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The band-edge optical response of transition metal dichalcogenides, an emerging class of atomically thin semiconductors, is dominated by tightly bound excitons localized at the corners of the Brillouin zone (valley excitons). A fundamental yet unknown property of valley excitons in these materials is the intrinsic homogeneous linewidth, which reflects irreversible quantum dissipation arising from system (exciton) and bath (vacuum and other quasiparticles) interactions and determines the timescale during which excitons can be coherently manipulated. Here we use optical two-dimensional Fourier transform spectroscopy to measure the exciton homogeneous linewidth in monolayer tungsten diselenide (WSe2). The homogeneous linewidth is found to be nearly two orders of magnitude narrower than the inhomogeneous width at low temperatures. We evaluate quantitatively the role of exciton–exciton and exciton–phonon interactions and population relaxation as linewidth broadening mechanisms. The key insights reported here—strong many-body effects and intrinsically rapid radiative recombination—are expected to be ubiquitous in atomically thin semiconductors., The band-edge optical response of transition metal dichalcogenides is dominated by tightly bound valley excitons. Here, the authors use optical two-dimensional Fourier transform spectroscopy to determine the exciton homogeneous linewidth in monolayer tungsten diselenide.

We investigate the carrier dynamics in Landau-quantized graphene within the density matrix formalism. In particular, we focus on the carrier-light interaction addressing the impact of higher-order polarizations beyond the optical selection rules. We find that these terms are in general negligible, however, there are regimes, where they even become crucial for the carrier dynamics. Our calculations show that for short excitation pulses, very small Landau level broadenings, and certain configurations of magnetic field strength, Fermi energy, and excitation energy, higher-order polarizations need to be taken into account.

Terahertz (THz) technology has attracted enormous interest with conceivable applications ranging from basic science to advanced technology. One of the main challenges remains the realization of a well controlled and easily tunable THz source. Here, we predict the occurrence of a long-lived population inversion in Landau-quantized graphene (i.e. graphene in an external magnetic field) suggesting the design of tunable THz Landau level lasers. The unconventional non-equidistant quantization in graphene offers optimal conditions to overcome the counteracting Coulomb- and phonon-assisted scattering channels. In addition to the tunability of the laser frequency, we show that also the polarization of the emitted light can be controlled. Based on our microscopic insights into the underlying many-particle mechanisms, we propose two different experimentally realizable schemes to design tunable graphene-based THz Landau level lasers.

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.

We reveal the ultrafast intervalley dynamics in monolayer WS 2 with a spectrally-resolved ultrafast pump-probe experiment and a microscopic theory. We find strong intervalley Coulomb coupling in the atomically thin semiconductor.

We combine ultrafast time-resolved THz spectroscopy and microscopic modeling to study the hot-carrier relaxation and cooling dynamics in graphene; we obtain quantitative agreement without the need to invoke disorder effects and demonstrate that the dynamics are the result of the intricate interplay between carrier-carrier and carrier-phonon interactions.

Hybrid nanostructures are an emerging field in current research. The goal is to tailor material systems with desired electronic or optical properties by functionalization with molecules. Based on the density matrix formalism, we present a theoretical study on the optical properties of graphene functionalized with photoactive spiropyran molecules. Our calculations reveal the impact of the functionalization conditions on the absorption spectrum of graphene-based hybrid nanostructures. In particular, we find that the molecular coverage has a significant effect on the optical transition energy and shape, while the molecular dipole orientation plays a minor role. The external molecular dipole field induces changes in the optical properties of graphene. Inset: The photoactive spiropyran molecules can be optically switched into the merocyanine configuration that is characterized by a pronounced dipole moment [after Guo et al., J. Am. Chem. Soc. 127(43), 15045 (2005)].

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 energy (similar to 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 energy. 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 40ps.

