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In our study we employ a powerful method, namely a three-pulse pump-probe technique, that was first suggested by Kim et al.1, to explore the possibility to achieve transient gain photon energies below the optical phonon energy (∼ 200 meV) in graphene. Intriguingly, this technique is not widely established and to our knowledge has never been used in the mid- or far-infrared spectral range. The principle behind this method relies on the effect of a strong pre-pump pulse of 1.55 eV photons, which can cause a transient population inversion at lower energies. This population inversion is evidenced by a sign flip of the mid-infrared (86 meV photon energy) pump-probe signal that is related to either absorption or stimulated emission of mid-infrared photons of the pump beam. We present the results on multilayer graphene obtained under various experimental configurations. Our findings shed light into the completion of rapid thermalization via Coulomb scattering and carrier cooling via optical phonons. 1. Kim, K.; Urayama, J.; Norris, T.; Singh, J.; Phillips, J.; Bhattacharya, P. Appl. Phys. Lett., 2002, 81, 670-672.

Nonlinear optical properties of graphene have been discussed for a more than a decade [1]. Experimentally, the most prominent nonlinear effect is high harmonic generation in the THz range [2]. This phenomenon is caused by a reduced conductivity of hot thermalized electrons. In our study, we investigate an effect beyond the response of thermalized hot carriers, which by nature is isotropic. We observe anisotropic THz-induced bleaching related to a change in effective mass of charge carriers under strong THz excitation. We investigated monolayer and bilayer graphene on SiC with carrier concentrations of 1.0 x 10^13 cm-2 and 6.5 × 10^12 cm−2, respectively. In degenerate pump-probe experiments at 3.4 THz utilizing linearly polarized radiation, the differential transmission was recorded for co- and cross-polarized probe beams. For bilayer graphene, co-polarized probing yields signals that are about two times larger as compared to the cross-polarized case (cf. Fig. 1) [3]. Since the response of thermalized carriers is isotropic, it cannot explain the observed anisotropic bleaching. We describe the physical origin of the anisotropic nonlinear response using a simple semiclassical model: In essence, the change in effective mass in x-direction differs strongly for carriers excited along or perpendicular to the direction of the probe field. For a quantitative comparison, modelling based on the density matrix formalism with a phenomenological scattering time was performed. For a momentum scattering time of 50 fs good agreement with the experimental data is obtained. The monolayer sample shows qualitatively similar behavior, however, the scaling of the induced transmission with the pump electric field is different. In summary, time-resolved THz nonlinear spectroscopy turns out as a powerful method to explore nonlinearities directly related to the bandstructure of Dirac materials. [1] S. A. Mikhailov and K. Ziegler, J. Phys.: Condens. Matter 20, 384204 (2008). [2] H. A. Hafez et al., Nature 561, 507 (2018). [3] A. Seidl et al., Phys. Rev. B. 105, 085404 (2022).

We investigate the carrier dynamics in the system of Landau-levels LL-2, LL-1, LL1, and LL2 of multi-layer graphene on SiC at 10 K. We perform degenerate pump-probe experiments at 75 meV with circularly polarized radiation addressing the transitions LL-2 → LL1 and LL-1 → LL2 selectively. In the co-polarized configurations, we observe bleaching of the LL-2 → LL1 and LL-1 → LL2 transition, respectively. We discuss the dependence of scattering on the number of photoexcited carriers. The existence of a pump-probe signal in cross-polarized configurations points towards thermalization of carriers across the Landau ladder on a ps timescale.

"Analysis_code_Final" contains the theoretical calculations. "FELmeasurements" contains the raw data of the pump-probe measurements with the FEL. "LabBook" contains the corresponding lab book pages.

