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We report on investigations of the carrier dynamics in graphene close to the Dirac point by nonlinear terahertz spectroscopy. At terahertz frequencies and low temperatures, optical-phonon scattering is suppressed. In this case, the decay of the pump-induced anisotropy in the carrier distribution is observed to be very slow, long as several ps, which is theoretically explained by non-collinear Coulomb scattering. In Landau-quantized graphene, degenerate four-wave mixing experiments in resonance to the lowest Landau level transition allow us to investigate the induced coherent polarization and to compare its dependence on THz field strength and B-field detuning with theoretical expectations.

Graphene has been in discussion as a candidate as a strong THz nonlinear material for a long time, because of its linear band structure [1,2]. However, an experimental demonstration of strong nonlinearities in Graphene in this spectral range is still missing. For Landau-quantized Graphene, in which the absorption is resonantly enhanced for allowed transitions between the Landau-levels, theory predicts a strongly enhanced nonlinearity, too [3]. In our joint experimental and theoretical work we study the third order nonlinearity in Landau-quantized graphene by employing a degenerate timeintegrated four-wave mixing experiment (FWM) in the mid-infrared spectral range. The free-electron laser FELBE was tuned to a photon energy of 78meV and the graphene sample was kept at 10K in a thin helium gas atmosphere. The magnetic field was set to 4.5T bringing the LL-1→LL0 and LL0→LL1 transition into resonance with the linearly polarized beams (see Fig.1a). The measured FWM signal (see Fig.1c) features a faster dynamics than the pump-probe signal (see Fig.1b) and is beyond the time resolution of our experiment. Nevertheless, we can recover the expected field dependencies of the studied third order nonlinearity in the experiment. The resonance behavior is measured by sweeping the magnetic field and is in agreement with our theoretical calculation. Furthermore, we derive a value of χ(3) from our experimental data that confirms the predicted strongly enhanced nonlinearity [4]. References [1] S. A. Mikhailov and K. Ziegler, J. Phys.: Condens. Matter, 20, 384204, (2008) [2] Z. Zhang and P. L. Voss, Opt. Lett., 36, 4569, (2011) [3] X. Yao and A. Belyanin, Phys. Rev. Lett., 108, 255503, (2012) [4] J. C. König-Otto, Y. Wang, A. Belyanin, C. Berger, W. A. de Heer, M. Orlita, A. Pashkin, H. Schneider, M. Helm, and S. Winnerl, Nano Lett., 17, 2184, (2017)

Here we studied various combinations (two symmetric and two asymmetric designs) of stripline widths for stripline photoconductive emitters fabricated on semi-insulating GaAs. We found out that the THz emission efficiency depends strongly on the anode width. The wider the anode, the higher is the THz amplitude. Cathode width does not play a significant role in THz emission performance.

A joint experiment-theory investigation of the carrier dynamics in graphene, in particular in the energetic vicinity of the Dirac point, is reviewed. Radiation of low photon energy is employed in order to match the intrinsic energy scales of the material, i.e. the optical phonon frequency (~200 meV) and the Fermi energy (10-20 meV), respectively. Significant slower carrier cooling is predicted and observed for photon energies below the optical phonon frequency. Furthermore, a strongly anisotropic distribution of electrons in k-space upon excitation with linearly polarized radiation is discussed. Depending on photon energy, the anisotropic distribution decays either rapidly via optical phonon emission, or slowly via non-collinear Coulomb scattering. Finally, a room temperature operated ultra-broadband hot-electron bolometer is demonstrated. It covers the spectral range from the THz to visible region with a single detector element featuring a response time of 40 ps.

Finding nonlinear optical materials for the THz and mid-infrared regimes is not straightforward. State-of-the-art devices with a high third-order optical susceptibility are often processed as complex multiquantum-well structures designed to feature one specific resonance frequency. In our work we study Landau-quantized graphene as a tunable and simple to produce nonlinear material. To this end we perform time-integrated degenerate four-wave mixing (FWM) experiments at a photon energy of 78 meV resonant to the transitions between the Landau levels LL−1, LL0 and LL1 at a magnetic field of roughly 4 T. We can recover expected scaling of the FWM-signal with the incident fields and the resonance behavior. The value of the third-order surface susceptibility in this material is in agreement with our calculations based on the density matrix formalism. We find the order of 𝜒(3) of Landau-quantized graphene to be competitive with more complex and elaborated solutions.

The third-order nonlinear susceptibility of Landau-quantized graphene is studied by degenerate time-integrated four-wave mixing in the THz regime. The revealed resonance behavior and the observed field dependencies are in agreement with our theoretical calculations.

