Nanoscale force sensing of an ultrafast nonlinear optical response.

The nonlinear optical response of a material is a sensitive probe of electronic and structural dynamics under strong light fields. The induced microscopic polarizations are usually detected via their far-field light emission, thus limiting spatial resolution. Several powerful near-field techniques circumvent this limitation by employing local nanoscale scatterers; however, their signal strength scales unfavorably as the probe volume decreases. Here, we demonstrate that time-resolved atomic force microscopy is capable of temporally and spatially resolving the microscopic, electrostatic forces arising from a nonlinear optical polarization in an insulating dielectric driven by femtosecond optical fields. The measured forces can be qualitatively explained by a second-order nonlinear interaction in the sample. The force resulting from this nonlinear interaction has frequency components below the mechanical resonance frequency of the cantilever and is thus detectable by regular atomic force microscopy methods. The capability to measure a nonlinear polarization through its electrostatic force is a powerful means to revisit nonlinear optical effects at the nanoscale, without the need for emitted photons or electrons from the surface.

Dielectric Engineering of Electronic Correlations in a van der Waals Heterostructure.

Heterostructures of van der Waals bonded layered materials offer unique means to tailor dielectric screening with atomic-layer precision, opening a fertile field of fundamental research. The optical analyses used so far have relied on interband spectroscopy. Here we demonstrate how a capping layer of hexagonal boron nitride (hBN) renormalizes the internal structure of excitons in a WSe2 monolayer using intraband transitions. Ultrabroadband terahertz probes sensitively map out the full complex-valued mid-infrared conductivity of the heterostructure after optical injection of 1s A excitons. This approach allows us to trace the energies and line widths of the atom-like 1s-2p transition of optically bright and dark excitons as well as the densities of these quasiparticles. The excitonic resonance red shifts and narrows in the WSe2/hBN heterostructure compared to the bare monolayer. Furthermore, the ultrafast temporal evolution of the mid-infrared response function evidences the formation of optically dark excitons from an initial bright population. Our results provide key insight into the effect of nonlocal screening on electron-hole correlations and open new possibilities of dielectric engineering of van der Waals heterostructures.

Exciton Diffusion and Halo Effects in Monolayer Semiconductors.

We directly monitor exciton propagation in freestanding and SiO_{2}-supported WS_{2} monolayers through spatially and time-resolved microphotoluminescence under ambient conditions. We find a highly nonlinear behavior with characteristic, qualitative changes in the spatial profiles of the exciton emission and an effective diffusion coefficient increasing from 0.3 to more than 30 cm^{2}/s, depending on the injected exciton density. Solving the diffusion equation while accounting for Auger recombination allows us to identify and quantitatively understand the main origin of the increase in the observed diffusion coefficient. At elevated excitation densities, the initial Gaussian distribution of the excitons evolves into long-lived halo shapes with µm-scale diameter, indicating additional memory effects in the exciton dynamics.

Zeeman Splitting and Inverted Polarization of Biexciton Emission in Monolayer WS_{2}.

Atomically thin semiconductors provide an ideal testbed to investigate the physics of Coulomb-bound many-body states. We shed light on the intricate structure of such complexes by studying the magnetic-field-induced splitting of biexcitons in monolayer WS_{2} using polarization-resolved photoluminescence spectroscopy in out-of-plane magnetic fields up to 30 T. The observed g factor of the biexciton amounts to about -3.9, closely matching the g factor of the neutral exciton. The biexciton emission shows an inverted circular field-induced polarization upon linearly polarized excitation; i.e., it exhibits preferential emission from the high-energy peak in a magnetic field. This phenomenon is explained by taking into account the hybrid configuration of the biexciton constituents in momentum space and their respective energetic behavior in magnetic fields. Our findings reveal the critical role of dark excitons in the composition of this many-body state.

Direct Observation of Ultrafast Exciton Formation in a Monolayer of WSe2.

