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MoTe$_2$ monolayers and bilayers are unique within the family of van-der-Waals materials since they pave the way towards atomically thin infrared light-matter quantum interfaces, potentially reaching the important telecommunication windows. Here, we report emergent exciton-polaritons based on MoTe$_2$ monolayer and bilayer in a low-temperature open micro-cavity in a joint experiment-theory study. Our experiments clearly evidence both the enhanced oscillator strength and enhanced luminescence of MoTe$_2$ bilayers, signified by a 38 \% increase of the Rabi-splitting and a strongly enhanced relaxation of polaritons to low-energy states. The latter is distinct from polaritons in MoTe$_2$ monolayers, which feature a bottleneck-like relaxation inhibition. Both the polaritonic spin-valley locking in monolayers and the spin-layer locking in bilayers are revealed via the Zeeman effect, which we map and control via the light-matter composition of our polaritonic resonances., Comment: 6 pages, 3 figures

In the last decade atomically thin 2D materials have emerged as a perfect platform for studying and tuning light-matter interaction and electronic properties in nanostructures. The optoelectronic properties in layered materials such as transition-metal-dichalcogenides (TMDs) are governed by excitons, Coulomb bound electron-hole pairs, even at room temperature. The energy, wave function extension, spin and valley properties of optically excited conduction electrons and valence holes are controllable via multiple experimentally accessible knobs, such as lattice strain, varying atomic registries, dielectric engineering as well as electric and magnetic fields. This results in a multitude of fascinating physical phenomena in optics and transport linked to excitons with very specific properties, such as bright and dark excitons, interlayer and charge transfer excitons as well as hybrid and moir\'e excitons. In this book chapter we introduce general optoelectronic properties of 2D materials and energy landscapes in TMD monolayers as well as their vertical and lateral heterostructures, including twisted TMD hetero- and homobilayer bilayers with moir\'e excitons and lattice recombination effects. We review the recently gained insights and open questions on exciton diffusion, strain- and field-induced exciton drift. We discuss intriguing non-linear many-particle effects, such as exciton halo formation, negative and anomalous diffusion, the surprising anti-funneling of dark excitons., Comment: 88 pages, 27 figures

Dark excitons in transition metal dichalcogenides (TMD) have been so far neglected in the context of polariton physics due to their lack of oscillator strength. However, in tungsten-based TMDs, dark excitons are known to be the energetically lowest states and could thus provide important scattering partners for polaritons. In this joint theory-experiment work, we investigate the impact of the full exciton energy landscape on polariton absorption and reflectance. By changing the cavity detuning, we vary the polariton energy relative to the unaffected dark excitons in such a way that we open or close specific phonon-driven scattering channels. We demonstrate both in theory and experiment that this controlled switching of scattering channels manifests in characteristic sharp changes in optical spectra of polaritons. These spectral features can be exploited to extract the position of dark excitons. Our work suggests new possibilities for exploiting polaritons for fingerprinting nanomaterials via their unique exciton landscape.

Efficient scattering into the exciton polariton ground state is a key prerequisite for generating Bose-Einstein condensates and low-threshold polariton lasing. However, this can be challenging to achieve at low densities due to the polariton bottleneck effect that impedes phonon-driven scattering into low-momentum polariton states. The rich exciton landscape of transition metal dichalcogenides (TMDs) provides potential intervalley scattering pathways via dark excitons to rapidly populate these polaritons. Here, we present a microscopic study exploring the time- and momentum-resolved relaxation of exciton polaritons supported by a \ce{MoSe2} monolayer integrated within a Fabry-Perot cavity. By exploiting phonon-assisted transitions between momentum-dark excitons and the lower polariton branch, we demonstrate that it is possible to circumvent the bottleneck region and efficiently populate the polariton ground state. Furthermore, this intervalley pathway is predicted to give rise to, yet unobserved, angle-resolved phonon sidebands in low-temperature photoluminescence spectra that are associated with momentum-dark excitons. This represents a distinctive experimental signature for efficient phonon-mediated polariton-dark-exciton interactions.