Chemical functionalization of atomically thin nanostructures presents a promising strategy to create new hybrid nanomaterials with remarkable and externally controllable properties. Here, we review our research in the field of theoretical modeling of carbon nanotubes, graphene, and transition metal dichalcogenides located in molecular dipole fields. In particular, we provide a microscopic view on the change of the optical response of these technologically promising nanomaterials due to the presence of photo-active spiropyran molecules. The feature article presents a review of recent theoretical work providing microscopic view on the optical response of chemically functionalized carbon nanotubes, graphene, and monolayered transition metal dichalcogenides. In particular, we propose a novel sensor mechanism based on the molecule-induced activation of dark excitons. This results in a pronounced additional peak presenting an unambiguous optical fingerprint for the attached molecules.

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.

Carrier multiplication is a many-particle process giving rise to the generation of multiple electron-hole pairs. This process holds the potential to increase the power conversion efficiency of photovoltaic devices. In graphene, carrier multiplication has been theoretically predicted and recently experimentally observed. However, due to the absence of a bandgap and competing phonon-induced electron-hole recombination, the extraction of charge carriers remains a substantial challenge. Here we present a new strategy to benefit from the gained charge carriers by introducing a Landau quantization that offers a tunable bandgap. Based on microscopic calculations within the framework of the density matrix formalism, we report a significant carrier multiplication in graphene under Landau quantization. Our calculations reveal a high tunability of the effect via externally accessible pump fluence, temperature, and the strength of the magnetic field., 6 pages, 5 figures

In our work we combined experimental and theoretical investigations of the relaxation dynamics of the single wall carbon nanotubes (SW-CNTs) in solution samples with enriched chiralities of $(7,5)$ and $(7,6)$ species. In two-color pump-probe studies we observe three-exponential decay in the differential transmission spectra in the range of few picoseconds, tens of picoseconds, and hundreds of picoseconds. Decay curves are very similar for both SW-CNT chiralities under resonant excitation and probing of excited and ground state transition energies, respectively. Both types of tubes exhibit no changes in decay for the different excitation energies in the range $\ifmmode\pm\else\textpm\fi{}50\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ around the excited state. By tuning the probe pulse towards energies higher then ground state (up to $+350\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$) we observe acceleration of the first decay component from $5.8\phantom{\rule{0.16em}{0ex}}\mathrm{ps}$ down to $1.6\phantom{\rule{0.16em}{0ex}}\mathrm{ps}$. Our experimental results are supported by time resolved microscopic calculations based on carbon nanotube Bloch equations proving the fast decay component behavior being dominated through scattering with acoustic phonons.

Efficient nonradiative carrier recombination strongly counteracts the appearance of optical gain in graphene. Based on a microscopic and fully quantum-mechanical study of the coupled carrier, phonon, and photon dynamics in graphene, we present a strategy to obtain a long-lived gain: Integrating graphene into a high quality photonic crystal nanocavity and applying a high-dielectric substrate suppresses the nonradiative recombination channels and gives rise to pronounced coherent light emission. This suggests the design of graphene-based laser devices covering a broad spectral range.

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.

We present a microscopic study on the pump fluence dependent carrier relaxation dynamics in optically excited graphene. Our investigation focuses on the particular role of efficient Auger processes on the carrier dynamics in different excitation regimes. It turns out that for low fluence excitations, the carrier generating impact excitation prevails over the Auger recombination resulting in a significant multiplication of optically excited carriers. In contrast, for strong excitations, we show the occurrence of a transient population inversion that quickly decays due to the predominant process of Auger recombination.

We present a microscopic study of optical properties of Bernal-stacked bilayer graphene. Our focus lies on the absorption spectrum explicitly including the impact of fully momentum-dependent optical and Coulomb matrix elements. Our approach is based on the density matrix formalism combined with tight-binding wave functions. The energy dispersion of bilayer graphene exhibits four parabolic bands resulting in interesting optical features: We find a pronounced low-energy peak, which can be clearly ascribed to cross transitions at the Dirac point. Furthermore, the bilayer spectrum shows two energetically close absorption peaks in the ultraviolet region resulting from interband transitions at the saddle point of the Brillouin zone. We discuss the impact of the carrier-light coupling element containing the optical selection rules and determining the oscillator strength of all possible optical transitions. Furthermore, we show the influence of the Coulomb interaction accounting for a considerable overall energy renormalization and the formation of electron-hole pairs at the saddle point.

