Resonant Four-Wave Mixing in Landau-Quantized Graphene

Graphene in magnetic fields is a unique material because of its anomalous Landau level spectrum. Due to the linear density of states in graphene the energy of the Landau-levels scales with the square root of the index number and a zeroth level exists [1] (cf. Fig. 2a). Consequently individual Landau-level transitions can be addressed by varying the photon energy, in contrast to a classical Landau-quantized two-dimensional electron gas where the transition energies are degenerate. Pump-probe spectroscopy on Landau-quantized graphene (LQG) reveals fascinating effects such as an Auger-driven depopulation of an optically pumped level, recently demonstrated by some of us [2]. Theoretical calculations predict a giant non-linear χ(3) response for LQG [3]. We present for the first time results of a degenerated time-integrated transient four-wave mixing (FWM) experiment on LQG (cf. Fig. 1), where the photon energy of the linear polarized free-electron laser FELBE is resonant to the transitions from LL-1 (LL0) → LL0 (LL1) in a magnetic field of around 4.55T (cf. Fig. 2a). Comparing FWM (cf. Fig. 2c) and pump-probe (cf. Fig. 2b) signals at the same experimental conditions we observe a rapid dephasing (faster than pulse duration of ~4ps). Furthermore, we have confirmed the expected linear and quadratic dependencies of the FWM signal on the excitation intensities in directions k1 and k2, respectively. By sweeping the magnetic field and consequently shifting the energy difference between the Landau levels, the resonance behaviour of pump-probe and FWM signals was measured. In summary, we have experimentally verified that Landau-quantized graphene exhibits a significant nonlinear optical response despite the fact that it features a short dephasing time. It is an attractive nonlinear material, which allows one to tune the spectral position of the resonance by the magnetic field.

References
[1]. A. H. Castro Neto et al., Rev. Mod. Phys. 81, 109 (2009).
[2]. M. Mittendorff et al., Nat. Phys. 11, 75 (2015).
[3]. X. Yao and A. Belyanin, J. Phys. Condens. Matter 25, 054203 (2013).