We report the implementation of energy dispersive X-ray spectroscopy for layered semiconductors in the form of atomically thin transition metal dichalcogenides. The technique is based on a scanning electron microscope equipped with a silicon drift detector for energy dispersive X-ray analysis. By optimizing operational parameters in numerical simulations and experiments, we achieve layer-resolving sensitivity for few-layer crystals down to the monolayer limit and demonstrate elemental composition profiling in vertical and lateral heterobilayers of transition metal dichalcogenides. The technique can be straight-forwardly applied to other layered two-dimensional materials and van der Waals heterostructures, thus expanding the experimental toolbox for quantitative characterization of layer number, atomic composition, or alloy gradients for atomically thin materials and devices.
Resolving the momentum degree of freedom of excitons - electron-hole pairs bound by the Coulomb attraction in a photoexcited semiconductor, has remained a largely elusive goal for decades. In atomically thin semiconductors, such a capability could probe the momentum forbidden dark excitons, which critically impact proposed opto-electronic technologies, but are not directly accessible via optical techniques. Here, we probe the momentum-state of excitons in a WSe2 monolayer by photoemitting their constituent electrons, and resolving them in time, momentum and energy. We obtain a direct visual of…
The Kohn-Luttinger envelope-function method is generalized to the case of heterostructures with atomically sharp heterojunctions based on lattice-matched layers of related semiconductors with zinc-blende symmetry. For electron states near the Γpoint in (001) heterostructures the single-band effective-mass equation is derived, taking into account both the spatial dependence of the effective mass and effects associated with the atomically sharp heterojunctions. A small parameter is identified, in powers of which it is possible to classify the various contributions to this equation. For hole stat…
Interfaces of dye molecules and two-dimensional transition metal dichalcogenides (TMDCs) combine strong molecular dipole excitations with high carrier mobilities in semiconductors. Förster type energy transfer is one key mechanism for the coupling between both constituents. We report microscopic calculations of a spectrally resolved Förster induced transition rate from dye molecules to a TMDC layer. Our approach is based on microscopic Bloch equations which are solved self-consistently together with Maxwells equations. This approach allows to incorporate the dielectric environment of a TMDC se…
As hosts for tightly-bound electron-hole pairs carrying quantized angular momentum, atomically-thin semiconductors of transition metal dichalcogenides provide an appealing platform for optically addressing the valley degree of freedom. In particular, the valleytronic properties of neutral and charged excitons in these systems have been widely investigated. Meanwhile, correlated quantum states involving more particles are so far elusive and controversial. Here we present experimental evidence for valleytronic four-particle biexcitons and five-particle exciton-trions in high-quality monolayer tu…
In monolayers of transition metal dichalcogenides the nonlocal nature of the effective dielectric screening leads to large binding energies of excitons. Additional lateral confinement gives rise to exciton localization in quantum dots. By assuming parabolic confinement for both the electron and the hole, we derive model wave functions for the relative and the center-of-mass motions of electron-hole pairs, and investigate theoretically resonant energy transfer among excitons localized in two neighboring quantum dots. We quantify the probability of energy transfer for a direct-gap transition by …
The electronic properties of ultrathin crystals of molybdenum disulfide consisting of N = 1, 2, ... 6 S-Mo-S monolayers have been investigated by optical spectroscopy. Through characterization by absorption, photoluminescence, and photoconductivity spectroscopy, we trace the effect of quantum confinement on the material's electronic structure. With decreasing thickness, the indirect band gap, which lies below the direct gap in the bulk material, shifts upwards in energy by more than 0.6 eV. This leads to a crossover to a direct-gap material in the limit of the single monolayer. Unlike the bulk…
Atomically thin layers of transition metal dichalcogenides (TMDCs) exhibit exceptionally strong Coulomb interaction between charge carriers due to the two-dimensional carrier confinement in connection with weak dielectric screening. The van der Waals nature of interlayer coupling makes it easy to integrate TMDC layers into heterostructures with different dielectric or metallic substrates. This allows to tailor electronic and optical properties of these materials, as Coulomb interaction inside atomically thin layers is very susceptible to screening by the environment. Here we theoretically inve…