Momentum-indirect excitons composed of electrons and holes in different valleys define optoelectronic properties of many semiconductors, but are challenging to detect due to their weak coupling to light. The identification of an excitons' valley character is further limited by complexities associated with momentum-selective probes. Here, we study the photoluminescence of indirect excitons in controllably strained prototypical 2D semiconductors (WSe$_2$, WS$_2$) at cryogenic temperatures. We find that these excitons i) exhibit valley-specific energy shifts, enabling their valley fingerprinting, and ii) hybridize with bright excitons, becoming directly accessible to optical spectroscopy methods. This approach allows us to identify multiple previously inaccessible excitons with wavefunctions residing in K, $\Gamma$, or Q valleys in the momentum space as well as various types of defect-related excitons. Overall, our approach is well-suited to unravel and tune intervalley excitons in various semiconductors., Comment: 9 pages, 4 figures, 1 table

Any sports competition needs a timetable, specifying when and where teams meet each other. The recent International Timetabling Competition (ITC2021) on sports timetabling showed that, although it is possible to develop general algorithms, the performance of each algorithm varies considerably over the problem instances. This paper provides an instance space analysis for sports timetabling, resulting in powerful insights into the strengths and weaknesses of eight state-of-the-art algorithms. Based on machine learning techniques, we propose an algorithm selection system that predicts which algorithm is likely to perform best when given the characteristics of a sports timetabling problem instance. Furthermore, we identify which characteristics are important in making that prediction, providing insights in the performance of the algorithms, and suggestions to further improve them. Finally, we assess the empirical hardness of the instances. Our results are based on large computational experiments involving about 50 years of CPU time on more than 500 newly generated problem instances., Comment: This is the peer-reviewed author-version of https://doi.org/10.1016/j.ejor.2024.06.005, published in the European Journal of Operational Research. Copyright 2024. This manuscript version is made available under the LCC-BY-NC-ND 4.0 license (https://creativecommons.org/licenses/by-nc-nd/4.0/)

The existence of bound charge transfer (CT) excitons at the interface of monolayer lateral heterojunctions has been debated in literature, but contrary to the case of interlayer excitons in vertical heterostructure their observation still has to be confirmed. Here, we present a microscopic study investigating signatures of bound CT excitons in photoluminescence spectra at the interface of hBN-encapsulated lateral MoSe$_2$-WSe$_2$ heterostructures. Based on a fully microscopic and material-specific theory, we reveal the many-particle processes behind the formation of CT excitons and how they can be tuned via interface- and dielectric engineering. For junction widths smaller than the Coulomb-induced Bohr radius we predict the appearance of a low-energy CT exciton. The theoretical prediction is compared with experimental low-temperature photoluminescence measurements showing emission in the bound CT excitons energy range. Our joint theory-experiment study presents a significant step towards a microscopic understanding of optical properties of technologically promising 2D lateral heterostructures., Comment: 10 pagers, 4 figures

Atomically thin semiconductors such as transition metal dichalcogenide (TMD) monolayers exhibit a very strong Coulomb interaction, giving rise to a rich exciton landscape. This makes these materials highly attractive for efficient and tunable optoelectronic devices. In this article, we review the recent progress in the understanding of exciton optics, dynamics and transport, which crucially govern the operation of TMD-based devices. We highlight the impact of hBN-encapsulation, which reveals a plethora of many-particle states in optical spectra, and we outline the most novel breakthroughs in the field of exciton-polaritonics. Moreover, we underline the direct observation of exciton formation and thermalization in TMD monolayers and heterostructures in recent time-resolved ARPES studies. We also show the impact of exciton density, strain and dielectric environment on exciton diffusion and funneling. Finally, we put forward relevant research directions in the field of atomically thin semiconductors for the near future.

Integrating 2D materials into high-quality optical microcavities opens the door to fascinating many-particle phenomena including the formation of exciton-polaritons. These are hybrid quasi-particles inheriting properties of both the constituent photons and excitons. In this work, we investigate the so-far overlooked impact of dark excitons on the momentum-resolved absorption spectra of hBN-encapsulated WSe$_2$ and MoSe$_2$ monolayers in the strong-coupling regime. In particular, thanks to the efficient phonon-mediated scattering of polaritons into energetically lower dark exciton states, the absorption of the lower polariton branch in WSe$_2$ is much higher than in MoSe$_2$. It shows unique step-like increases in the momentum-resolved profile indicating opening of specific scattering channels. We study how different externally accessible quantities, such as temperature or mirror reflectance, change the optical response of polaritons. Our study contributes to an improved microscopic understanding of exciton-polaritons and their interaction with phonons, potentially suggesting experiments that could determine the energy of dark exciton states via momentum-resolved polariton absorption., Comment: 10 pages, 5 figures

