Theory of ultrafast spatio-temporal dynamics in semiconductor heterostructures

Strong Coupling of Two-Dimensional Excitons and Plasmonic Photonic Crystals: Microscopic Theory Reveals Triplet Spectra

Monolayers of transition metal dichalcogenides (TMDCs) are direct-gap semiconductors with strong light-matter interactions featuring tightly bound excitons, while plasmonic crystals (PCs), consisting of metal nanoparticles that act as meta-atoms, exhibit collective plasmon modes and allow one to tailor electric fields on the nanoscale. Recent experiments show that TMDC-PC hybrids can reach the strong-coupling limit between excitons and plasmons, forming new quasiparticles, so-called plexcitons. To describe this coupling theoretically, we develop a self-consistent Maxwell-Bloch theory for TMDC-PC hybrid structures, which allows us to compute the scattered light in the near- and far-fields explicitly and provide guidance for experimental studies. One of the key findings of the developed theory is the necessity to differentiate between bright and originally momentum-dark excitons. Our calculations reveal a spectral splitting signature of strong coupling of more than 100 meV in gold-MoSe2 structures with 30 nm nanoparticles, manifesting in a hybridization of the plasmon mode with momentum-dark excitons into two effective plexcitonic bands. The semianalytical theory allows us to directly infer the characteristic asymmetric line shape of the hybrid spectra in the strong coupling regime from the energy distribution of the momentum-dark excitons. In addition to the hybridized states, we find a remaining excitonic mode with significantly smaller coupling to the plasmonic near-field, emitting directly into the far-field. Thus, hybrid spectra in the strong coupling regime can contain three emission peaks.

Time-domain observation of interlayer exciton formation and thermalization in a MoSe2/WSe2 heterostructure

Vertical heterostructures of transition metal dichalcogenides (TMDs) host interlayer excitons with electrons and holes residing in different layers. With respect to their intralayer counterparts, interlayer excitons feature longer lifetimes and diffusion lengths, paving the way for room temperature excitonic optoelectronic devices. The interlayer exciton formation process and its underlying physical mechanisms are largely unexplored. Here we use ultrafast transient absorption spectroscopy with a broadband white-light probe to simultaneously resolve interlayer charge transfer and interlayer exciton formation dynamics in a MoSe2/WSe2 heterostructure. We observe an interlayer exciton formation timescale nearly an order of magnitude (~1 ps) longer than the interlayer charge transfer time (~100 fs). Microscopic calculations attribute this relative delay to an interplay of a phonon-assisted interlayer exciton cascade and thermalization, and excitonic wave-function overlap. Our results may explain the efficient photocurrent generation observed in optoelectronic devices based on TMD heterostructures, as the interlayer excitons are able to dissociate during thermalization.

Impact of Optically Pumped Nonequilibrium Steady States on Luminescence Emission of Atomically Thin Semiconductor Excitons

The interplay of the nonequivalent corners in the Brillouin zone of transition metal dichalcogenides (TMDCs) has been investigated extensively. While experimental and theoretical works contributed to a detailed understanding of the relaxation of selective optical excitations and the related relaxation rates, only limited microscopic descriptions of stationary experiments are available so far. Here we present microscopic calculations for the nonequilibrium steady state properties of excitons during continuous wave pumping exemplary for monolayer MoSe_{2}. We find sharp features in photoluminescence excitation spectra and degree of polarization which result from phonon assisted excitonic transitions dominating over exciton recombination and intervalley exchange coupling.

Disentangling Many-Body Effects in the Coherent Optical Response of 2D Semiconductors

In single-layer (1L) transition metal dichalcogenides, the reduced Coulomb screening results in strongly bound excitons which dominate the linear and the nonlinear optical response. Despite the large number of studies, a clear understanding on how many-body and Coulomb correlation effects affect the excitonic resonances on a femtosecond time scale is still lacking. Here, we use ultrashort laser pulses to measure the transient optical response of 1L-WS₂. In order to disentangle many-body effects, we perform exciton line-shape analysis, and we study its temporal dynamics as a function of the excitation photon energy and fluence. We find that resonant photoexcitation produces a blue shift of the A exciton, while for above-resonance photoexcitation the transient response at the optical bandgap is largely determined by a reduction of the exciton oscillator strength. Microscopic calculations based on excitonic Heisenberg equations of motion quantitatively reproduce the nonlinear absorption of the material and its dependence on excitation conditions.