The electron transport properties of atomically thin semiconductors such as MoS2 have attracted significant recent scrutiny and controversy. In this work, the scattering mechanisms responsible for limiting the mobility of single layer semiconductors are evaluated. The roles of individual scattering rates are tracked as the 2D electron gas density is varied over orders of magnitude at various temperatures. From a comparative study of the individual scattering mechanisms, we conclude that all current reported values of mobilities in atomically thin transition-metal dichalcogenide semiconductors …
Atomically thin two-dimensional semiconducting transition metal dichalcogenides (TMDs) can withstand large levels of strain before their irreversible damage occurs. This unique property offers a promising route for control of the optical and electronic properties of TMDs, for instance by depositing them on nano-structured surfaces, where position-dependent strain can be produced on the nano-scale. Here, we demonstrate strain-induced modifications of the optical properties of mono- and bilayer TMD WSe$_2 $ placed on photonic nano-antennas made from gallium phosphide (GaP). Photoluminescence (PL…
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 t…
We perform absorption and photoluminescence spectroscopy of trions in hBN-encapsulated WSe$_2$, WS$_2$, MoSe$_2$, and MoS$_2$ monolayers, depending on temperature. The different trends for W- and Mo-based materials are excellently reproduced considering a Fermi-Dirac distribution of bright and dark trions. We find a dark trion, $\rm{X_D^-}$ 19 meV $\textit{below}$ the lowest bright trion, $\rm{X}_1^-$ in WSe$_2$ and WS$_2$. In MoSe$_2$, $\rm{X_D^-}$ lies 6 meV $\textit{above}$ $\rm{X}_1^-$, while $\rm{X_D^-}$ and $\rm{X}_1^-$ almost coincide in MoS$_2$. Our results agree with GW-BSE $\textit{a…
Modification of electromagnetic quantum fluctuations in the form of quadrature-squeezing is a central quantum resource, which can be generated from nonlinear optical processes. Such a process is facilitated by coherent two-photon excitation of the strongly bound biexciton in atomically thin semiconductors. We show theoretically that interfacing an atomically thin semiconductor with an optical cavity allows to harness this two-photon resonance and use the biexcitonic parametric gain to generate squeezed light with input power an order of magnitude below current state-of-the-art devices with con…
The realization of mixtures of excitons and charge carriers in van-der-Waals materials presents a new frontier for the study of the many-body physics of strongly interacting Bose-Fermi mixtures. In order to derive an effective low-energy model for such systems, we develop an exact diagonalization approach based on a discrete variable representation that predicts the scattering and bound state properties of three charges in two-dimensional transition metal dichalcogenides. From the solution of the quantum mechanical three-body problem we thus obtain the bound state energies of excitons and trio…
Transition metal dichalcogenide semiconductors represent elementary components of layered heterostructures for emergent technologies beyond conventional opto-electronics. In their monolayer form they host electrons with quantized circular motion and associated valley polarization and valley coherence as key elements of opto-valleytronic functionality. Here, we introduce two-dimensional polarimetry as means of direct imaging of the valley pseudospin degree of freedom in monolayer transition metal dichalcogenides. Using MoS$_2$ as a representative material with valley-selective optical transitio…
The interaction of optically excited excitons in atomically thin semiconductors with residual doping densities leads to many-body effects which are continuously tunable by external gate voltages. Here, we develop a fully microscopic theory to describe the doping-dependent manipulation of the excitonic properties in atomically thin transition metal dichalcogenides. In particular, we establish a diagonalization approach for the Schrödinger equation which characterizes the interaction of a virtual exciton with the Fermi sea of dopants. Solving this many-body Schrödinger equation provides access t…
Nonlinear optical effects such as four-wave mixing and generation of squeezed light are ubiquitous in optical devices and light sources. For new devices operating at low optical power, the resonant nonlinearity arising from the two-photon sensitive bound biexciton in a semiconductor microcavity is an interesting prospective platform. Due to the particularly strong Coulomb interaction in atomically thin semiconductors, these materials have strongly bound biexcitons and operate in the visible frequency range of the electromagnetic spectrum. To remove the strong pump laser from the generated ligh…
