Low energy carrier dynamics in Landau quantized graphene and HgCdTe - Perspectives for optical gain?

Over six decades ago, the potential of relativistic electrons to emit electromagnetic radiation was initially reported [1]. The discovery of graphene with a band structure resembling massless Dirac fer-mions revitalized the search for Landau-level lasing schemes [2, 3] that started earlier on non-parabolic semiconductors. The realization of a maser based on this concept, with tuning through changes in magnetic field, holds significant appeal, especially for applications within the terahertz frequency range.
The initial steps towards reaching optical gain are selective pumping of individual Landau levels (LLs) and characterizing the lifetimes in these levels. The carrier dynamics in the three-level system LL-1, LL0 and LL1 of the non-equidistant Landau ladder in graphene was investigated by pump-probe ex-periments. Circularly polarized radiation was utilized to selectively pump and probe the energetically degenerate transitions LL-1 → LL0 and LL0 → LL1 [4]. The experiments were carried out at a photon energy of 75 meV (wavelength 16.5 µm) using the free-electron laser FELBE as a source for intense ps pulses [5]. Our findings indicate, fast Auger scattering rapidly redistributes the carriers [4]. Since several Landau laser schemes [2, 3] involve the levels LL1 and LL2, we performed pump-probe experiments on the transitions LL-1 → LL2 and LL-2 → LL1.
Pumping and probing with co-polarized radiation results in higher pump-probe signals as compared to counter-polarized configurations (cf. Fig. 1). Note that in the absence of scattering, the coun-ter-polarized configuration would provide no signal as it probes levels that are not directly affected by optical pumping. The results show that within the temporal resolution of the experiment, a non-equilibrium distribution is achieved. However, it rapidly thermalizes as indicated by the induced transmission in counter-polarized configurations that reaches a maximum a few ps later than the signals in co-polarized configuration. In summary, while the linear band structure is ideal for selective optical pumping, our experiments indicate that rapid Coulomb scattering severely limits potential to achieve population inversion in Landau-quantized graphene. For comparison, we have explored the dynamics in HgCdTe. Materials with a Cd concentration of 17 % feature (three dimensional) linear dispersion along with flat bands. The main difference to graphene is the strong spin-orbit coupling in this material. As a consequence, the energy Eigenvalues are modified to a non-equidistant ladder that does not comprise pairs of levels that match energetically for Auger scattering. Pump-probe experiments on the lowest levels reveal lifetimes of 0.5 ns, i.e. two orders of magnitude longer than in graphene, indicating that indeed Auger scattering is strongly suppressed. In this material, tunable classical cyclotron emission in the THz range has been realized upon electrical excitation.
References:
[1] J. Schneider, Phys. Rev. Lett. 2, 504 (1959).
[2] Y. R. Wang, M. Tokman, A. Belyanin, Phys. Rev. A 91, 033821 (2015).
[3] S. Brem, F. Wendler, S. Winnerl, E. Malic, Phys. Rev. Mater. 2, 034002 (2018)
[4] M. Mittendorff et al. Nature Phys. 11, 75 (2015).
[5] M. Helm et al., Eur. Phys. J. Plus 138, 158 (2023).
[6] D.B. But et al., Nat. Photonics 13, 783 (2019).