Graphene patterned into plasmonic structures like ribbons or discs strongly increases the linear and nonlinear optical interaction at resonance. The nonlinear optical response is governed by hot carriers, leading to a red-shift of the plasmon frequency. In magnetic fields, the plasmon hybridizes with the cyclotron resonance, resulting in a splitting of the plasmonic absorption into two branches. Here we present how this splitting can be exploited to tune the nonlinear optical response of graphene discs. In the absence of a magnetic field, a strong pump-induced increase in on-resonant transmission can be observed, but fields in the range of 3 T can change the characteristics completely, leading to an inverted nonlinearity. A two temperature model is provided that describes the observed behavior well.

Landau level spectroscopy is a powerful tool to determine the Fermi velocity in Dirac-like materials. In our study, we investigate the optical properties of charge neutral graphene on SiC in presence of strong magnetic fields applied perpendicularly to the sample. For details about this neutral large-area monolayer graphene, see [1]. We measured the linear transmission in dependence of the magnitude of the magnetic fields from 0 to 8 T for photon energies up to 100 meV. We observe a broad resonance resulting from the LL-1(LL0)→LL0(LL1) transition. It corresponds to a low Fermi velocity of 0.85x106 m/s, which is the limit of low electron-electron interaction [2]. The efficient screening is supported by the dielectric environment of the polymer layer on top of the graphene [3]. We support our understanding of the low Fermi velocity by density functional theory (DFT) calculations. In addition, we studied the dynamics of the LL-1→LL0 and LL0→LL1 transitions using circularly polarized light at 75 meV. We observe a fast decay of about 10 ps. Addressing the transitions with all four combinations of pump and probe beam polarizations, we obtain only one negative differential transmission signal. Following [4], we attribute this and the fast decay to very efficient Auger scattering processes. The observed fluence dependence of the relaxation with time constants decreasing with increasing fluence is also in accordance with this interpretation. [1] H. He, K. H. Kim, A. Danilov et al., Nat. Comm., 9, (2018) 3956. [2] D. Siegel, C.-H. Park, C. Hwang et al., PNAS, 108, 28 (2011) pp. 11365-11369. [3] P. Yadav and S. Ghosh, AIP Conference Proceedings, 1665, (2015) 050075. [4] M. Mittendorff, F. Wendler, E. Malic et al., Nat. Phys., 11 (2015) pp. 75-81.

Plasmons in subwavelength-structured graphene surfaces exhibit strong light–matter interaction and prominent resonance effects in the terahertz/mid-IR frequency range. Due to its exceptionally small electronic specific heat, graphene shows strong photoinduced hot electron effects that significantly alter the plasmon response. This can enable fast control of plasmon resonance through transient heating of carriers. We employ nonlinear pump–probe measurements on subwavelength graphene ribbons to explore the effect of photoinduced hot carriers on graphene plasmons. Measurements taken above and below the plasmon resonance frequency clearly demonstrate an optically induced red-shift of the plasmon resonance, which is a signature of hot carriers in the graphene. The observed photoinduced change in plasmon resonance exhibits very strong (of order 10%) and fast response times (few picoseconds), which are governed by the cooling rate of hot electrons. The results presented here contribute to the understanding of plasmonic hot carriers in graphene and can find applications in fast terahertz modulation and switching.

Graphene plasmonic circuits critically depend on convertingincident light into propagating graphene plasmons (GPs), and on controlling their propagation and focusing to enhance light-matter interactions. Here, the theoretical analysis and experimental studies are mainly focused on the GP induced hot-carrier generation and injection on graphene when energy transferred at different SPP interference states. We characterize the ultrafast carrier dynamics in the hybrid metal/graphene nanostructures using ultrafast pump-probe spectroscopy in the mid-inferred range. The renormalized plasmon dispersions in the interface of the metal/graphene nanostructures are investigated. And, the characterization of nonlinearity phase of the high order harmonic generation signals of the hybrid nanostructures are also demonstrated.