Electric field-controlled, two-dimensional (2D) exciton dynamics in transition metal dichalcogenide monolayers is a current research focus in condensed matter physics. We have experimentally investigated the spectral and temporal properties of the A-exciton in a molybdenum diselenide (MoSe2) monolayer under controlled variation of a vertical, electric dc field at room temperature. By using steady-state and time-resolved photoluminescence spectroscopies, we have observed dc field-induced spectral shifts and linewidth broadenings that are consistent with the shortening of the exciton's non-radia…
Transition metal dichalcogenide monolayers are promising candidates for exploring new electronic and optical phenomena and for realizing atomically thin optoelectronic devices. They host tightly bound electron-hole pairs (excitons) that can be efficiently excited by resonant light fields. Here, we demonstrate that a single monolayer of molybdenum diselenide (MoSe2) can dramatically modify light transmission near the excitonic resonance, acting as an electrically switchable mirror that reflects up to 85% of incident light at cryogenic temperatures. This high reflectance is a direct consequence …
Graphene is no longer alone; a family of atomically thin 2D semiconductors has emerged. Optoelectronics and photonics applications are in their experimental infancy but the future holds much promise.
Long-range and fast transport of coherent excitons is important for development of high-speed excitonic circuits and quantum computing applications. However, most of these coherent excitons have only been observed in some low-dimensional semiconductors when coupled with cavities, as there are large inhomogeneous broadening and dephasing effects on the exciton transport in their native states of the materials. Here, by confining coherent excitons at the 2D quantum limit, we firstly observed molecular aggregation enabled super-transport of excitons in atomically thin two-dimensional (2D) organic…
Atomically thin semiconductors made from transition metal dichalcogenides (TMDs) are model systems for investigations of strong light-matter interactions and applications in nanophotonics, opto-electronics and valley-tronics. However, the photoluminescence spectra of TMD monolayers display a large number of features that are particularly challenging to decipher. On a practical level, monochromatic TMD-based emitters would be beneficial for low-dimensional devices but this challenge is yet to be resolved. Here, we show that graphene, directly stacked onto TMD monolayers enables single and narro…
Recent advances in guiding and localizing light at the nanoscale exposed the enormous potential of ultra-scaled plasmonic devices. In this context, the decay of surface plasmons to hot carriers triggers a variety of applications in boosting the efficiency of energy-harvesting, photo-catalysis and photo-detection. However, a detailed understanding of plasmonic hot carrier generation and particularly the transfer at metal-semiconductor interfaces is still elusive. In this paper, we introduce a monolithic metal-semiconductor (Al-Ge) heterostructure device, providing a platform to examine surface …
Two-dimensional dilute magnetic semiconductors can provide fundamental insights in the very nature of magnetic orders and their manipulation through electron and hole doping. Despite the fundamental physics, due to the large charge density control capability in these materials, they can be extremely important in spintronics applications such as spin valve and spin-based transistors. In this article, we studied a two-dimensional dilute magnetic semiconductors consisting of phosphorene monolayer doped with cobalt atoms in substitutional and interstitial defects. We show that these defects can be…
Dispersion engineering is a powerful and versatile tool that can vary the speed of light signals and induce negative-mass effects in the dynamics of particles and quasiparticles. Here, we show that dissipative coupling between bound electron-hole pairs (excitons) and photons in an optical microcavity can lead to the formation of exciton polaritons with an inverted dispersion of the lower polariton branch and hence a negative mass. We perform direct measurements of the anomalous dispersion in atomically thin (monolayer) WS$_2$ crystals embedded in planar microcavities and demonstrate that the p…
