Nonlinear and Negative Effective Diffusivity of Interlayer Excitons in Moiré-Free Heterobilayers.

Interlayer exciton diffusion is studied in atomically reconstructed MoSe_{2}/WSe_{2} heterobilayers with suppressed disorder. Local atomic registry is confirmed by characteristic optical absorption, circularly polarized photoluminescence, and g-factor measurements. Using transient microscopy we observe propagation properties of interlayer excitons that are independent from trapping at moiré- or disorder-induced local potentials. Confirmed by characteristic temperature dependence for free particles, linear diffusion coefficients of interlayer excitons at liquid helium temperature and low excitation densities are almost 1000 times higher than in previous observations. We further show that exciton-exciton repulsion and annihilation contribute nearly equally to nonlinear propagation by disentangling the two processes in the experiment and simulations. Finally, we demonstrate effective shrinking of the light emission area over time across several hundreds of picoseconds at the transition from exciton- to the plasma-dominated regimes. Supported by microscopic calculations for band gap renormalization to identify the Mott threshold, this indicates transient crossing between rapidly expanding, short-lived electron-hole plasma and slower, long-lived exciton populations.

Diffusion of Excitons in a Two-Dimensional Fermi Sea of Free Charges.

Propagation of light-emitting quasiparticles is of central importance across the fields of condensed matter physics and nanomaterials science. We experimentally demonstrate diffusion of excitons in the presence of a continuously tunable Fermi sea of free charge carriers in a monolayer semiconductor. Light emission from tightly bound exciton states in electrically gated WSe2 monolayer is detected using spatially and temporally resolved microscopy. The measurements reveal a nonmonotonic dependence of the exciton diffusion coefficient on the charge carrier density in both electron and hole doped regimes. Supported by analytical theory describing exciton-carrier interactions in a dissipative system, we identify distinct regimes of elastic scattering and quasiparticle formation determining exciton diffusion. The crossover region exhibits a highly unusual behavior of an increasing diffusion coefficient with increasing carrier densities. Temperature-dependent diffusion measurements further reveal characteristic signatures of freely propagating excitonic complexes dressed by free charges with effective mobilities up to 3 × 103 cm2/(V s).

Tailoring the Electron and Hole Landé Factors in Lead Halide Perovskite Nanocrystals by Quantum Confinement and Halide Exchange.

The tunability of the optical properties of lead halide perovskite nanocrystals makes them highly appealing for applications. Halide anion exchange and quantum confinement enable tailoring of the band gap. For spintronics, the Landé g-factors of electrons and holes are essential. Using empirical tight-binding and k·p methods, we calculate them for nanocrystals of all-inorganic lead halide perovskites CsPbX3 (X = I, Br, Cl). The hole g-factor band gap dependence follows the universal law found for bulk perovskites, while for electrons, a considerable modification is predicted. Based on the k·p analysis, we conclude that this difference arises from the interaction of the bottom conduction band with the spin-orbit split electron states. These predictions are confirmed experimentally for electron and hole g-factors in CsPbI3 nanocrystals in a glass matrix, measured by time-resolved Faraday ellipticity in a magnetic field at cryogenic temperatures.

Submillisecond Spin Relaxation in CsPb(Cl,Br)3 Perovskite Nanocrystals in a Glass Matrix.

Lead halide perovskite nanocrystals in a glass matrix are a promising platform for optoelectronic applications due to their excellent optical properties combined with outstanding stability against the environment. We reveal the potential of this system for spintronics by studying the electron spin properties of CsPb(Cl,Br)3 nanocrystals in a fluorophosphate glass matrix. Using optical spin orientation and spin depolarization with a radio frequency field, we measure longitudinal spin relaxation time, T1, reaching several hundreds of microseconds at low temperatures. This time T1 corresponds to a spin state with a small g factor, which we attribute to a weakly exchange-coupled electron-hole pair with antiparallel spins.

Nonclassical Exciton Diffusion in Monolayer WSe_{2}.

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 semiphenomenological 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.

Autoionization and Dressing of Excited Excitons by Free Carriers in Monolayer WSe_{2}.

We experimentally demonstrate dressing of the excited exciton states by a continuously tunable Fermi sea of free charge carriers in a monolayer semiconductor. It represents an unusual scenario of two-particle excitations of charged excitons previously inaccessible in conventional material systems. We identify excited state trions, accurately determine their binding energies in the zero-density limit for both electron- and hole-doped regimes, and observe emerging many-body phenomena at elevated doping. Combining experiment and theory we gain access to the intra-exciton coupling facilitated by the interaction with free charge carriers. We provide evidence for a process of autoionization for quasiparticles, a unique scattering pathway available for excited states in atomic systems. Finally, we demonstrate a complete transfer of the optical transition strength from the excited excitons to dressed Fermi-polaron states as well as the associated light emission from their nonequilibrium populations.

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.

Highly-Polarized Emission Provided by Giant Optical Orientation of Exciton Spins in Lead Halide Perovskite Crystals.