The ultrafast onset of exciton formation in 2D semiconductors

The equilibrium and non-equilibrium optical properties of single-layer transition metal dichalcogenides (TMDs) are determined by strongly bound excitons. Exciton relaxation dynamics in TMDs have been extensively studied by time-domain optical spectroscopies. However, the formation dynamics of excitons following non-resonant photoexcitation of free electron-hole pairs have been challenging to directly probe because of their inherently fast timescales. Here, we use extremely short optical pulses to non-resonantly excite an electron-hole plasma and show the formation of two-dimensional excitons in single-layer MoS₂ on the timescale of 30 fs via the induced changes to photo-absorption. These formation dynamics are significantly faster than in conventional 2D quantum wells and are attributed to the intense Coulombic interactions present in 2D TMDs. A theoretical model of a coherent polarization that dephases and relaxes to an incoherent exciton population reproduces the experimental dynamics on the sub-100-fs timescale and sheds light into the underlying mechanism of how the lowest-energy excitons, which are the most important for optoelectronic applications, form from higher-energy excitations. Importantly, a phonon-mediated exciton cascade from higher energy states to the ground excitonic state is found to be the rate-limiting process. These results set an ultimate timescale of the exciton formation in TMDs and elucidate the exceptionally fast physical mechanism behind this process.

The formation dynamics of excitons in 2D transition metal dichalcogenides are challenging to probe directly because of their inherently fast timescales. Here, the authors use extremely short optical pulses to excite an electron-hole plasma, and show the formation of 2D excitons in MoS₂ on the timescale of 30 fs.

Exciton-Scattering-Induced Dephasing in Two-Dimensional Semiconductors

Enhanced Coulomb interactions in monolayer transition metal dichalcogenides cause tightly bound electron-hole pairs (excitons) that dominate their linear and nonlinear optical response. The latter includes bleaching, energy renormalizations, and higher-order Coulomb correlation effects like biexcitons and excitation-induced dephasing. While the first three are extensively studied, no theoretical footing for excitation-induced dephasing in exciton-dominated semiconductors is available so far. In this Letter, we present microscopic calculations based on excitonic Heisenberg equations of motion and identify the coupling of optically pumped excitons to exciton-exciton scattering continua as the leading mechanism responsible for an optical-power-dependent linewidth broadening (excitation-induced dephasing) and sideband formation. Performing time-, momentum-, and energy-resolved simulations, we quantitatively evaluate the exciton-induced dephasing for the most common monolayer transition metal dichalcogenides and find an excellent agreement with recent experiments.

Intrinsic lifetime of higher excitonic states in tungsten diselenide monolayers

The reduced dielectric screening in atomically thin transition metal dichalcogenides allows to study the hydrogen-like series of higher exciton states in optical spectra even at room temperature. The width of excitonic peaks provides information about the radiative decay and phonon-assisted scattering channels limiting the lifetime of these quasi-particles. While linewidth studies so far have been limited to the exciton ground state, encapsulation with hBN has recently enabled quantitative measurements of the broadening of excited exciton resonances. Here, we present a joint experiment-theory study combining microscopic calculations with spectroscopic measurements on the intrinsic linewidth and lifetime of higher exciton states in hBN-encapsulated WSe₂ monolayers. Surprisingly, despite the increased number of scattering channels, we find both in theory and experiment that the linewidth of higher excitonic states is similar or even smaller compared to the ground state. Our microscopic calculations ascribe this behavior to a reduced exciton-phonon scattering efficiency for higher excitons due to spatially extended orbital functions.