Optical and transport properties of doped monolayer semiconductors are dominated by trions, which are three-particle compounds formed by two electrons and one hole or vice versa. In this work, we investigate the trion-phonon interaction on a microscopic footing and apply our model to the exemplary case of a molybdenum diselenide (MoSe2) monolayer. We determine the trion series of states and their internal quantum structure by solving the trion Schrödinger equation. Transforming the system into a trion basis and solving equations of motion, including the trion-phonon interaction within the seco…
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 d…
Understanding and controlling the nanoscale transport of excitonic quasiparticles in atomically thin 2D semiconductors is crucial to produce highly efficient nano-excitonic devices. Here, we present a nano-gap device to selectively confine excitons or trions of 2D transition metal dichalcogenides at the nanoscale, facilitated by the drift-dominant exciton funnelling into the strain-induced local spot. We investigate the spatio-spectral characteristics of the funnelled excitons in a WSe2 monolayer (ML) and converted trions in a MoS2 ML using hyperspectral tip-enhanced photoluminescence (TEPL) i…
We show that a transition metal dichalcogenide monolayer with a radiatively broadened exciton resonance would exhibit perfect extinction of a transmitted field. This result holds for s- or p-polarized weak resonant light fields at any incidence angle, due to the conservation of in-plane momentum of excitons and photons in a flat defect-free two dimensional crystal. In contrast to extinction experiments with single quantum emitters, exciton-exciton interactions lead to an enhancement of reflection with increasing power for incident fields that are blue detuned with respect to the exciton resona…
Transition metal dichalcogenide (TMD) monolayers are direct bandgap semiconductors that feature tightly bound excitons, strong spin-orbit coupling, and spin-valley degrees of freedom. Depending on the spin configuration of the electron-hole pairs, intra-valley excitons of TMD monolayers can be either optically bright or dark. Dark excitons involve nominally spin-forbidden optical transitions with zero in-plane transition dipole moment, making their detection with conventional far-field optical techniques challenging. Here, we introduce a new method for probing the optical properties of two-dim…
We demonstrate a new approach for dynamically manipulating the optical response of an atomically thin semiconductor, a monolayer of MoSe2, by suspending it over a metallic mirror. First, we show that suspended van der Waals heterostructures incorporating a MoSe2 monolayer host spatially homogeneous, lifetime-broadened excitons. Then, we interface this nearly ideal excitonic system with a metallic mirror and demonstrate control over the exciton-photon coupling. Specifically, by electromechanically changing the distance between the heterostructure and the mirror, thereby changing the local photo…
Unique structural and optical properties of atomically thin two-dimensional semiconducting transition metal dichalcogenides enable in principle their efficient coupling to photonic cavities with optical modes volumes close to or below the diffraction limit. Recently, it has become possible to make all-dielectric nano-cavities with reduced mode volumes and negligible non-radiative losses. Here, we realise low-loss high-refractive-index dielectric gallium phosphide (GaP) nano-antennas with small mode volumes coupled to atomic mono- and bilayers of WSe$_2$. We observe a photoluminescence enhancem…
We continue to develop a new approach to description of charge kinetics in disordered semiconductors. It is based on fractional diffusion equations. This article is devoted to transient processes in structures under dispersive transport conditions. We demonstrate that this approach allows us (i) to take into account energetic and topological types of disorder in common, (ii) to consider transport in samples with spatial distributions of localized states, and (iii) to describe transport in non-homogeneous materials with distributed dispersion parameter. Using fractional approach provides some s…
Motivated by the triumph and limitation of graphene for electronic applications, atomically thin layers of group VI transition metal dichalcogenides are attracting extensive interest as a class of graphene-like semiconductors with a desired band-gap in the visible frequency range. The monolayers feature a valence band spin splitting with opposite sign in the two valleys located at corners of 1st Brillouin zone. This spin-valley coupling, particularly pronounced in tungsten dichalcogenides, can benefit potential spintronics and valleytronics with the important consequences of spin-valley interp…