In the strong light-matter coupling regime realized e.g. by integrating semiconductors into optical microcavities, polaritons as new hybrid light-matter quasi-particles are formed. The corresponding change in the dispersion relation has a large impact on optics, dynamics and transport behaviour of semiconductors. In this work, we investigate the strong-coupling regime in hBN-encapsulated MoSe$_2$ monolayers focusing on exciton-polariton diffusion. Applying a microscopic approach based on the exciton density matrix formalism combined with the Hopfield approach, we predict a drastic increase of the diffusion coefficients by two to three orders of magnitude in the strong coupling regime. We explain this behaviour by the much larger polariton group velocity and suppressed polariton-phonon scattering channels with respect to the case of bare excitons. Our study contributes to a better microscopic understanding of polariton diffusion in atomically thin semiconductors., Comment: 10 pages, 4 figures

Nanobubbles formed in monolayers of transition metal dichalcogenides (TMDCs) on top of a substrate feature localized potentials, in which electrons can be captured. We show that the captured electronic density can exhibit a non-trivial spatiotemporal dynamics, whose movements can be mapped to states in a two-level system illustrated as points of an electronic Poincar\'e sphere. These states can be fully controlled, i.e, initialized and switched, by multiple electronic wave packets. Our results could be the foundation for novel implementations of quantum circuits., Comment: This document is the Author's version of a Work that was accepted for publication in Nano Letters, copyright American Chemical Society after peer review

We experimentally demonstrate time-resolved exciton propagation in a monolayer semiconductor at cryogenic temperatures. Monitoring phonon-assisted recombination of dark states, we find a highly unusual case of exciton diffusion. While at 5 K the diffusivity is intrinsically limited by acoustic phonon scattering, we observe a pronounced decrease of the diffusion coefficient with increasing temperature, far below the activation threshold of higher-energy phonon modes. This behavior corresponds neither to well-known regimes of semiclassical free-particle transport nor to the thermally activated hopping in systems with strong localization. Its origin is discussed in the framework of both microscopic numerical and semi-phenomenological analytical models illustrating the observed characteristics of nonclassical propagation. Challenging the established description of mobile excitons in monolayer semiconductors, these results open up avenues to study quantum transport phenomena for excitonic quasiparticles in atomically-thin van der Waals materials and their heterostructures.

Atomically thin semiconductors provide an excellent platform to study intriguing many-particle physics of tightly-bound excitons. In particular, the properties of tungsten-based transition metal dichalcogenides are determined by a complex manifold of bright and dark exciton states. While dark excitons are known to dominate the relaxation dynamics and low-temperature photoluminescence, their impact on the spatial propagation of excitons has remained elusive. In our joint theory-experiment study, we address this intriguing regime of dark state transport by resolving the spatio-temporal exciton dynamics in hBN-encapsulated WSe$_2$ monolayers after resonant excitation. We find clear evidence of an unconventional, time-dependent diffusion during the first tens of picoseconds, exhibiting strong deviation from the steady-state propagation. Dark exciton states are initially populated by phonon emission from the bright states, resulting in creation of hot excitons whose rapid expansion leads to a transient increase of the diffusion coefficient by more than one order of magnitude. These findings are relevant for both fundamental understanding of the spatio-temporal exciton dynamics in atomically thin materials as well as their technological application by enabling rapid diffusion., Comment: 12 pages, 4 figures, supplementary info (7 pages, 6 figures)

Monolayers of transition metal dichalcogenides (TMDs) have a remarkable excitonic landscape with deeply bound bright and dark exciton states. Their properties are strongly affected by lattice distortions that can be created in a controlled way via strain. Here, we perform a joint theory-experiment study investigating exciton diffusion in strained tungsten disulfide (WS$_2$) monolayers. We reveal a non-trivial and non-monotonic influence of strain. Lattice deformations give rise to different energy shifts for bright and dark excitons changing the excitonic landscape, the efficiency of intervalley scattering channels, and the weight of single exciton species to the overall exciton diffusion. We predict a minimal diffusion coefficient in unstrained WS$_2$ followed by a steep speed-up by a factor of 3 for tensile biaxial strain at about 0.6\% strain - in excellent agreement with our experiments. The obtained microscopic insights on the impact of strain on exciton diffusion are applicable to a broad class of multi-valley 2D materials., Comment: 8 pages, 4 figures, supplementary info (10 pages, 5 figures)