Graphene is an ideal material to study fundamental Coulomb- and phonon-induced carrier scattering processes. Its remarkable gapless and linear band structure opens up new carrier relaxation channels. In particular, Auger scattering bridging the valence and the conduction band changes the number of charge carriers and gives rise to a significant carrier multiplication - an ultrafast many-particle phenomenon that is promising for the design of highly efficient photodetectors. Furthermore, the vanishing density of states at the Dirac point combined with ultrafast phonon-induced intraband scattering results in an accumulation of carriers and a population inversion suggesting the design of graphene-based terahertz lasers. Here, we review our work on the ultrafast carrier dynamics in graphene and Landau-quantized graphene is presented providing a microscopic view on the appearance of carrier multiplication and population inversion., 17 pages, 10 figures

Graphene, a gapless two-dimensional semiconductor, features constant optical absorption in a wide spectral range. In presence of a magnetic field, the linear band structure of graphene at low energies splits up into a series of non-equidistant Landau levels (LLs). Consequently, the optical absorption is redistributed into Landau-level resonances. Population inversion [1, 2] and strong optical nonlinearities [3] have been predicted for Landau-quantized graphene. Experimentally the population dynamics has been studied and direct evidence for strong Auger scattering in the time domain has been found [4]. In this presentation we show first experiments on the polarization dynamics and the scaling behavior of the four-wave mixing (FWM) signal. The experiments were performed on almost intrinsic layers of epitaxial multilayer graphene grown on the C-terminated side of SiC. The sample was kept at 10 K in a split coil magnet with optical access. Using linearly polarized radiation at a frequency of 19 THz we investigated the LL-1 → LL0 and LL0 → LL1 transition, which were tuned into resonance by a magnetic field of 4.5 T. Employing radiation pulses with a duration of 4 ps from the free-electron laser FELBE, the degenerate FWM signals were recorded and compared to pump-probe signals. The FWM signal is essentially symmetric and reflects the pulse duration of radiation pulses. This indicates that the dephasing time of the microscopic polarization is faster than the pulse duration. The excited population, on the other hand, is present on much longer timescales. At low intensities, the FWM scales quadratically with the power of the incident beam, that delivers two photons for the FWM process. At incident fields above ~10 kV/cm saturation is observed. Furthermore, the magnetic field was tuned while keeping the photon energy fixed. This reveals a considerably smaller linewidth of the third-order susceptibility resonance as compared to the linewidth of the linear absorption measured by Fourier transform spectroscopy. This is consistent with the nonlinear scaling of the FWM signal. Our experimental results, in particular also the deduced value for the surface susceptibility of the order of 10-19 m3/V2, are in accord with theoretical predictions based on the density matrix formalism. In summary, Landau-quantized graphene represents a strong nonlinear medium with a resonance tunable by the magnetic field. This may be interesting for nonlinear THz applications, such as frequency mixing and parametric generation. We are grateful to C. Berger and W. A. de Heer from Georgia Tech and M. Orlita from LNCMI-CNRS in Grenoble for sample growth and linear magneto-spectroscopy measurements, respectively. References [1] F. Wendler and E. Malic, Sci. Rep. 5, 12646, 2015. [2] Y. Wang, M. Tokman, and A. Belyanin Phys. Rev. Lett. 91, 033821 (2015). [3] X. Yao and A. Belyanin, Phys. Rev. Lett. 108, 255503 (2012). [4] M. Mittendorff, F. Wendler, E. Malic, E. Knorr, M. Orlita, M. Potemski, C. Berger, W. A. de Heer, H. Schneider, M. Helm, and S. Winnerl, Nature Phys. 11, 75 (2015).

The ultrafast dynamics in graphene, which is of great interest from both a fundamental as well as an application oriented point of view, has been studied intensively during the last years and ascinating effects such as carrier multiplication have been found. Here we focus on the Coulomb scattering dynamics in the energetic vicinity of the Dirac point. Utilizing an optical anisotropy, we reveal the twofold nature of Coulomb scattering in graphene by polarization resolved pump-probe experiments. Coulomb scattering is the main mechanism that transforms an optical excited non-equilibrium carrier distribution into a thermalized one and dominates the initial carrier dynamics. Many publications report extremely fast Coulomb scattering rates and thermalization times in the order of tens of fs often only estimated because of limited time resolution in experiments. This is comprehensible as the linear band structure of graphene allows carriers to scatter along a line easily since this inherently fulfils energy and momentum conservation. However, in case of excitation with linearly polarized light, the initial carrier distribution is anisotropic in k space. This means thermalization needs also a redistribution in momentum direction additionally to the equilibration in energy. When scattering with optical phonons is suppressed by photo excitation at low energy, noncollinear Coulomb scattering is limiting the thermalization time to surprisingly long times (several ps) [1]. This contrasting behaviour, namely a fast equilibration in energy but a slow one in momentum space, is what we refer to as the twofold nature of Coulomb scattering in graphene. [1] J. C. König-Otto, M. Mittendorff, T. Winzer, F. Kadi, E. Malic, A. Knorr, C. Berger, W. A. de Heer, A. Pashkin, H. Schneider, M. Helm, and S. Winnerl, Phys. Rev. Lett. 117, 087401 (2016).