We investigate the interactions between exciton-polaritons in N two-dimensional semiconductor layers embedded in a planar microcavity. In the limit of low-energy scattering, where we can ignore the composite nature of the excitons, we obtain exact analytical expressions for the spin-triplet and spin-singlet interaction strengths, which go beyond the Born approximation employed in previous calculations. Crucially, we find that the strong light-matter coupling enhances the strength of polariton-polariton interactions compared to that of the exciton-exciton interactions, due to the Rabi coupling …
Atomically-thin transition metal dichalcogenide crystals (TMDCs) hold great promise for future semiconductor optoelectronics due to their unique electronic and optical properties. In particular, electron-hole pairs (excitons) in TMDCs are stable at room temperature and interact strongly with light. When TMDCs are embedded in an optical microcavity, the excitons can hybridise with cavity photons to form exciton polaritons (polaritons herein), which display both ultrafast velocities and strong interactions. The ability to manipulate and trap polaritons on a microchip is critical for future appli…
Monolayers of transition metal dichalcogenides (TMDCs) exhibit an exceptionally strong Coulomb interaction between charge carriers due to the two-dimensional carrier confinement in connection with weak dielectric screening. High densities of excited charge carriers in the various band-structure valleys cause strong many-body renormalizations that influence both the electronic properties and the optical response of the material. We investigate electronic and optical properties of the typical monolayer TMDCs MoS$_2$, MoSe$_2$, WS$_2$ and WSe$_2$ in the presence of excited carriers by solving sem…
The dynamics of a mobile quantum impurity in a degenerate Fermi system is a fundamental problem in many-body physics. The interest in this field has been renewed due to recent ground-breaking experiments with ultra-cold Fermi gases. Optical creation of an exciton or a polariton in a two-dimensional electron system embedded in a microcavity constitutes a new frontier for this field due to an interplay between cavity-coupling favoring ultra-low mass polariton formation and exciton-electron interactions leading to polaron or trion formation. Here, we present cavity spectroscopy of gate-tunable mo…
Atomically thin semiconductors such as monolayer MoS2 and WS2 exhibit nonlinear exciton-exciton annihilation at notably low excitation densities (below ~10 excitons/um2 in MoS2). Here, we show that the density threshold at which annihilation occurs can be tuned by changing the underlying substrate. When the supporting substrate is changed from SiO2 to Al2O3 or SrTiO3, the rate constant for second-order exciton-exciton annihilation, k_XX [cm2/s], is reduced by one or two orders of magnitude, respectively. Using transient photoluminescence microscopy, we measure the effective room-temperature ex…
Room-temperature tuning and probing of Fermi polarons in atomically thin semiconductors on a plasmonic metasurface
Nanyang Technological University（南洋理工大学）；Universidad Autónoma de Madrid（马德里自治大学）；Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid（马德里自治大学凝聚态物理中心（IFIMAC））；Jilin University（吉林大学）；Zhejiang University（浙江大学）
Semiconductor p-n junctions are essential building blocks for modern electronics and optoelectronics. In conventional semiconductors, a p-n junction produces depletion regions of free charge carriers at equilibrium and built-in potentials associated with uncompensated dopant atoms. Carrier transport across the junction occurs by diffusion and drift processes defined by the spatial extent of this region. With the advent of atomically thin van der Waals (vdW) materials and their heterostructures, we are now able to realize a p-n junction at the ultimate quantum limit. In particular, vdW junction…
Next-generation electronics calls for new materials beyond silicon for increased functionality, performance, and scaling in integrated circuits. Carbon nanotubes and semiconductor nanowires are at the forefront of these materials, but have challenges due to the complex fabrication techniques required for large-scale applications. Two-dimensional (2D) gapless graphene and semiconducting transition metal dichalcogenides (TMDCs) have emerged as promising electronic materials due to their atomic thickness, chemical stability and scalability. Difficulties in the assembly of 2D electronic structures…
Two-dimensional (2D) semiconductors provide a unique opportunity for optoelectronics due to their layered atomic structure, electronic and optical properties. To date, a majority of the application-oriented research in this field has been focused on field-effect electronics as well as photodetectors and light emitting diodes. Here we present a perspective on the use of 2D semiconductors for photovoltaic applications. We discuss photonic device designs that enable light trapping in nanometer-thickness absorber layers, and we also outline schemes for efficient carrier transport and collection. W…