Exciton Relaxation Cascade in two-dimensional Transition Metal Dichalcogenides

Monolayers of transition metal dichalcogenides (TMDs) are characterized by an extraordinarily strong Coulomb interaction giving rise to tightly bound excitons with binding energies of hundreds of meV. Excitons dominate the optical response as well as the ultrafast dynamics in TMDs. As a result, a microscopic understanding of exciton dynamics is the key for a technological application of these materials. In spite of this immense importance, elementary processes guiding the formation and relaxation of excitons after optical excitation of an electron-hole plasma has remained unexplored to a large extent. Here, we provide a fully quantum mechanical description of momentum- and energy-resolved exciton dynamics in monolayer molybdenum diselenide (MoSe2) including optical excitation, formation of excitons, radiative recombination as well as phonon-induced cascade-like relaxation down to the excitonic ground state. Based on the gained insights, we reveal experimentally measurable features in pump-probe spectra providing evidence for the exciton relaxation cascade.

Phonon Sidebands in Monolayer Transition Metal Dichalcogenides

Excitons dominate the optical properties of monolayer transition metal dichalcogenides (TMDs). Besides optically accessible bright exciton states, TMDs exhibit also a multitude of optically forbidden dark excitons. Here, we show that efficient exciton-phonon scattering couples bright and dark states and gives rise to an asymmetric excitonic line shape. The observed asymmetry can be traced back to phonon-induced sidebands that are accompanied by a polaron redshift. We present a joint theory-experiment study investigating the microscopic origin of these sidebands in different TMD materials taking into account intra- and intervalley scattering channels opened by optical and acoustic phonons. The gained insights contribute to a better understanding of the optical fingerprint of these technologically promising nanomaterials.

Direct exciton emission from atomically thin transition metal dichalcogenide heterostructures near the lifetime limit

We demonstrate the reduction of the inhomogeneous linewidth of the free excitons in atomically thin transition metal dichalcogenides (TMDCs) MoSe₂, WSe₂ and MoS₂ by encapsulation within few nanometre thick hBN. Encapsulation is shown to result in a significant reduction of the 10 K excitonic linewidths down to ∼3.5 meV for n-MoSe₂, ∼5.0  meV for p-WSe₂ and ∼4.8 meV for n-MoS₂. Evidence is obtained that the hBN environment effectively lowers the Fermi level since the relative spectral weight shifts towards the neutral exciton emission in n-doped TMDCs and towards charged exciton emission in p-doped TMDCs. Moreover, we find that fully encapsulated MoS₂ shows resolvable exciton and trion emission even after high power density excitation in contrast to non-encapsulated materials. Our findings suggest that encapsulation of mechanically exfoliated few-monolayer TMDCs within nanometre thick hBN dramatically enhances optical quality, producing ultra-narrow linewidths that approach the homogeneous limit.

Unconventional double-bended saturation of carrier occupation in optically excited graphene due to many-particle interactions

Saturation of carrier occupation in optically excited materials is a well-established phenomenon. However, so far, the observed saturation effects have always occurred in the strong-excitation regime and have been explained by Pauli blocking of the optically filled quantum states. On the basis of microscopic theory combined with ultrafast pump-probe experiments, we reveal a new low-intensity saturation regime in graphene that is purely based on many-particle scattering and not Pauli blocking. This results in an unconventional double-bended saturation behaviour: 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 demonstrate that this new and unexpected behaviour can be ascribed to an interplay between time-dependent many-particle scattering and phase-space filling effects.

Excitonic linewidth and coherence lifetime in monolayer transition metal dichalcogenides

Atomically thin transition metal dichalcogenides are direct-gap semiconductors with strong light–matter and Coulomb interactions. The latter accounts for tightly bound excitons, which dominate their optical properties. Besides the optically accessible bright excitons, these systems exhibit a variety of dark excitonic states. They are not visible in the optical spectra, but can strongly influence the coherence lifetime and the linewidth of the emission from bright exciton states. Here, we investigate the microscopic origin of the excitonic coherence lifetime in two representative materials (WS₂ and MoSe₂) through a study combining microscopic theory with spectroscopic measurements. We show that the excitonic coherence lifetime is determined by phonon-induced intravalley scattering and intervalley scattering into dark excitonic states. In particular, in WS₂, we identify exciton relaxation processes involving phonon emission into lower-lying dark states that are operative at all temperatures.

The interplay between dark and bright excitons has a significant impact on the optical properties of semiconducting transition metal dichalcogenides. Here, the authors perform computational and experimental studies which unveil the microscopic origin of the excitonic coherence lifetime in WS₂ and MoSe₂.