Using ultrafast optical-pump terahertz-probe spectroscopy, we study the THz dynamics and electronic cooling in few-layer epitaxial and CVD graphene; a microscopic theory of carrier-carrier and carrier-phonon interactions accounts quantitatively for the observed dynamics.

We present a joint theory-experiment study on ultrafast photoluminescence from photoexcited graphene. On the basis of a microscopic theory, we reveal two distinct mechanisms behind the occurring photoluminescence: besides the well-known incoherent contribution driven by nonequilibrium carrier occupations, we found a coherent part that spectrally shifts with the excitation energy. In our experiments, we demonstrate for the first time the predicted appearance and spectral shift of the coherent photoluminescence.

Carbon nanostructures are ideal substrates for functionalization with molecules since they consist of a single atomic layer giving rise to an extraordinary sensitivity to changes in their surrounding. The functionalization opens a new research field of hybrid nanostructures with tailored properties. Here, we present a microscopic view on the substrate–molecule interaction in the exemplary hybrid material consisting of graphene functionalized with perylene molecules. First experiments on similar systems have been recently realized illustrating an extremely efficient transfer of excitation energy from adsorbed molecules to the carbon substrate, a process with a large application potential for high-efficiency photovoltaic devices and biomedical imaging and sensing. So far, there has been no microscopically founded explanation for the observed energy transfer. Based on first-principle calculations, we have explicitly investigated the different transfer mechanisms revealing the crucial importance of Förster coupling. Due to the efficient Coulomb interaction in graphene, we obtain strong Förster rates in the range of 1/fs. We investigate its dependence on the substrate–molecule distance R and describe the impact of the momentum transfer q for an efficient energy transfer. Furthermore, we find that the Dexter transfer mechanism is negligibly small due to the vanishing overlap between the involved strongly localized orbital functions. The gained insights are applicable to a variety of carbon-based hybrid nanostructures., We thank the Einstein Foundation Berlin and the Deutsche Forschungsgemeinschaft (within the collaborative research center SFB 658) for financial support. O.T.H. acknowledges the support from FWF (Project: J 3285-N20). A.R. acknowledges financial support from the European Research Council (ERC-2010-AdG-267374), Spanish Grant (FIS2010-21282-C02-01), Grupos Consolidados UPV/EHU del Gobierno Vasco (IT578-13), and the EU Project (280879-2 CRONOS CP-FP7).

We investigate the polarization dependence of the carrier excitation and relaxation in epitaxial multilayer graphene. Degenerate pump-probe experiments with a temporal resolution of 30 fs are performed for different rotation angles of the pump-pulse polarization with respect to the polarization of the probe pulse. A pronounced dependence of the pump-induced transmission on this angle is found. It reflects a strong anisotropy of the pump-induced occupation of photogenerated carriers in momentum space even though the band structure is isotropic. Within 150 fs after excitation an isotropic carrier distribution is established. Our observations imply the predominant role of collinear scattering preserving the initially optically generated anisotropy in the carrier distribution. The experiments are well described by microscopic time-, momentum, and angle-resolved modelling, which allows us to unambiguously identify non-collinear carrier-phonon scattering to be the main relaxation mechanism giving rise to an isotropic distribution in the first hundred fs after optical excitation.