Quantum technologic and spintronic applications require reliable material platforms that enable significant and long-living spin polarization of excitations, the ability to manipulate it optically in external fields, and the possibility to implement quantum correlations between spins, i.e., entanglement. Here it is demonstrated that these conditions are met in bulk crystals of lead halide perovskites. A giant optical orientation of 85% of excitons, approaching the ultimate limit of unity, in FA0.9Cs0.1PbI2.8Br0.2 crystals is reported. The exciton spin orientation is maintained during the exciton lifetime of 55 ps resulting in high circular polarization of the exciton emission. The optical orientation is robust to detuning of the excitation energy up to 0.3 eV above the exciton resonance and remains larger than 20% up to detunings of 0.9 eV. It evidences pure chiral selection rules and suppressed spin relaxation of electrons and holes, even with large kinetic energies. The exciton and electron-hole recombinations are distinguished by means of the spin dynamics detected via coherent spin quantum beats in magnetic field. Further, electron-hole spin correlations are demonstrated through linear polarization beats after circularly polarized excitation. These findings are supported by atomistic calculations. All-in-all, the results establish lead halide perovskite semiconductors as suitable platform for quantum technologies.

Doping-control of excitons and magnetism in few-layer CrSBr.

Magnetism in two-dimensional materials reveals phenomena distinct from bulk magnetic crystals, with sensitivity to charge doping and electric fields in monolayer and bilayer van der Waals magnet CrI3. Within the class of layered magnets, semiconducting CrSBr stands out by featuring stability under ambient conditions, correlating excitons with magnetic order and thus providing strong magnon-exciton coupling, and exhibiting peculiar magneto-optics of exciton-polaritons. Here, we demonstrate that both exciton and magnetic transitions in bilayer and trilayer CrSBr are sensitive to voltage-controlled field-effect charging, exhibiting bound exciton-charge complexes and doping-induced metamagnetic transitions. Moreover, we demonstrate how these unique properties enable optical probes of local magnetic order, visualizing magnetic domains of competing phases across metamagnetic transitions induced by magnetic field or electrostatic doping. Our work identifies few-layer CrSBr as a rich platform for exploring collaborative effects of charge, optical excitations, and magnetism.

High-lying valley-polarized trions in 2D semiconductors.

Optoelectronic functionalities of monolayer transition-metal dichalcogenide (TMDC) semiconductors are characterized by the emergence of externally tunable, correlated many-body complexes arising from strong Coulomb interactions. However, the vast majority of such states susceptible to manipulation has been limited to the region in energy around the fundamental bandgap. We report the observation of tightly bound, valley-polarized, UV-emissive trions in monolayer TMDC transistors: quasiparticles composed of an electron from a high-lying conduction band with negative effective mass, a hole from the first valence band, and an additional charge from a band-edge state. These high-lying trions have markedly different optical selection rules compared to band-edge trions and show helicity opposite to that of the excitation. An electrical gate controls both the oscillator strength and the detuning of the excitonic transitions, and therefore the Rabi frequency of the strongly driven three-level system, enabling excitonic quantum interference to be switched on and off in a deterministic fashion.

Lead-Dominated Hyperfine Interaction Impacting the Carrier Spin Dynamics in Halide Perovskites.

The outstanding optical quality of lead halide perovskites inspires studies of their potential for the optical control of carrier spins as pursued in other materials. Entering largely uncharted territory, time-resolved pump-probe Kerr rotation is used to explore the coherent spin dynamics of electrons and holes in bulk formamidinium caesium lead iodine bromide (FA0.9 Cs0.1 PbI2.8 Br0.2 ) and to determine key parameters characterizing interactions of their spins, such as the g-factors and relaxation times. The demonstrated long spin dynamics and narrow g-factor distribution prove the perovskites as promising competitors for conventional semiconductors in spintronics. The dynamic nuclear polarization via spin-oriented holes is realized and the identification of the lead (207 Pb) isotope in optically detected nuclear magnetic resonance proves that the hole-nuclei interaction is dominated by the lead ions. A detailed theoretical analysis accounting for the specifics of the lead halide perovskite materials allows the evaluation of the underlying hyperfine interaction constants, both for electrons and holes. Recombination and spin dynamics evidence that at low temperatures, photogenerated electrons and holes are localized at different regions of the perovskite crystal, resulting in their long lifetimes up to 44 µs. The findings form the base for the tailored development of spin-optoelectronic applications for the large family of lead halide perovskites and their nanostructures.

Efficient phonon cascades in WSe2 monolayers.

Energy relaxation of photo-excited charge carriers is of significant fundamental interest and crucial for the performance of monolayer transition metal dichalcogenides in optoelectronics. The primary stages of carrier relaxation affect a plethora of subsequent physical mechanisms. Here we measure light scattering and emission in tungsten diselenide monolayers close to the laser excitation energy (down to ~0.6 meV). We reveal a series of periodic maxima in the hot photoluminescence intensity, stemming from energy states higher than the A-exciton state. We find a period ~15 meV for 7 peaks below (Stokes) and 5 peaks above (anti-Stokes) the laser excitation energy, with a strong temperature dependence. These are assigned to phonon cascades, whereby carriers undergo phonon-induced transitions between real states above the free-carrier gap with a probability of radiative recombination at each step. We infer that intermediate states in the conduction band at the Λ-valley of the Brillouin zone participate in the cascade process of tungsten diselenide monolayers. This provides a fundamental understanding of the first stages of carrier-phonon interaction, useful for optoelectronic applications of layered semiconductors.