Saturable absorption due to Pauli blocking is a fundamental optical phenomenon that can be described fully analytically for a two-level system. In solids, the related carrier dynamics is typically much more complex. Nevertheless, the fluence dependence of the induced bleaching is typically qualitatively similar to the behaviour of a two-level system. Saturable absorbers are important photonic devices for realizing short laser pulses. We present a joint theory-experiment study, where the bleaching of graphene is studied in a wide range of fluences. In pump-probe experiments utilizing 30 fs near-infrared (wavelength 800 nm) pulses the pump-induced transmission is measured. The study reveals an unusual double-bended saturation behaviour. For fluences in the mJ/cm2 range the induced transmission saturates due to Pauli blocking. Interestingly, a qualitatively similar behaviour is found at fluences that are 1000 times smaller. In this range one would expect a linear fluence dependence of the induced transmission. Microscopic theory based on the density matrix formalism shows that the unexpected saturation at low fluences is related to intensity dependent many-particle scattering. The crucial point is the balance between in- and out-scattering of electrons from the optically excited k-space regions. The occupation of this region determines the observed transmission [1]. Full understanding of the saturation behaviour in graphene is of relevance for graphene-based saturable absorbers. Graphene is an interesting material for this purpose as it can be applied in a very broad spectral range from THz to UV [2,3]. Also the high damage threshold, which is verified in our experiments, is an attractive feature. [1] T. Winzer et al., Nature Commun. 8 (2017) 15042 [2] V. Bianchi et al., Nature Commun. 8 (2017) 15763 [3] D. G. Purdie et al., Appl. Phys. Lett. 106 (2015) 253101

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)

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).

We present a joint theory-experiment study on the transmission/absorption saturation after ultrafast pulse excitation in graphene. We reveal an unconventional double-bended saturation behavior: Both bendings separately follow the standard saturation model exhibiting two saturation fluences, however, the corresponding fluences differ by three orders of magnitude and have different physical origin. Our results reveal that this new and unexpected behavior can be ascribed to an interplay between fluence- and time-dependent many-particle scattering processes and phase-space filling effects.

Utilizing the anisotropy of the optical excitation in graphene, we reveal the twofold nature of Coulomb scattering in graphene. The initial nonequilibrium charge carrier distribution in graphene created by linearly polarized light possesses a pronounced anisotropy, which has been observed in our recent experiment [1]. In the present study we perform polarization-dependent pump-probe measurements using a photon energy of 88 meV to suppress efficiently the optical phonon scattering. In this case the relaxation dynamics leading to an isotropic distribution is dominated by noncollinear Coulomb scattering. By varying the pump fluence over a range of several orders of magnitudes we are able to successfully control the efficiency of this process. This reveals a surprising twofold nature of Coulomb scattering in graphene: Whereas collinear Coulomb scattering is known to be a very fast process on the fs timescale, noncollinear scattering is remarkably slow, resulting in a thermalization time of several ps in our experiment. Our experimental findings are complemented by the results of microscopic modelling. [1] M. Mittendorff et al., Nano Lett. 14, 1504 (2014).

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).

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 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).

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.

Anisotropic carrier distribution in optically excited graphene: The role of Coulomb scattering

We demonstrate that in graphene a nonequelibrium charge carrier distribution retains its anisotropic nature on a 10 ps timescale if the photon energy is below the optical phonon energy. Recently evidence for an anisotropic carrier distribution has been found in near-infrared pump-probe experiments with varied angle between the orientation of pump and probe polarization [1]. This anisotropy vanishes after 150 fs due to electron optical-phonon scattering. Extending this study to the mid-infrared range (E_Photon = 74 meV), i.e. to energies below the optical phonon energy, allows to strongly suppress this scattering mechanism. In accord with microscopic theory, traces of an anisotropic distribution on a 10 ps timescale are found. Note that carrier-carrier scattering, acting on a 10 fs timescale, is mainly colinear and therefor preserves the anisotropic distribution on rather long timsecales. [1] M. Mittendorff, T. Winzer, E. Malic, A. Knorr, C. Berger, W. A. de Heer, H. Schneider, M. Helm and S. Winnerl Nano Lett. 2014, 14, 1504-1507