Low-temperature photoluminescence (PL) of hBN-encapsulated monolayer tungsten diselenide (WSe$_2$) shows a multitude of sharp emission peaks below the bright exciton. Some of them have been recently identified as phonon sidebands of momentum-dark states. However, the exciton dynamics behind the emergence of these sidebands has not been revealed yet. In this joint theory-experiment study, we theoretically predict and experimentally observe time-resolved PL providing microscopic insights into thermalization of hot excitons formed after optical excitation. In good agreement between theory and experiment, we demonstrate a spectral red-shift of phonon sidebands on a timescale of tens of picoseconds reflecting the phonon-driven thermalization of hot excitons in momentum-dark states. Furthermore, we predict the emergence of a transient phonon sideband that vanishes in the stationary PL. The obtained microscopic insights are applicable to a broad class of 2D materials with multiple exciton valleys., Comment: 10 pages, 5 figures

Tightly bound excitons in monolayer semiconductors represent a versatile platform to study two-dimensional propagation of neutral quasiparticles. Their intrinsic properties, however, can be severely obscured by spatial energy fluctuations due to a high sensitivity to the immediate environment. Here, we take advantage of the encapsulation of individual layers in hexagonal boron nitride to strongly suppress environmental disorder. Diffusion of excitons is then directly monitored using time- and spatially-resolved emission microscopy at ambient conditions. We consistently find very efficient propagation with linear diffusion coefficients up to 10\,cm$^2$/s, corresponding to room temperature effective mobilities as high as 400\,cm$^2$/Vs as well as a correlation between rapid diffusion and short population lifetime. At elevated densities we detect distinct signatures of many-particle interactions and consequences of strongly suppressed Auger-like exciton-exciton annihilation. A combination of analytical and numerical theoretical approaches is employed to provide pathways towards comprehensive understanding of the observed linear and non-linear propagation phenomena. We emphasize the role of dark exciton states and present a mechanism for diffusion facilitated by free electron hole plasma from entropy-ionized excitons.

While exciton relaxation in transition metal dichalcogenides (TMDs) has been intensively studied, spatial exciton propagation has received only little attention - in spite of being a key process for optoelectronics and having already shown interesting unconventional behaviours (e.g. spatial halos). Here, we study the spatiotemporal dynamics in TMDs and track the way of optically excited excitons in time, momentum, and space. In particular, we investigate the temperature-dependent exciton diffusion including the remarkable exciton landscape constituted by bright and dark states. Based on a fully quantum mechanical approach, we show at low temperatures an unexpected negative transient diffusion. This phenomenon can be traced back to the existence of dark exciton states in TMDs and is a result of an interplay between spatial exciton diffusion and intervalley exciton-phonon scattering., Comment: 6 pages, 5 figures

The interplay of optics, dynamics and transport is crucial for the design of novel optoelectronic devices, such as photodetectors and solar cells. In this context, transition metal dichalcogenides (TMDs) have received much attention. Here, strongly bound excitons dominate optical excitation, carrier dynamics and diffusion processes. While the first two have been intensively studied, there is a lack of fundamental understanding of non-equilibrium phenomena associated with exciton transport that is of central importance e.g. for high efficiency light harvesting. In this work, we provide microscopic insights into the interplay of exciton propagation and many-particle interactions in TMDs. Based on a fully quantum mechanical approach and in excellent agreement with photoluminescence measurements, we show that Auger recombination and emission of hot phonons act as a heating mechanism giving rise to strong spatial gradients in excitonic temperature. The resulting thermal drift leads to an unconventional exciton diffusion characterized by spatial exciton halos.

Transition metal dichalcogenide monolayers have attracted wide attention due to their remarkable optical, electronic and mechanical properties. In these materials local strain distributions effectively form quasi zero-dimensional potentials, whose localized states may be populated by carrier capture from the continuum states. Using a recently developed Lindblad single-particle approach, here we study the phonon-induced carrier capture in a MoSe$_2$ monolayer. Although one decisive control parameter is the energy selection rule, which links the energy of the incoming carriers to that of the final state via the emitted phonon, we show that additionally the spatio-temporal dynamics plays a crucial role. By varying the direction of the incoming carriers with respect to the orientation of the localized potential, we introduce a new control mechanism for the carrier capture: the spatial control., Comment: 10 pages, 4 figures, 1 ancillary movie