We investigate strip line photoconductive terahertz (THz) emitters in a regime where both the direct emission of accelerated carriers in the semiconductor and the antenna-mediated emission from the strip line play a significant role. In particular, asymmetric strip line structures are studied. The widths of the two electrodes have been varied from 2 µm to 50 µm. The THz emission efficiency is observed to increase linearly with the width of the anode, which acts here as a plasmonic antenna giving rise to enhanced THz emission. In contrast, the cathode width does not play any significant role on THz emission efficiency. This is a consequence of the emission being caused by photoexcited electrons while the effect of photoexcited holes is negligible.

We present a fast detector (rise time 40 ps) operating at room temperature that is capable to detect radiation from the THz to visible spectral range (demonstrated wavelengths 500 µm – 780 nm) [1]. The detector consists of a CVD-grown graphene flake contacted by a broadband logarithmic periodic antenna. SiC acts as a substrate material that does not interfere with the detection mechanism in the desired frequency range, even within the Reststrahlen band of SiC (6 – 12 µm). The detector is ideal for timing purposes. Near infrared (mid- and far infrared) pulse energies of the order of 10 pJ (1 nJ) are sufficient to obtain good signal-to-noise ratios. We suggest that the bandwidth is limited by the antenna dimensions (typically several mm) on the long wavelength side and by the bandgap of SiC (380 nm) on the short wavelength side. [1] M. Mittendorff et al., Opt. Express 23, 28728 (2015).

We investigate the nonlinear plasmonic absorption in graphene ribbons by THz pump-probe spectroscopy. The optical nonlinearity is increased by more than one order of magnitude, which is in excellent agreement with theoretical calculations.

By using broadband absorber materials, bolometric detectors can typically cover an extremely large spectral range. However, since their response relies on the lattice temperature of the employed material, they exhibit slow response times. Hot electron bolometers (HEBs), on the other hand, can be extremely fast, because they exploit a change in device resistance caused by a varying electron temperature. A major drawback of HEBs based on superconductors is the required cooling to very low temperatures. We have developed a detector for room temperature operation, where the broadband absorption of the gapless material graphene is utilized. To this end, a graphene flake grown by chemical vapor deposition (CVD) is transferred to a SiC substrate and coupled to a logarithmic periodic antenna. Fast detection with a rise time of 40 ps is demonstrated for frequencies ranging from 0.6 THz to 390 THz [1]. Interestingly, the detector properties do not deteriorate for wavelength within the Reststrahlen band of SiC (25 – 50 THz). With a noise-equivalent power of 20 µW/Hz½ (800 µW/Hz½) in the near infrared (mid- and far infrared) the detector is capable of recording pulses with energies of the order of 10 pJ (1 nJ). We show that the detector is a versatile device for timing measurements in multi-color ultrafast spectroscopy studies. [1] M. Mittendorff et al., Opt. Express 23, 28728 (2015).

Subwavelength graphene structures support localized plasmonic resonances in the terahertz and mid-infrared spectral regimes. The strong field confinement at the resonant frequency is predicted to significantly enhance the light-graphene interaction, which could enable nonlinear optics at low intensity in atomically thin, subwavelength devices. To date, the nonlinear response of graphene plasmons and their energy loss dynamics have not been experimentally studied. We measure and theoretically model the terahertz nonlinear response and energy relaxation dynamics of plasmons in graphene nanoribbons. We employ a terahertz pump − terahertz probe technique at the plasmon frequency and observe a strong saturation of plasmon absorption followed by a 10 ps relaxation time. The observed nonlinearity is enhanced by 2 orders of magnitude compared to unpatterned graphene with no plasmon resonance. We further present a thermal model for the nonlinear plasmonic absorption that supports the experimental results. The model shows that the observed strong linearity is caused by an unexpected red shift of plasmon resonance together with a broadening and weakening of the resonance caused by the transient increase in electron temperature. The model further predicts that even greater resonant enhancement of the nonlinear response can be expected in high-mobility graphene, suggesting that nonlinear graphene plasmonic devices could be promising candidates for nonlinear optical processing.