Many of the fundamental optical and electronic properties of atomically thin transition metal dichalcogenides are dominated by strong Coulomb interactions between electrons and holes, forming tightly bound atom-like states called excitons. Here, we directly trace the ultrafast formation of excitons by monitoring the absolute densities of bound and unbound electron-hole pairs in single monolayers of WSe2 on a diamond substrate following femtosecond nonresonant optical excitation. To this end, phase-locked mid-infrared probe pulses and field-sensitive electro-optic sampling are used to map out the full complex-valued optical conductivity of the nonequilibrium system and to discern the hallmark low-energy responses of bound and unbound pairs. While the spectral shape of the infrared response immediately after above-bandgap injection is dominated by free charge carriers, up to 60% of the electron-hole pairs are bound into excitons already on a subpicosecond time scale, evidencing extremely fast and efficient exciton formation. During the subsequent recombination phase, we still find a large density of free carriers in addition to excitons, indicating a nonequilibrium state of the photoexcited electron-hole system.

Direct Observation of the Band Gap Transition in Atomically Thin ReS2.

ReS2 is considered as a promising candidate for novel electronic and sensor applications. The low crystal symmetry of this van der Waals compound leads to a highly anisotropic optical, vibrational, and transport behavior. However, the details of the electronic band structure of this fascinating material are still largely unexplored. We present a momentum-resolved study of the electronic structure of monolayer, bilayer, and bulk ReS2 using k-space photoemission microscopy in combination with first-principles calculations. We demonstrate that the valence electrons in bulk ReS2 are-contrary to assumptions in recent literature-significantly delocalized across the van der Waals gap. Furthermore, we directly observe the evolution of the valence band dispersion as a function of the number of layers, revealing the transition from an indirect band gap in bulk ReS2 to a direct gap in the bilayer and the monolayer. We also find a significantly increased effective hole mass in single-layer crystals. Our results establish bilayer ReS2 as an advantageous building block for two-dimensional devices and van der Waals heterostructures.

Characterization of highly crystalline lead iodide nanosheets prepared by room-temperature solution processing.

Two-dimensional (2D) semiconducting materials are particularly appealing for many applications. Although theory predicts a large number of 2D materials, experimentally only a few of these materials have been identified and characterized comprehensively in the ultrathin limit. Lead iodide, which belongs to the transition metal halides family and has a direct bandgap in the visible spectrum, has been known for a long time and has been well characterized in its bulk form. Nevertheless, studies of this material in the nanometer thickness regime are rather scarce. In this article we demonstrate an easy way to synthesize ultrathin, highly crystalline flakes of PbI2 by precipitation from a solution in water. We thoroughly characterize the produced thin flakes with different techniques ranging from optical and Raman spectroscopy to temperature-dependent photoluminescence and electron microscopy. We compare the results to ab initio calculations of the band structure of the material. Finally, we fabricate photodetectors based on PbI2 and study their optoelectronic properties.

Coherent and Incoherent Coupling Dynamics between Neutral and Charged Excitons in Monolayer MoSe2.

The optical properties of semiconducting transition metal dichalcogenides are dominated by both neutral excitons (electron-hole pairs) and charged excitons (trions) that are stable even at room temperature. While trions directly influence charge transport properties in optoelectronic devices, excitons may be relevant through exciton-trion coupling and conversion phenomena. In this work, we reveal the coherent and incoherent nature of exciton-trion coupling and the relevant time scales in monolayer MoSe2 using optical two-dimensional coherent spectroscopy. Coherent interaction between excitons and trions is definitively identified as quantum beating of cross peaks in the spectra that persists for a few hundred femtoseconds. For longer times up to 10 ps, surprisingly, the relative intensity of the cross peaks increases, which is attributed to incoherent energy transfer likely due to phonon-assisted up-conversion and down-conversion processes that are efficient even at cryogenic temperature.

Excitonic Valley Effects in Monolayer WS2 under High Magnetic Fields.

Transition-metal dichalcogenides can be easily produced as atomically thin sheets, exhibiting the possibility to optically polarize and read out the valley pseudospin of extremely stable excitonic quasiparticles present in these 2D semiconductors. Here, we investigate a monolayer of tungsten disulfide in high magnetic fields up to 30 T via photoluminescence spectroscopy at low temperatures. The valley degeneracy is lifted for all optical features, particularly for excitons, singlet and triplet trions, for which we determine the g factor separately. While the observation of a diamagnetic shift of the exciton and trion resonances gives us insight into the real-space extension of these quasiparticles, magnetic field-induced valley polarization effects shed light onto the exciton and trion dispersion relations in reciprocal space. The field dependence of the trion valley polarizations is in line with the predicted trion splitting into singlet and triplet configurations.