International audience; Photoluminescence excitation measurements in semi-conducting carbon nanotubes show a systematic non-resonant contribution between the well known excitonic resonances. Using a global analysis method, we were able to delineate the contribution of each chiral species including its tiny non-resonant component. By comparison with the recently reported excitonic absorption cross-section on the S22 resonance, we found a universal non-resonant absorbance which turns out to be of the order of one half of that of an equivalent graphene sheet. This value as well as the absorption line-shape in the non-resonant window is in excellent agreement with microscopic calculations based on the density matrix formalism. This non-resonant absorption of semi-conducting nanotubes is essentially frequency independent over 0.5 eV wide windows and reaches approximately the same value betweeen the S11 and S22 resonances or between the S22 and S33 resonances. In addition, the non-resonant absorption cross-section turns out to be the same for all the chiral species we measured in this study. From a practical point of view, this study puts firm basis on the sample content analysis based on photoluminescence studies by targeting specific excitation wavelengths that lead to almost uniform excitation of all the chiral species of a sample within a given diameter range. In contrast to graphene, single-wall carbon nanotubes (SWNTs) show marked resonances in their optical spectrum that primarily reflect the one-dimensional quantum confinement of carriers. These resonances that combine one-dimensional and excitonic characteristics have been extensively investigated and are widely used as finger prints of the (n, m) species [1]. However, spectroscopic studies reveal that the absorption of nanotubes does not vanish between resonances and consists of a wealth of tiny structures, such as phonon side-bands, crossed exci-tons (S ij), or higher excitonic states [2–5]. In ensemble measurements, the non-resonant absorption is even more congested due to the contribution of residual catalyst or amorphous carbon and due to light scattering [6]. In total , a relatively smooth background showing an overall increase with photon energy is observed, from which it is challenging to extract any quantitative information. In this study, we show that thorough photolumines-cence excitation (PLE) measurements yield a much finer insight into the non-resonant absorption of carbon nan-otubes, that reveals the universal features of light-matter interaction in carbon nano-structures [7]. In particular, we show that the non-resonant absorption of SWNTs per unit area well above the S 11 or S 22 resonances reaches an universal value of 0.013±0.003 in good agreement with the value α √ 3 (where α is the fine structure constant) predicted by a simple band-to-band theory. Our study of non-resonant absorption is based on the global analysis of PLE maps of ensembles of carbon nan-otubes that allows us to deconvolute the contribution of each (n, m) species while keeping a high signal to noise

We illustrate the potential of the density matrix theory for investigation of optical properties of arbitrary single-walled carbon nanotubes (CNTs). We have performed microscopic calculations of excitonic absorption spectra for CNTs of different chiral angles and diameters. The obtained results are in good agreement with experiments, in particular the excitonic binding energies match well both experiments and ab initio calculations. Furthermore, we show the strength of our approach by presenting calculations of the ultrafast Coulomb driven non-equilibrium dynamics in CNTs. We find excitation induced dephasing on the picosecond time scale depending on the excitation strength. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We present an analytical investigation of the optical absorption spectrum of monolayer molybdenum-disulfide. Based on the density matrix formalism, our approach gives insights into the microscopic origin of excitonic transitions, their relative oscillator strength, and binding energy. We show analytical expressions for the carrier-light coupling element, which contains the optical selection rules and describes well the valley-selective polarization in ${\mathrm{MoS}}_{2}$. In agreement with experimental results, we find the formation of strongly bound electron-hole pairs due to the efficient Coulomb interaction. The absorption spectrum of MoS${}_{2}$ features two pronounced peaks corresponding to the A and B exciton. For MoS${}_{2}$ on a SiO${}_{2}$ substrate, these are characterized by binding energies of 455 meV and 465 meV, respectively. Our calculations reveal their relative oscillator strength and predict the appearance of further low-intensity excitonic transitions at higher energies. The presented approach is applicable to other transition metal dichalcogenides and can be extended to investigations of trion and biexcitonic effects.

The knowledge of the intrinsic absorption intensity of each carbon nanotube is of crucial importance for the optical assignment of nanotube species and the estimation of their abundance in a sample. Based on a microscopic approach, we calculate excitonic absorption spectra for a variety of semiconducting and metallic nanotubes, revealing a clear diameter, chirality, and family dependence of the absorption intensity. In particular, we also study the appearance of excited excitonic transitions, which are shown to be well pronounced for semiconducting nanotubes, reaching intensities of up to 10% of the main transition. We find that nanotubes with large diameters show the most pronounced absorption intensities, confirming well the experimentally observed trend. Depending on the CNT family and transition, the absorption is enhanced or reduced with the chiral angle. This behavior reflects well the qualitative chirality dependence of the analytically derived optical matrix element.