Slow Noncollinear Coulomb Scattering in the Vicinity of the Dirac Point in Graphene

The Coulomb scattering dynamics in graphene in energetic proximity to the Dirac point is investigated by polarization resolved pump-probe spectroscopy and microscopic theory. Collinear Coulomb scattering rapidly thermalizes the carrier distribution in k directions pointing radially away from the Dirac point. Our study reveals, however, that, in almost intrinsic graphene, full thermalization in all directions relying on noncollinear scattering is much slower. For low photon energies, carrier-optical-phonon processes are strongly suppressed and Coulomb mediated noncollinear scattering is remarkably slow, namely on a ps time scale. This effect is very promising for infrared and THz devices based on hot carrier effects.

Microscopic origins of the terahertz carrier relaxation and cooling dynamics in graphene

The ultrafast dynamics of hot carriers in graphene are key to both understanding of fundamental carrier–carrier interactions and carrier–phonon relaxation processes in two-dimensional materials, and understanding of the physics underlying novel high-speed electronic and optoelectronic devices. Many recent experiments on hot carriers using terahertz spectroscopy and related techniques have interpreted the variety of observed signals within phenomenological frameworks, and sometimes invoke extrinsic effects such as disorder. Here, we present an integrated experimental and theoretical programme, using ultrafast time-resolved terahertz spectroscopy combined with microscopic modelling, to systematically investigate the hot-carrier dynamics in a wide array of graphene samples having varying amounts of disorder and with either high or low doping levels. The theory reproduces the observed dynamics quantitatively without the need to invoke any fitting parameters, phenomenological models or extrinsic effects such as disorder. We demonstrate that the dynamics are dominated by the combined effect of efficient carrier–carrier scattering, which maintains a thermalized carrier distribution, and carrier–optical–phonon scattering, which removes energy from the carrier liquid.

Design of high-speed graphene-based devices relies on understanding of its ultrafast carrier dynamics. Here, the authors combine time-resolved terahertz spectroscopy and microscopic modelling to unveil the interplay between the scattering mechanisms dominating the ultrafast relaxation pathways in graphene.

Ultrafast Coulomb-Induced Intervalley Coupling in Atomically Thin WS2

Monolayers of semiconducting transition metal dichalcogenides hold the promise for a new paradigm in electronics by exploiting the valley degree of freedom in addition to charge and spin. For MoS2, WS2, and WSe2, valley polarization can be conveniently initialized and read out by circularly polarized light. However, the underlying microscopic processes governing valley polarization in these atomically thin equivalents of graphene are still not fully understood. Here, we present a joint experiment-theory study on the ultrafast time-resolved intervalley dynamics in monolayer WS2. Based on a microscopic theory, we reveal the many-particle mechanisms behind the observed spectral features. We show that Coulomb-induced intervalley coupling explains the immediate and prominent pump-probe signal in the unpumped valley and the seemingly low valley polarization degrees typically observed in pump-probe measurements compared to photoluminescence studies. The gained insights are also applicable to other light-emitting monolayer transition metal dichalcogenides, such as MoS2 and WSe2, where the Coulomb-induced intervalley coupling also determines the initial carrier dynamics.

Impact of doping on the carrier dynamics in graphene

We present a microscopic study on the impact of doping on the carrier dynamics in graphene, in particular focusing on its influence on the technologically relevant carrier multiplication in realistic, doped graphene samples. Treating the time- and momentum-resolved carrier-light, carrier-carrier, and carrier-phonon interactions on the same microscopic footing, the appearance of Auger-induced carrier multiplication up to a Fermi level of 300 meV is revealed. Furthermore, we show that doping favors the so-called hot carrier multiplication occurring within one band. Our results are directly compared to recent time-resolved ARPES measurements and exhibit an excellent agreement on the temporal evolution of the hot carrier multiplication for n- and p-doped graphene. The gained insights shed light on the ultrafast carrier dynamics in realistic, doped graphene samples.

Tunable terahertz emission through multiple Rabi flopping in a dc-biased quantum well: a new strategy

By exploiting the Rabi-flopping-induced coherent density oscillations in a weakly dc-biased quantum well, we describe a new method for producing very intense (roughly kilovolts per centimeter), tunable terahertz transients. We achieved tunability by simply varying the area of the input optical pulse.