Magnetic-Field-Induced Rotation of Polarized Light Emission from Monolayer WS_{2}.

We control the linear polarization of emission from the coherently emitting K^{+} and K^{-} valleys (valley coherence) in monolayer WS_{2} with an out-of-plane magnetic field of up to 25 T. The magnetic-field-induced valley Zeeman splitting causes a rotation of the emission polarization with respect to the excitation by up to 35° and reduces the polarization degree by up to 16%. We explain both of these phenomena with a model based on two noninteracting coherent two-level systems. We deduce that the coherent light emission from the valleys decays with a time constant of τ_{c}=260 fs.

Ultrafast Charge-Transfer Dynamics in Twisted MoS2/WSe2 Heterostructures.

Two-dimensional transition metal dichalcogenides offer a fascinating platform for creating van der Waals heterojunctions with exciting physical properties. Because of their typical type-II band alignment, photoexcited electrons and holes can separate via interfacial charge transfer. Furthermore, the relative crystallographic alignment of the individual layers in these heterostructures represents an important degree of freedom. Based on both effects, various fascinating ideas for applications in optoelectronics and valleytronics have been suggested. Despite its utmost importance for the design and efficiency of potential devices, the nature and the dynamics of ultrafast charge transfer are not yet well understood. This is mainly because the charge transfer can be surprisingly fast, usually faster than the temporal resolution of previous experimental approaches. Here, we apply time- and polarization-resolved second-harmonic imaging microscopy to investigate the charge-transfer dynamics for three MoS2/WSe2 heterostructures with different stacking angles at a previously unattainable time resolution of ≈10 fs. For 1.70 eV excitation energy, electron transfer from WSe2 to MoS2 is found to depend considerably on the stacking angle with the fastest transfer time observed to be as short as 12 fs. At 1.85 eV excitation energy, ultrafast hole transfer from MoS2 to hybridized states at the Γ-point and to the K-points of WSe2 has to be considered. Surprisingly, the corresponding decay dynamics show only a minor stacking-angle dependence indicating that radiative recombination of momentum-space indirect Γ-K excitons becomes the dominant decay route for all samples.

Trion Valley Coherence in Monolayer Semiconductors.

The emerging field of valleytronics aims to exploit the valley pseudospin of electrons residing near Bloch band extrema as an information carrier. Recent experiments demonstrating optical generation and manipulation of exciton valley coherence (the superposition of electron-hole pairs at opposite valleys) in monolayer transition metal dichalcogenides (TMDs) provide a critical step towards control of this quantum degree of freedom. The charged exciton (trion) in TMDs is an intriguing alternative to the neutral exciton for control of valley pseudospin because of its long spontaneous recombination lifetime, its robust valley polarization, and its coupling to residual electronic spin. Trion valley coherence has however been unexplored due to experimental challenges in accessing it spectroscopically. In this work, we employ ultrafast two-dimensional coherent spectroscopy to resonantly generate and detect trion valley coherence in monolayer MoSe2 demonstrating that it persists for a few-hundred femtoseconds. We conclude that the underlying mechanisms limiting trion valley coherence are fundamentally different from those applicable to exciton valley coherence.

Giant magnetic splitting inducing near-unity valley polarization in van der Waals heterostructures.

Monolayers of semiconducting transition metal dichalcogenides exhibit intriguing fundamental physics of strongly coupled spin and valley degrees of freedom for charge carriers. While the possibility of exploiting these properties for information processing stimulated concerted research activities towards the concept of valleytronics, maintaining control over spin-valley polarization proved challenging in individual monolayers. A promising alternative route explores type II band alignment in artificial van der Waals heterostructures. The resulting formation of interlayer excitons combines the advantages of long carrier lifetimes and spin-valley locking. Here, we demonstrate artificial design of a two-dimensional heterostructure enabling intervalley transitions that are not accessible in monolayer systems. The resulting giant effective g factor of -15 for interlayer excitons induces near-unity valley polarization via valley-selective energetic splitting in high magnetic fields, even after nonselective excitation. Our results highlight the potential to deterministically engineer novel valley properties in van der Waals heterostructures using crystallographic alignment.