Recently we have demonstrated anisotropic excitation and relaxation of charge carriers in graphene [1]. A near-infrared pump probe experiment with varied angle between pump and probe polarization revealed anisotropic carrier populations on a 100 fs timescale as predicted by microscopic theory. An isotropic distribution is then reached by scattering via optical phonons. Now we perform an experiment where scattering of electrons with optical phonons is strongly suppressed. To this end a photon energy of 88 meV, i.e. far below the optical phonon energy, is applied and the sample is kept at 20 K. The experiments, where the free-electron laser FELBE was used as a source, revealed an anisotropic charge carrier distribution on timescales of up to 10 ps (cf. Fig. 1). In particular we investigate the dependence of the pump-probe signals on pump fluence. We find that the anisotropy is most pronounced for low fluences and vanishes for fluences in the µJ/cm2 range. These results, complemented by microscopic theory, give clear insights in the role of Coulomb scattering on the carrier dynamics. Due to the predominantly collinear nature of Coulomb scattering, the anisotropy at low fluences is preserved on timescales larger than the ~30 fs timescale of the thermalization due to Coulomb scattering. At high fluences, however, Coulomb scattering efficiently redistributes carriers towards an isotropic distribution. References [1] M. Mittendorff, T. Winzer, E. Malic, A. Knorr, C. Berger, W. A. de Heer, H. Schneider, M. Helm and S. Winnerl, Nano Lett., 14, 1504-1507, (2014)

We present an analytical expression for the differential transmission of a delta-shaped light field in Landauquantized graphene. This enables a direct comparison of experimental spectra to theoretical calculations reflecting the carrier dynamics including all relevant scattering channels. In particular, the relation is used to provide evidence for strong Auger scattering in Landau-quantized graphene.

Coulomb interaction is the main mechanism that transforms a nonequilibrium carrier distribution in graphene into a hot Fermi-Dirac distribution. In many experiments carriers are assumed to be thermalized on a timescale well below 100 fs. However, we have recently observed that the carrier distribution is strongly anisotropic in k-space when graphene is excited with near infrared pulses (photon energy 1.5 eV, duration 30 fs). The anisotropy induced by the polarization of light vanishes on a timescale of 150 fs due to scattering with optical phonons [1]. Exciting with photon energies of 75 meV, i.e. well below the optical phonon energy (~200 meV), strongly quenches the scattering via phonons and allows one to study pure Coulomb scattering in the vicinity of the Dirac point. At low fluences the transition from the anisotropic distribution to an isotropic one is very slow (~5 ps at 10 K) since Coulomb scattering is predominantly collinear and thus preserves the anisotropic distribution. At higher fluences the strength of Coulomb scattering increases, resulting in a faster decay of the anisotropy. In a second experiment we study the relaxation dynamics in Landau quantized graphene [2]. By applying circularly polarized radiation in the pump-probe experiments individual low-index Landau level transitions can be addressed. Here a surprising effect is revealed, namely a change in sign of a pump-probe signal with respect to the expectation considering single-particle interactions only (cf.Fig.1). This is caused by strong Auger scattering that depletes the zeroth Landau level even though it is optically pumped at the same time. [1] M. Mittendorff. et al. Nano Lett., 14 2014, 1504 [2] M. Mittendorff. et al. Nature Phys., 11 2015, 75

While the carrier dynamics in graphene in absence of magnetic fields is well researched in a large spectral range ranging from UV to THz, the dynamics in Landau quantized graphene is almost unexplored. We investigate the carrier dynamics within the system of Landau levels (LLs) of index n = -1, n = 0 and n = 1 by pump-probe experiments complemented by microscopic modelling. Using circularly polarized terahertz radiation (at 18 THz) allows one to selectively excite the two energetically degenerate transitions LL-1 → LL0 and LL0 → LL1, respectively (at B  4 T). While three of the four possible configurations give intuitive results (bleaching, when pumping and probing with the same polarization, induced absorption with opposite polarizations), surprisingly, one configuration counterintuitively leads to bleaching while pumping and probing with opposite polarizations (Fig. 1 lower panel). This implies that even though LL0 is being optically pumped, its population decreases [1] ! Calculations show that LL0 is actually depleted by strong Auger scattering. Note that the two configurations shown in the Figure are distinguishable only because of the slight (n-type) doping of the graphene sample. We discuss the role of carrier-carrier and carrier-phonon scattering in Landau quantized graphene and provide an outlook on the application potential of this system for tunable THz lasers.