1. Introduction - The Carbon Age 2. Theoretical Framework 3. Experimental techniques for the Study of Ultrafast Nonequilibrium Carrier Dynamics in Graphene Part One: Electronic Properties - Carrier Relaxation Dynamics 4. Relaxation dynamics in graphene 5. Carrier Dynamics in Carbon Nanotubes Part Two: Optical Properties - Absorption Spectra 6. Absorption Spectra of Carbon Nanotubes 7. Absorption Spectrum of Graphene A Introduction to the Appendices B Observables in Optical Experiments C Second Quantization D Equations of Motion E Mean-Field and Correlation Effects

The carrier dynamics in optically excited graphene is determined by an interplay between the Coulomb- and phonon-induced scattering processes. The pump fluence of the excitation pulse plays a crucial role: for high fluences the ultrafast relaxation dynamics is determined by carrier–carrier scattering, whereas for low fluences the carrier–phonon relaxation channels are predominant. On the basis of a microscopic approach, we shed light on the influence of the pump fluence on the temporal evolution of carrier and phonon occupations as well as on the many-particle dephasing of the microscopic polarization. The new insights obtained contribute to a better understanding of the ultrafast carrier dynamics in graphene and can guide future pump–probe experiments.

Applying the density matrix formalism, we obtain microscopic access to the time- and momentum-resolved carrier relaxation dynamics driven by acoustic and optical phonons in semiconducting carbon nanotubes. Our calculations predict two clearly distinguishable relaxation times: the ultrafast component in the femtosecond range is ascribed to the scattering with optical phonons, while the slower component on a time scale of a few picoseconds stems from acoustic phonons. Investigating a number of different nanotubes sheds light on the diameter and chirality dependence of the phonon-induced carrier relaxation dynamics. The difference in the carrier–phonon coupling elements and in the dispersion relation for optical and acoustic phonons explains the significant variation in the efficiency of the corresponding relaxation channels.

The ultrafast carrier dynamics in graphene has been intensively investigated in recent years. From the theoretical side the graphene Bloch equations have been successfully applied to explain linear absorption and various features observed in optical pump-probe experiments. Here, we present a detailed derivation of the graphene Bloch equations and discuss different contributions resulting from the electron-electron and electron-phonon interaction.

International audience; In this paper, we present direct time-domain investigations of therelaxation of currents in graphene due to hot carrier scattering. We use coherent control with ultrashort optical pulses to photoinject a current and detect the terahertz (THz) radiation emitted by the resulting current surge.We pre-inject a background of hot carriers using a separate pump pulse, with a variable delay between the pump and current-injection pulses. We find the effect of the hot carrier background is to reduce the current and hence the emitted THz radiation. The current damping is determined simply by the density (or temperature) of the thermal carriers. The experimental behavior is accurately reproduced in a microscopic theory, which correctly incorporates the non conservation of velocity in scattering between Dirac fermions. The results indicate that hot carriers are effective in damping the current, and are expected to be important for understanding the operation of high-speed graphene electronic devices.

Auger processes are of great importance for both fundamental research and technological applications, since they change the number of charge carriers in a system. Here, we present a microscopic study on the influence of Auger relaxation channels on the carrier dynamics in graphene. The presented time-, momentum-, and angle-resolved calculations reveal the importance of the impact excitation giving rise to a significant multiplication of optically excited carriers and a remarkable Coulomb-induced carrier cooling effect. We propose low pump fluence, high excitation energy, and low ambient temperature as optimal conditions for an efficient carrier multiplication reaching values of up to $2.5$ even in the presence of phonons. The optimal regime is confirmed by an analytic expression for the carrier multiplication, which gives further insights into the role of Auger processes for a Dirac-like carrier system. Our results can help to guide future experiments to demonstrate the carrier multiplication in graphene and related structures.

We use semiconductor Bloch equations to describe excitonic absorption spectra of metallic carbon nanotubes. In particular, we focus on the formation of exciton-phonon induced sidebands. Our approach is based on the density matrix formalism combining zone-folded tight-binding wave functions and electron-phonon coupling, allowing a straight-forward description of temporal and spectral many-body interactions. We observe clear excitonic features in the spectra of metallic carbon nanotubes in agreement with recent experimental and theoretical studies. Furthermore, depending on the temperature, we find significant exciton-phonon sidebands on both sides of the zero-phonon excitonic line. We investigate the polaronic shift and the transfer of the spectral weight to the sidebands for a variety of metallic nanotubes with different chiral angles and diameters.