In view of the ultrashort spatial and temporal scales involved, carrier capture processes in nanostructures are genuine quantum phenomena. To describe such processes, methods with different levels of approximations have been developed. By properly tailoring the Lindblad-based nonlinear single-particle density matrix equation provided by an alternative Markov approach, in this work we present a Lindblad superoperator to describe how the phonon-induced carrier capture affects the spatio-temporal quantum dynamics of a flying wave packet impinging on a quantum dot. We compare the results with non-Markovian quantum kinetics calculations and discuss the advantages and drawbacks of the two approaches., Comment: 15 pages, 10 figures

We investigate the propagation of electron wavepackets in single-walled carbon nanotubes via a Lindblad-based density-matrix approach that enables us to account for both dissipation and decoherence effects induced by various phonon modes. We show that, while in semiconducting nanotubes the wavepacket experiences the typical dispersion of conventional materials, in metallic nanotubes its shape remains essentially unaltered, even in the presence of the electron-phonon coupling, up to micron distances at room temperature., Comment: 4 pages, 2 figures, accepted by Appl. Phys. Lett

A recently proposed Markov approach provides Lindblad-type scattering superoperators, which ensure the physical (positive-definite) character of the many-body density matrix. We apply the mean-field approximation to such many-body equation, in the presence of one- and two-body scattering mechanisms, and we derive a closed equation of motion for the electronic single-particle density matrix, which turns out to be non-linear as well as non-Lindblad. We prove that, in spite of its nonlinear and non-Lindblad structure, the mean-field approximation does preserve the positive-definite character of the single-particle density matrix, an essential prerequisite of any reliable kinetic treatment of semiconductor quantum devices. This result is in striking contrast with conventional (non-Lindblad) Markov approaches, where the single-particle mean-field equations can lead to positivity violations and to unphysical results. Furthermore, the proposed single-particle formulation is extended to the case of quantum systems with spatial open boundaries, providing a formal derivation of a recently proposed density-matrix treatment based on a Lindblad-like system-reservoir scattering superoperator., Comment: 10 pages, 1 figure (submitted to Phys. Rev. B)

Our primary goal is to provide a rigorous treatment of scattering nonlocality in semiconductor nanostructures. On the one hand, starting from the conventional density-matrix formulation and employing as ideal instrument for the study of the semiclassical limit the well-known Wigner-function picture, we shall perform a fully quantum-mechanical derivation of the space-dependent Boltzmann equation. On the other hand, we shall examine the validity limits of such semiclassical framework, pointing out, in particular, regimes where scattering-nonlocality effects may play a relevant role; to this end we shall supplement our analytical investigation with a number of simulated experiments, discussing and further expanding preliminary studies of scattering-induced quantum diffusion in GaN-based nanomaterials. As for the case of carrier-carrier relaxation in photoexcited semiconductors, our analysis will show the failure of simplified dephasing models in describing phonon-induced scattering nonlocality, pointing out that such limitation is particularly severe for the case of quasielastic dissipation processes., Comment: 18 pages, 10 figures

In view of its local character, the semiclassical or Boltzmann theory is intrinsically unable to describe transport phenomena on ultrashort space and time scales, and to this purpose genuine quantum-transport approaches are imperative. By employing a density-matrix simulation strategy recently proposed, we shall demonstrate its power and flexibility in describing quantum-diffusion phenomena in nanoscale semiconductors. In particular, as for the case of carrier-carrier relaxation in photoexcited semiconductors, our analysis will show the failure of simplified dephasing models in describing phonon-induced scattering non-locality, pointing out that such limitation is particularly severe for the case of quasielastic dissipation processes., Comment: 6 pages, 6 figures

The Wigner-function formalism is a well known approach to model charge transport in semiconductor nanodevices. Primary goal of the present article is to point out and explain intrinsic limitations of the conventional quantum-device modeling based on such Wigner-function paradigm, providing a definite answer to open questions related to the application of the conventional spatial boundary-condition scheme to the Wigner transport equation. Our analysis shows that (i) in the absence of energy dissipation (coherent limit) the solution of the Wigner equation equipped with given boundary conditions is not unique, and (ii) when decoherence/dissipation phenomena are taken into account via a relaxation-time approximation the solution, although unique, is not necessarily a physical Wigner function., Comment: 18 pages, 8 figures, accepted by Phys. Rev. B