,28,29 , observable even at room temperature 30 , and other. Electrodynamic properties of graphene, which have been studied both experimentally 31,32,33,34 and theoretically 5,15,16,24,28,29,35,36,37,38,39,40,41,42,43,44,45,46,47,48 , also demonstrate non-trivial features in the frequency dependent conductivity 15,…”