Bulk chromium tri-iodide (CrI 3 ) has long been known as a layered van der Waals ferromagnet 1 . However, its monolayer form was only recently isolated and confirmed to be a truly two-dimensional (2D) ferromagnet 2 , providing a new platform for investigating light-matter interactions and magnetooptical phenomena in the atomically thin limit. Here, we report spontaneous circularly polarized photoluminescence in monolayer CrI 3 under linearly polarized excitation, with heli city determined by the monolayer magnetization direction. In contrast, the bilayer CrI 3 photoluminescence exhibits vanishing circular polarization, supporting the recently uncovered anomalous antiferromagnetic interlayer coupling in CrI 3 bilayers 2 . Distinct from the Wannier-Mott excitons that dominate the optical response in well-known 2D van der Waals semiconductors 3 , our absorption and layer-dependent photoluminescence measurements reveal the importance of ligandfield and charge-transfer transitions to the optoelectronic response of atomically thin CrI 3 . We attribute the photoluminescence to a parity-forbidden d-d transition characteristic of Cr 3+ complexes, which displays broad linewidth due to strong vibronic coupling and thickness-independent peak energy due to its localized molecular orbital nature.Van der Waals layered materials offer fascinating opportunities for studying light-matter interactions in the 2D limit. For instance, monolayer semiconducting transition metal dichalcogenides (for example, WSe 2 ) enable coupling between the helicity of light and the valley degree of freedom 4 . In all non-metallic 2D materials to date, it has been established that tightly bound Wannier-Mott excitons dominate the intrinsic optical response 3 , and there has been rapid progress in studying 2D excitonic interactions, dynamics and spin/valley physics 3,5 . However, none of these 2D materials possesses long-range magnetic order. A monolayer semiconductor or insulator with intrinsic magnetism would enable the study of novel photo-physical phenomena and the interplay with underlying magnetic order, possibly involving physics incompatible with the Wannier-Mott excitonic picture.On the other hand, the exploration of ferromagnetism in non-metallic bulk materials has a long history. Early studies examined the intrinsic ferromagnetic ordering of a variety of insulating and semiconducting materials, including, for example, the ferrites and ferrospinels 6 , Cr trihalides 7 , Eu chalcogenides 8 and Cr spinels 9 . Later, with the introduction of magnetic dopants into non-magnetic II-VI and III-V semiconductors, diluted magnetic semiconductors captured widespread attention 10 , boosted by the discovery of ferromagnetism in Mn-doped InAs (ref.11 ) and GaAs (ref.1 ) in the 1990s 12 . Central to progress in these fields, optical experiments have led to a deep understanding of electronic structure, magnetization dynamics and interactions between magnetism and light 8,[13][14][15] . While the fascinating physics in the quantum structures of diluted magnet...

Tungsten-based monolayer transition metal dichalcogenides host a long-lived “dark” exciton, an electron-hole pair in a spin-triplet configuration. The long lifetime and unique spin properties of the dark exciton provide exciting opportunities to explore light-matter interactions beyond electric dipole transitions. Here we demonstrate that the coupling of the dark exciton and an optically silent chiral phonon enables the intrinsic photoluminescence of the dark-exciton replica in monolayer WSe 2 . Gate and magnetic-field dependent PL measurements unveil a circularly-polarized replica peak located below the dark exciton by 21.6 meV, equal to E″ phonon energy from Se vibrations. First-principles calculations show that the exciton-phonon interaction selectively couples the spin-forbidden dark exciton to the intravalley spin-allowed bright exciton, permitting the simultaneous emission of a chiral phonon and a circularly-polarized photon. Our discovery and understanding of the phonon replica reveals a chirality dictated emission channel of the phonons and photons, unveiling a new route of manipulating valley-spin.

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It is well-known that excitonic effects can dominate the optical properties of two-dimensional materials. These effects, however, can be substantially modified by doping free carriers. We investigate these doping effects by solving the first-principles Bethe-Salpeter equation. Dynamical screening effects, included via the sum-rule preserving generalized plasmon-pole model, are found to be important in the doped system. Using monolayer MoS2 as an example, we find that upon moderate doping, the exciton binding energy can be tuned by a few hundred millielectronvolts, while the exciton peak position stays nearly constant due to a cancellation with the quasiparticle band gap renormalization. At higher doping densities, the exciton peak position increases linearly in energy and gradually merges into a Fermi-edge singularity. Our results are crucial for the quantitative interpretation of optical properties of two-dimensional materials and the further development of ab initio theories of studying charged excitations such as trions.