Microscopic calculations on carrier dynamics in graphene are applied to study the optically induced generation of a current density and its decay via Coulomb- and phonon-induced scattering channels.

We perform two-color pump-probe experiments on (8,7), (10,2), (11,3) and (12,1) nanotubes. The density matrix formalism reveals that the measured few picosecond component of the relaxation dynamics is due to intraband carrier-acoustic phonon scattering.

Based on microscopic calculations, we predict a transient femtosecond population inversion in graphene suggesting graphene as a new active gain material covering a broad frequency range. In this paper, we microscopically shed light on the underlying elementary many-particle processes: Transient gain and population inversion occur due to an interplay of strong optical pumping and carrier cooling that fills states close to the Dirac point giving rise to a relaxation bottleneck. The subsequent femtosecond decay of the optical gain is mainly driven by Coulomb-induced Auger recombination. Our findings are in excellent agreement with recent experimental data.

We investigate the relaxation kinetics of optically excited charge carriers in graphene focusing on the time-, momentum-, and angle-resolved interplay between carrier-carrier and carrier-phonon scattering channels. To benchmark the theoretical approach, we first discuss the linear absorption spectrum of graphene. In agreement with recent experimental results, our calculations reveal: (i) a pronounced excitonic effect at the saddle point, (ii) a constant absorbance in the visible region, and (iii) a drop-off for energies close to the Dirac point. After a nonlinear optical excitation, we observe that $\ensuremath{\Gamma}$-LO phonons efficiently and quickly redistribute the initially highly anisotropic nonequilibrium carrier distribution. In contrast, Coulomb-induced carrier relaxation is preferably carried out directly toward the Dirac point leading to an ultrafast thermalization of the carrier system. We evaluate the temporal dynamics of optical and acoustic phonons and discuss the energy dissipation arising from phonon-induced intra- and interband scattering. Furthermore, we investigate the influence of diagonal and off-diagonal many-particle dephasing on the ultrafast carrier relaxation dynamics. The gained insights contribute to a better microscopic understanding of optical and electronic properties of graphene.

Nonequilibrium carrier dynamics in single exfoliated graphene layers on muscovite substrates are studied by ultrafast optical pump-probe spectroscopy and compared with microscopic theory. The very high 10-fs-time resolution allows for mapping the ultrafast carrier equilibration into a quasi-Fermi distribution and the subsequent slower relaxation stages. Coulomb-mediated carrier-carrier and carrier-optical phonon scattering are essential for forming hot separate Fermi distributions of electrons and holes which cool by intraband optical phonon emission. Carrier cooling and recombination are influenced by hot phonon effects.

We evaluate a density matrix theory for the description of ultrafast relaxation processes in low-dimensional carbon nanostructures. The theory is based on Bloch equations describing the temporal dynamics of charge carrier population and transition probabilities. In combination with tight-binding wavefunctions, the approach allows the microscopic calculation of linear and nonlinear optical properties of graphene and carbon nanotubes with arbitrary chirality. This way, we have access to time- and momentum-resolved relaxation dynamics of non-equilibrium charge carriers. We study absorption spectra in graphene and carbon nanotubes illustrating the importance of excitonic effects in these structures including the formation of exciton-phonon induced side-bands in carbon nanotubes. Furthermore, we illustrate the relaxation of optically excited charge carriers toward equilibrium via electron-phonon and electron-electron scattering. We observe an ultrafast thermalization of excited carriers within the first hundred femtoseconds followed by a cooling of the electronic system on the picosecond time scale. Moreover, we investigate phonon-induced intersubband relaxation between the two energetically lowest transitions in nanotubes leading to a better understanding of photoluminescence excitation (PLE) experiments.