Neutral and charged inter-valley biexcitons in monolayer MoSe2.

In atomically thin transition metal dichalcogenides (TMDs), reduced dielectric screening of the Coulomb interaction leads to strongly correlated many-body states, including excitons and trions, that dominate the optical properties. Higher-order states, such as bound biexcitons, are possible but are difficult to identify unambiguously using linear optical spectroscopy methods. Here, we implement polarization-resolved two-dimensional coherent spectroscopy (2DCS) to unravel the complex optical response of monolayer MoSe2 and identify multiple higher-order correlated states. Decisive signatures of neutral and charged inter-valley biexcitons appear in cross-polarized two-dimensional spectra as distinct resonances with respective ∼20 and ∼5 meV binding energies-similar to recent calculations using variational and Monte Carlo methods. A theoretical model considering the valley-dependent optical selection rules reveals the quantum pathways that give rise to these states. Inter-valley biexcitons identified here, comprising of neutral and charged excitons from different valleys, offer new opportunities for developing ultrathin biexciton lasers and polarization-entangled photon sources.

Spectral focusing of broadband silver electroluminescence in nanoscopic FRET-LEDs.

Few inventions have shaped the world like the incandescent bulb. Edison used thermal radiation from ohmically heated conductors, but some noble metals also exhibit 'cold' electroluminescence in percolation films, tunnel diodes, electromigrated nanoparticle aggregates, optical antennas or scanning tunnelling microscopy. The origin of this radiation, which is spectrally broad and depends on applied bias, is controversial given the low radiative yields of electronic transitions. Nanoparticle electroluminescence is particularly intriguing because it involves localized surface-plasmon resonances with large dipole moments. Such plasmons enable very efficient non-radiative fluorescence resonance energy transfer (FRET) coupling to proximal resonant dipole transitions. Here, we demonstrate nanoscopic FRET-light-emitting diodes which exploit the opposite process, energy transfer from silver nanoparticles to exfoliated monolayers of transition-metal dichalcogenides. In diffraction-limited hotspots showing pronounced photon bunching, broadband silver electroluminescence is focused into the narrow excitonic resonance of the atomically thin overlayer. Such devices may offer alternatives to conventional nano-light-emitting diodes in on-chip optical interconnects.

Coulomb engineering of the bandgap and excitons in two-dimensional materials.

The ability to control the size of the electronic bandgap is an integral part of solid-state technology. Atomically thin two-dimensional crystals offer a new approach for tuning the energies of the electronic states based on the unusual strength of the Coulomb interaction in these materials and its environmental sensitivity. Here, we show that by engineering the surrounding dielectric environment, one can tune the electronic bandgap and the exciton binding energy in monolayers of WS2 and WSe2 by hundreds of meV. We exploit this behaviour to present an in-plane dielectric heterostructure with a spatially dependent bandgap, as an initial step towards the creation of diverse lateral junctions with nanoscale resolution.

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.

Trion fine structure and coupled spin-valley dynamics in monolayer tungsten disulfide.

Monolayer transition-metal dichalcogenides have recently emerged as possible candidates for valleytronic applications, as the spin and valley pseudospin are directly coupled and stabilized by a large spin splitting. The optical properties of these two-dimensional crystals are dominated by tightly bound electron-hole pairs (excitons) and more complex quasiparticles such as charged excitons (trions). Here we investigate monolayer WS2 samples via photoluminescence and time-resolved Kerr rotation. In photoluminescence and in energy-dependent Kerr rotation measurements, we are able to resolve two different trion states, which we interpret as intravalley and intervalley trions. Using time-resolved Kerr rotation, we observe a rapid initial valley polarization decay for the A exciton and the trion states. Subsequently, we observe a crossover towards exciton-exciton interaction-related dynamics, consistent with the formation and decay of optically dark A excitons. By contrast, resonant excitation of the B exciton transition leads to a very slow decay of the Kerr signal.