Ultrafast carrier dynamics in Landau-quantized graphene

Abstract

Abstract:In an external magnetic field, the energy of massless charge carriers in graphene is quantized into non-equidistant degenerate Landau levels including a zero-energy level. This extraordinary electronic dispersion gives rise to a fundamentally new dynamics of optically excited carriers. Here, we review the state of the art of the relaxation dynamics in Landau-quantized graphene focusing on microscopic insights into possible many-particle relaxation channels. We investigate optical excitation into a non equilibrium distribution followed by ultrafast carriercarrier and carrier-phonon scattering processes. We reveal that surprisingly the Auger scattering dominates the relaxation dynamics in spite of the non-equidistant Landau quantization in graphene. Furthermore, we demonstrate how technologically relevant carrier multiplication can be achieved and discuss the possibility of optical gain in Landau-quantized graphene. The provided microscopic view on elementary many-particle processes can guide future experimental studies aiming at the design of novel graphene-based optoelectronic devices, such as highly efficient photodetectors, solar cells, and spectrally broad Landau level lasers. MotivationWith an ever-growing impact of technology on everyday life, the importance of semiconductor physics has constantly increased since the information revolution. Of particular interest is the field of optoelectronics enabling key technologies for modern communication. The fast techno-*Corresponding Author: Ermin Malic: Department of Applied Physics, Chalmers University of Technology, Gothenburg, Sweden, E-mail: ermin.malic@chalmers.se Florian Wendler: Department of Applied Physics, Chalmers University of Technology, Gothenburg, Sweden, E-mail: florian.wendler@tu-berlin.de Andreas Knorr: Institute of Theoretical Physics, Nonlinear Optics and Quantum Electronics, Technical University Berlin, Germany logical progress is accompanied by the demand for materials with new optical and electronic properties. One of the most promising materials in this regard is graphene [1][2][3][4], which was first grown epitaxially on top of SiC [5], but it was not until Novoselov and Geim prepared samples by mechanical exfoliation and demonstrated a graphenebased field-effect transistor [6] in 2004 that it received wide-spread attention.Graphene as a single layer of carbon atoms is the thinnest known two-dimensional material [3,7]. It exhibits extraordinary optical, electronic, thermal, mechanical, and chemical properties [3]. In particular, its linear electronic dispersion in the low-energy regime near the Dirac points in the Brillouin zone is most remarkable. Here, electrons move as if they were massless, just like photons in quantum electrodynamics providing the possibility to test the predictions of relativistic quantum mechanics, such as Klein tunneling [8,9], in a small-scale table top experiment.Besides the fascinating fundamental physics that can be explored in graphene, several optoelectronic applications were proposed [1], ranging fr...

Doping-dependent intraband carrier dynamics in Landau-quantized graphene

“…To microscopically model the Landau-level dynamics, we apply the Bloch equations of Landau-quantized graphene [15],…”

“…We have verified the validity of this approximation by performing calculations with and without taking into account the Coulomb interaction in different regimes. Since the optical phonon energies are much larger than the low-energy photons [15], the phononinduced relaxation should be also negligible [6]. However, to account for the rather fast experimentally observed decay of differential transmission [13,14], carrier-phonon scattering is included on a phenomenological level.…”

“…It is explicitly calculated by exploiting the self-consistent Born approximation [9,15,22]. In good approximation, it results in a Landau-level broadening of γ = v F e 0 B/A imp that depends on the Fermi velocity, the free-electron charge e 0 , the magnetic field B, and the parameter A imp determining the carrier-impurity interaction strength [22].…”

“…The nonequidistant Landau-level spectrum and the optical selection rules of Landau-quantized graphene allow the excitation of specific inter-LL transitions using circularly polarized light. As a result, one can track the path of excited electrons towards a thermalized Fermi distribution [5][6][7][8][9][10][11][12][13][14][15][16].…”

“…The applied microscopic approach is based on the density matrix formalism, a wellestablished method for modeling the many-particle-induced carrier dynamics in graphene with and without the influence of a magnetic field [9,15,[17][18][19]. In accordance with a recent pump-probe experiment [14], we consider terahertz photons with an energy of 14 meV which is well below the cyclotron energy ω c 36 meV √ B at magnetic field strengths of B = 1 T. In conventional semiconductors with an equidistant Landau quantization, the absorption of low-energy terahertz photons is generally strongly suppressed, unless the cyclotron energy coincides with the photon energy.…”