Interlayer exciton mediated second harmonic generation in bilayer MoS2.

Second-harmonic generation (SHG) is a non-linear optical process, where two photons coherently combine into one photon of twice their energy. Efficient SHG occurs for crystals with broken inversion symmetry, such as transition metal dichalcogenide monolayers. Here we show tuning of non-linear optical processes in an inversion symmetric crystal. This tunability is based on the unique properties of bilayer MoS2, that shows strong optical oscillator strength for the intra- but also interlayer exciton resonances. As we tune the SHG signal onto these resonances by varying the laser energy, the SHG amplitude is enhanced by several orders of magnitude. In the resonant case the bilayer SHG signal reaches amplitudes comparable to the off-resonant signal from a monolayer. In applied electric fields the interlayer exciton energies can be tuned due to their in-built electric dipole via the Stark effect. As a result the interlayer exciton degeneracy is lifted and the bilayer SHG response is further enhanced by an additional two orders of magnitude, well reproduced by our model calculations. Since interlayer exciton transitions are highly tunable also by choosing twist angle and material combination our results open up new approaches for designing the SHG response of layered materials.

Optical valley Hall effect for highly valley-coherent exciton-polaritons in an atomically thin semiconductor.

Spin-orbit coupling is a fundamental mechanism that connects the spin of a charge carrier with its momentum. In the optical domain, an analogous synthetic spin-orbit coupling is accessible by engineering optical anisotropies in photonic materials. Both yield the possibility of creating devices that directly harness spin and polarization as information carriers. Atomically thin transition metal dichalcogenides promise intrinsic spin-valley Hall features for free carriers, excitons and photons. Here we demonstrate spin- and valley-selective propagation of exciton-polaritons in a monolayer of MoSe2 that is strongly coupled to a microcavity photon mode. In a wire-like device we trace the flow and helicity of exciton-polaritons expanding along its channel. By exciting a coherent superposition of K and K' tagged polaritons, we observe valley-selective expansion of the polariton cloud without either an external magnetic field or coherent Rayleigh scattering. The observed optical valley Hall effect occurs on a macroscopic scale, offering the potential for applications in spin-valley-locked photonic devices.

Cavity-control of interlayer excitons in van der Waals heterostructures.

Monolayer transition metal dichalcogenides integrated in optical microcavities host exciton-polaritons as a hallmark of the strong light-matter coupling regime. Analogous concepts for hybrid light-matter systems employing spatially indirect excitons with a permanent electric dipole moment in heterobilayer crystals promise realizations of exciton-polariton gases and condensates with inherent dipolar interactions. Here, we implement cavity-control of interlayer excitons in vertical MoSe2-WSe2 heterostructures. Our experiments demonstrate the Purcell effect for heterobilayer emission in cavity-modified photonic environments, and quantify the light-matter coupling strength of interlayer excitons. The results will facilitate further developments of dipolar exciton-polariton gases and condensates in hybrid cavity - van der Waals heterostructure systems.

Author Correction: Coherent spin dynamics of electrons and holes in CsPbBr3 perovskite crystals.

The original version of this Article contained an error in Fig. 2c, in which the numbers on the y-axis were given in the wrong order: '800' at the bottom through to '0' at the top. This has been corrected in both the PDF and HTML versions of the Article.

Coherent spin dynamics of electrons and holes in CsPbBr3 perovskite crystals.

The lead halide perovskites demonstrate huge potential for optoelectronic applications, high energy radiation detectors, light emitting devices and solar energy harvesting. Those materials exhibit strong spin-orbit coupling enabling efficient optical orientation of carrier spins in perovskite-based devices with performance controlled by a magnetic field. Here we show that elaborated time-resolved spectroscopy involving strong magnetic fields can be successfully used for perovskites. We perform a comprehensive study of high-quality lead halide perovskite CsPbBr3 crystals by measuring the exciton and charge carrier g-factors, spin relaxation times and hyperfine interaction of carrier and nuclear spins by means of coherent spin dynamics. Owing to their 'inverted' band structure, perovskites represent appealing model systems for semiconductor spintronics exploiting the valence band hole spins, while in conventional semiconductors the conduction band electrons are considered for spin functionality.

Two-dimensional semiconductors in the regime of strong light-matter coupling.

The optical properties of transition metal dichalcogenide monolayers are widely dominated by excitons, Coulomb-bound electron-hole pairs. These quasi-particles exhibit giant oscillator strength and give rise to narrow-band, well-pronounced optical transitions, which can be brought into resonance with electromagnetic fields in microcavities and plasmonic nanostructures. Due to the atomic thinness and robustness of the monolayers, their integration in van der Waals heterostructures provides unique opportunities for engineering strong light-matter coupling. We review first results in this emerging field and outline future opportunities and challenges.