While the carrier dynamics in graphene in absence of magnetic fields is well researched in a large spectral range ranging from UV to THz, the dynamics in Landau quantized graphene is almost unexplored. We investigate the carrier dynamics within the system of Landau levels (LLs) of index n = -1, n = 0 and n = 1 by pump-probe experiments complemented by microscopic modelling. Using circularly polarized mid-infrared radiation (photon energy 75 meV) allows one to selectively excite the two energetically degenerate transitions LL-1 → LL0 and LL-1 → LL0, respectively. Surprisingly, induced transmission is observed in one configuration of pumping and probing with opposite configuration (cf. Fig 1 (c) and (d)). Considering single particle Pauli blocking, one would expect induced absorption in this case. The sign change indicates that LL0 is depleted by strong Auger scattering, even though it is optically pumped at the same time. We discuss the role of carrier-carrier and carrier-phonon scattering in Landau quantized graphene and provide an outlook on the application potential of this system for tunable THz lasers. References [1] M. Mittendorff, F. Wendler, E. Malic, A. Knorr, M. Orlita, M. Potemski, C. Berger, W. A. de Heer, H. Schneider, M. Helm, and S. Winnerl, " Nature Phys. 11, 75 (2015).

The non-equidistant Landau-level (LL) spectrum of graphene enables the investigation of the carrier dynamics of distinct LL transitions. We present pump-probe measurements on multilayer epitaxial graphene, complemented by microscopic modelling. The free-electron laser (FEL) FELBE served as radiation source at a wavelength of 16.5 µm, which corresponds to a photon energy of 75 meV. At a magnetic field of 4.2 T, the photon energy gets resonant with the energetically degenerate LL transitions LL-1 → LL0 and LL0 → LL1. Circularly polarized radiation allows one to address one of these transitions selectively. Besides a strong increase of the pump-probe signal at 4.2 T, we observe a complex set of pump-probe signals for all four combinations of pump and probe polarization. For contrarily polarized pump and probe radiation, one would expect negative pump-probe signals, as the initial state of the probed transition is populated (pump: σ+; probe: σ-) or the final state of the probe gets depopulated. Our measurements show the counterintuitive result of positive pump-probe signals for the case of σ+-polarized pump radiation. The experimental findings are well described by microscopic calculations based on the density matrix formalism, which helped to reveal the origin of this behavior.

We present a microscopic explanation of the controversially discussed transient negative differential transmission observed in degenerate optical pump-probe measurements in graphene. Our approach is based on the density matrix formalism allowing a time- and momentum-resolved study of carrier-light, carrier-carrier, and carrier-phonon interaction on microscopic footing. We show that phonon-assisted optical intraband transitions give rise to transient absorption in the optically excited hot carrier system counteracting pure absorption bleaching of interband transitions. While interband transition bleaching is relevant in the first hundreds of fs after the excitation, intraband absorption sets in at later times. In particular, in the low excitation regime, these intraband absorption processes prevail over the absorption bleaching resulting in a zero crossing of the differential transmission. Our findings are in good qualitative agreement with recent experimental pump-probe studies.