Bilayer van der Waals (vdW) heterostructures such as MoS2/WS2 and MoSe2/WSe2 have attracted much attention recently, particularly because of their type II band alignments and the formation of interlayer exciton as the lowest-energy excitonic state. In this work, we calculate the electronic and optical properties of such heterostructures with the first-principles GW+Bethe-Salpeter Equation (BSE) method and reveal the important role of interlayer coupling in deciding the excited-state properties, including the band alignment and excitonic properties. Our calculation shows that due to the interlayer coupling, the low energy excitons can be widely tunable by a vertical gate field. In particular, the dipole oscillator strength and radiative lifetime of the lowest energy exciton in these bilayer heterostructures is varied by over an order of magnitude within a practical external gate field. We also build a simple model that captures the essential physics behind this tunability and allows the extension of the ab initio results to a large range of electric fields. Our work clarifies the physical picture of interlayer excitons in bilayer vdW heterostructures and predicts a wide range of gate-tunable excited-state properties of 2D optoelectronic devices.

Understanding the remarkable excitonic effects and controlling the exciton binding energies in two-dimensional (2D) semiconductors are crucial in unlocking their full potential for use in future photonic and optoelectronic devices. Here, we demonstrate large excitonic effects and gate-tunable exciton binding energies in single-layer rhenium diselenide (ReSe2) on a back-gated graphene device. We used scanning tunneling spectroscopy and differential reflectance spectroscopy to measure the quasiparticle electronic and optical bandgap of single-layer ReSe2, respectively, yielding a large exciton binding energy of 520 meV. Further, we achieved continuous tuning of the electronic bandgap and exciton binding energy of monolayer ReSe2 by hundreds of milli–electron volts through electrostatic gating, attributed to tunable Coulomb interactions arising from the gate-controlled free carriers in graphene. Our findings open a new avenue for controlling the bandgap renormalization and exciton binding energies in 2D semiconductors for a wide range of technological applications.

We report many-body perturbation theory calculations of excited-state properties of distorted 1-T diamond-chain monolayer rhenium disulfide (ReS 2 ) and diselenide (ReSe 2 ). Electronic selfenergy substantially enhances their quasiparticle band gaps and, surprisingly, converts monolayer ReSe 2 to a direct-gap semiconductor, which was, however, regarded to be an indirect one by density-functional-theory calculations. Their optical absorption spectra are dictated by strongly bound excitons. Unlike hexagonal structures, the lowest-energy bright exciton of distorted 1-T ReS 2 exhibits a perfect figure-8 shape polarization dependence but those of ReSe 2 only exhibit a partial polarization dependence, which results from two nearly-degenerated bright excitons whose polarization preferences are not aligned. Our first-principles calculations are in excellent agreement with experiments and pave the way for optoelectronic applications. 1

Doped free carriers can substantially renormalize electronic self-energy and quasiparticle band gaps of two-dimensional (2D) materials. However, it is still challenging to quantitatively calculate this many-electron effect, particularly at the low doping density that is most relevant to realistic experiments and devices. Here we develop a first-principles-based effective-mass model within the GW approximation and show a dramatic band gap renormalization of a few hundred meV for typical 2D semiconductors. Moreover, we reveal the roles of different many-electron interactions: The Coulomb-hole contribution is dominant for low doping densities while the screened-exchange contribution is dominant for high doping densities. Three prototypical 2D materials are studied by this method, h-BN, MoS2, and black phosphorus, covering insulators to semiconductors. Especially, anisotropic black phosphorus exhibits a surprisingly large band gap renormalization because of its smaller density-of-state that enhances the screened-exchange interactions. Our work demonstrates an efficient way to accurately calculate band gap renormalization and provides quantitative understanding of doping-dependent many-electron physics of general 2D semiconductors.