We report on carrier relaxation dynamics close to the Dirac point in epitaxially grown graphene under pulsed excitation with 10 – 250 meV photons. With decreasing photon energy, we identify different regimes – induced transmission with bi- and single-exponential decay as well as induced absorption - and discuss their physical origin.

Microscopic calculations allow to track the ultrafast relaxation of optically excited charge carriers in graphene. Its unique band structure accounts for efficient Auger-type scattering channels resulting in a significant carrier multiplication.

We present microscopic calculations of the absorption spectra of metallic single-walled carbon nanotubes. We address the controversial question of the excitonic binding energies in metallic nanotubes as well as the excitonic character of higher transitions. In spite of the strong screening, we observe binding energies in the range of 100 meV for metallic nanotubes with diameters in the range of 1–2.2 nm. Characteristic features of the absorption spectra, such as peak splitting and an asymmetric peak shape, are observed. The splitting is due to the trigonal warping effect. The peak shoulder at high energies is a result of an overlap of the excitonic excitation with the free-particle Van Hove singularity. Furthermore, we find higher transitions to be also significantly influenced by excitons. Our approach is based on density matrix, which allows the investigation of the chirality and diameter dependence of the excitonic binding energy for the first four optical transitions for a variety of different metallic and semiconducting nanotubes. DOI: 10.1103/PhysRevB.82.035433 PACS numbers: 78.67.Ch, 73.22.f, 78.47.p

We present the lasing dynamics of an electrically pumped quantum dot vertical‐cavity surface‐emitting lasers (QD‐VCSELs) using self‐consistently combined QD‐WL Maxwell‐Bloch equations. In order to determine the dephasing times of the system, Coulomb and electron‐phonon scattering processes between the quantum dot (QD) states and the QD‐embedding wetting layer (WL) states are microscopically calculated and implemented into the material equations. The QD‐WL Maxwell‐Bloch equations are used to study the characteristics of the switch‐on dynamics which are crucial for high‐speed optical systems. The carrier dynamics and the electric field propagation are evaluated using the finite‐difference time‐domain (FDTD) method within the full structure of QD‐VCSELs.

We present microscopic calculations of the light emission and carrier dynamics in an electrically pumped quantum-dot emitter at low injection currents and room temperature. The modeled structure consists of a bulk semiconductor and self organized InGaAs/GaAs quantum-dot layers (embedded by a wetting layer). Carrier transport through the structure is driven by scattering with longitudinal optical phonons including the nonequilibrium phonon dynamics. Even though the phonon distribution remains at room temperature, a substantial carrier heating corresponding to more than 50 K above the phonon temperature occurs in the wetting layer. Surprisingly, this temperature difference is observed in particular at low pump currents. It can be attributed to a nonequilibrium in the sample due to energy level alignment and external pumping.

We present theoretical investigations of the ultrafast relaxation dynamics and the excitation-induced dephasing of excitonic polarization in single-walled carbon nanotubes. Our microscopic approach is based on the density-matrix theory combined with tight-binding wave functions allowing the calculation of tubes with arbitrary diameter and chiral angle. For excitations to the single-particle continuum, the initial nonequilibrium carrier distribution is thermalized within approximately 100 fs while the polarization adiabatically follows the excitation pulse. For excitations at the excitonic resonance, we find a dephasing of the excitonic polarization on a picosecond time scale depending on the excitation strength. With increasing field intensities, the dephasing time linearly decreases, which is in agreement with recent experiments.

Quantum dot based light emitters can be used as laser and single photon devices[1]. In particular, we focus on the theory of InAs/GaAs quantum dots (QDs) embedded in a two dimensional wetting layer (WL). For simulating real devices, the interactions between electrons and holes confined in the QDs and the wetting layer are important. Therefore, we include Coulomb interaction as well as electron-phonon coupling, considering multi-phonon processes based on an effective multiphonon Hamilton operator. Within this theoretical approach, the investigation in temporal domain is carried out for two limits

Nonlinear Auger-scattering-rates between wetting-layer and quantum-dot carriers are crucial in modeling the dynamic response of quantum-dot-lasers.We show that the response is characterized by decoupled electron- and hole dynamics in the dots.