In the energy region between –1 eV and 1 eV the band structure of graphene is in good approximation described by identical isotropic Dirac cones for electrons and holes, respectively. Therefore, optical properties for interband excitations are typically considered to be isotropic for photon energies below 2 eV. However, our pump-probe experiments at a photon energy of 1.6 eV reveal a pronounced anisotropy in both the excitation characteristics and the subsequent relaxation dynamics. The anisotropy with 2-fold symmetry is induced by the linear polarization of the pump radiation. We compare the experimental results with calculations based on the density matrix formalism and show that optical phonons are mainly responsible for reaching an isotropic carrier distribution. In the experiments, carried out on multilayer epitaxial graphene, the angle between the polarization of pump and probe beam was varied. Pumping and probing with parallel polarization resulted in two times larger pump-induced transmission as compared to pumping and probing with orthogonal polarization [1]. The initial relaxation after the transmission maximum is faster in the parallel polarization configuration. For time delays larger than 150 fs the induced transmission is similar for the two polarization configurations, indicating that an isotropic carrier distribution is reached. The observed anisotropy in the induced transmission is direct evidence for an anisotropic carrier distribution in k-space. This anisotropy has been predicted by theory [2]. Carriers are preferentially excited in directions perpendicular to the polarization vector of the pump beam. Microscopic modelling, which describes the experimental finding well, allows us to attribute the fast initial relaxation to collinear carrier-carrier scattering. Scattering via optical phonons is mainly responsible for reaching an isotropic distribution. The results are of fundamental importance as they concern an aspect of the carrier dynamics that has escaped experimental observation so far, despite the large number of publications describing near-infrared pump-probe experiments on graphene. With respect to applications our findings may enable all-optical switches that react differently to pulses of different polarization direction. References [1] M. Mittendorff, T. Winzer, E. Malic, A. Knorr, C. Berger, W.A. de Heer, H. Schneider, and M. Helm, Nano Lett. (2014) dx.doi.org/10.1021/nl404730y. [2] M. Malic, T. Winzer, and A. Knorr, Appl. Phys. Lett. 101, 221115 (2012).

The carrier dynamics within the system of Landau levels of index n = -1 to n = 0 and n = 1 in graphene is investigated by pump-probe experiments using circularly polarized terahertz radiation. The study, complemented by microscopic modelling, reveals a pronounced carrier redistribution caused by strong Auger scattering.

Graphene can serve as an attractive detector material for the whole visible and infrared spectral range. Due to the unique band structure of graphene, with a linear dispersion next to the Dirac point where valence and conduction band touch, the absorption is constant for nearly all photon energies. Furthermore the fast carrier relaxation in graphene allows one to build up fast detectors with an electrical response in the GHz range. We demonstrate a detector based on a graphene flake combined with a logarithmic-periodic antenna structure with an outer diameter of 1mm, which connects the flake via an interdigitated structure. The graphene flake was produced by the scotch-tape method on SiO2/Si. To maximize the photocurrent the two halves of the antenna were made of different metals. The metallization was patterned by electron beam lithography. One arm of the antenna consists of a 60nm thick layer of palladium, the other one of 20nm titanium combined with 40nm of gold. With the free-electron laser FELBE at Dresden-Rossendorf we proved room temperature operation in a wide spectral range (wavelength: 8µm-220µm), the coupling of the antenna was verified by measurements of the polarization dependence of the detector for different wavelengths. Additionally we measured FEL-pulses with pulse durations around 20 ps in the wavelength range of 30µm to 220µm. The rise time of the measured signal was approximately 50 ps, the pulse length was in the range of 200 ps. Even though the responsivity was fairly low (~ 1nA/W), this detector could be very useful for timing purposes in two-color experiments.

The unique band structure of graphene results in optical properties, which are promising with respect to graphene applications in detectors, saturable absorbers and frequency mixers. For these applications the knowledge of the carrier dynamics is essential. However, while the relaxation dynamics in graphene is extensively studied in pump-probe experiments involving pumping with near-infrared photons, only few studies exist for pumping in the mid-infrared and THz spectral range [1,2]. Here we present results of single-color pump probe experiments on epitaxial graphene on SiC studied in a wide range of photon energies (8 – 245 meV). A significant slowing down of the carrier relaxation is observed when the photon energy is reduced to values below the optical phonon energy of ~200 meV. For photon energies below twice the value of the Fermi energy (Ef ≈ -13 meV) negative pump-probe signals, i.e. induced absorption is observed. This is associated with intraband absorption contributions at energies, where interband absorption is initially not possible. Our experimental results are compared to microscopic calculations based on the density matrix formalism. Comparison of experiment and theory reveals the role of scattering via optical and acoustic phonons as well as contributions from Auger scattering processes. Applying a magnetic field perpendicular to the graphene layers leads to a not equidistant Landau-level splitting. Using circularly polarized radiation for pump-probe experiments allows one to selectively measure individual Landau-level transitions. The pump-probe signals exhibit a strong dependence on the polarization state of both pump and probe radiation. [1] S. Winnerl et al. Phys. Rev. Lett. 107, 237401 (2011). [2] S. Tani, F. Blanchard, and K. Tanaka, Phys. Rev. Lett. 109, 166603 (2012).

The pump-induced transmission of graphene grown epitaxially on hexagonal SiC was studied in degenerate pump-probe experiments with photon energies in the range from 10 to 250 meV. Different relaxation times ranging from 0.5 ps to 300 ps were found. A strong increase of the relaxation time was observed when the photon energy was below the optical phonon energy (~200 meV). The experiments were complemented by microscopic modelling based on the graphene Bloch equations. This allowed us to identify the physical processes which are responsible for the carrier relaxation channels. We discuss the role of Auger-type processes, optical and acoustic phonons. The modelling, which is in good agreement with the experimental results, reveals that optical phonon scattering becomes significantly less efficient when the energy of the excitation photons is below the optical phonon energy. Surprisingly, however, scattering via optical phonons is still the predominant relaxation channel, even at lower energies. This is attributed to the presence of hot carriers, which can still fulfil energy conservation requirements [1]. For photon energies about twice the value of the Fermi energy Ef, which is about 10 meV for the quasi-intrinsic layers of the epitaxial graphene, an interesting effect is observed. As the photon energy is reduced below 2Ef, a transition from pump-induced transmission to pump-induced absorption occurs. While the induced transmission is associated with Pauli blocking of carriers which underwent interband transition, the induced absorption is caused by a change of the electron temperature due to intraband absorption.

The relaxation dynamics of graphene has been investigated in various degenerate as well as two-color pump-probe studies at excitation energies E = 1.6 eV [1-5]. We report on degenerate pump-probe spectroscopy at much lower energies (E = 20 – 250 meV; radiation source: free-electron laser) on graphene multilayers grown by thermal decomposition. Relaxation times between 20 and 40 ps are found for photon energies E < 70 meV, where only acoustic phonons can contribute to the relaxation dynamics. At 245 meV a much faster relaxation with two time constants (tau_1 ≈ 1.2 ps, tau_2 = 4 – 8 ps) is observed and attributed to contributions of optical phonons. While the pump-induced transmission is positive for E > 30 meV, pump-induced absorption occurred for E < 20 meV (Fig. 1). The increased transmission for E > 30 meV is caused by bleaching of the interband transition. We attribute the induced absorption to heating of carriers by intraband free-carrier absorption for E < 2E_F (E_F: Fermi energy). [1] J.M. Dawlaty et al., Appl. Phys. Lett. 92, 042116 (2008). [2] D. Song et al., Phys. Rev. Lett. 101, 157402 (2008). [3] P.A. George et al., Nano Lett. 8 ,4248 (2008). [4] H. Wang et al., Appl. Phys. Lett., 96, 081917 (2010). [5] D. Sun et al., Phys. Rev. Lett. 104, 136802 (2010).

We describe experiments and microscopic modelling based on density matrix theory to study the relaxation dynamics in graphene. Experiments using the free-electron laser at FZD include also experiments in magnetic fields which will show how Landau quantization can quench relaxation channels.