Electronic and spintronic devices rely on the fact that free charge carriers in solids carry electric charge and spin, respectively. There are, however, other properties of charge carriers that might be exploited in new families of devices. In particular, if there are two or more conduction (or valence) band extrema in momentum space, then confining charge carriers in one of these valleys allows the possibility of valleytronic devices 1-4 . Such valley polarization has been demonstrated by using strain 5,6 and magnetic fields 7-10 , but neither of these approaches allow for dynamic control. Here we demonstrate that optical pumping with circularly-polarized light can achieve complete dynamic valley polarization in monolayer MoS 2 11,12 , a twodimensional (2D) non-centrosymmetric crystal with direct energy gaps at two valleys [13][14][15][16] . Moreover, this polarization is retained for longer than 1 ns. Our results, and similar results by Zeng et al. 17 , demonstrate the viability of optical valley control and valley-based electronic and optoelectronic applications in MoS 2 monolayers.Since optical photons do not carry significant momentum, they cannot selectively populate different valleys based on this attribute. For appropriate materials, however, carriers in different valleys are associated with well-defined, but different angular momenta. This suggests the possibility of addressing different valleys by control of the photon angular momentum, i.e., by the helicity (circular polarization state) of light. Indeed, just such valley-specific circular dichroism of interband transitions has been predicted in non-centrosymmetric materials 3,4,11,12 . Graphene with its two prominent K and K' valleys has been considered theoretically in this context 3,4 . For this approach to be applicable, however, the inherent inversion symmetry of the single-and bilayer graphene must be broken 3,4 , and the effect has not yet been realized experimentally. Monolayer MoS 2 , on the other hand, is a direct band gap semiconductor [13][14][15][16] that possesses a structure similar to graphene, but with explicitly broken inversion symmetry. It has recently been proposed as a suitable material for valleytronics 11,12 .Monolayer MoS 2 consists of a single layer of Mo atoms sandwiched between two layers of S atoms in a trigonal prismatic structure 18 (Fig. 1a). Inversion symmetry is broken since the two sublattices are occupied, respectively, by one Mo and two S atoms. At the K and K' valleys in momentum space, the highest energy valence bands (VB) and the lowest energy conduction bands (CB) are mainly of Mo d-orbital character 18 . Because of the broken inversion symmetry, spin-orbit (SO) interactions split the VBs by about 160 meV 11,19,20 (Fig. 1b). The spin projection along the c-axis of the crystal, S z , is well defined and the two bands are of spin down (! ↓ ) and spin up (! ↑ ) in character. This broken spin degeneracy, in combination with time reversal symmetry (! ↓ (!) = ! ↑ (−!), where ! is crystal momentum) implies tha...

Two-dimensional (2D) atomic crystals, such as graphene and transition-metal dichalcogenides, have emerged as a new class of materials with remarkable physical properties 1 . In contrast to graphene, monolayer MoS 2 is a non-centrosymmetric material with a direct energy gap 2-5 . Strong photoluminescence 2,3 , a current on-off ratio exceeding 10 8 in field-effect transistors 6 , and efficient valley and spin control by optical helicity 7-9 have recently been demonstrated in this material. Here we report the spectroscopic identification in doped monolayer MoS 2 of tightly bound negative trions, a quasi-particle composed of two electrons and a hole. These quasiparticles, which can be created with valley and spin polarized holes, have no analogue in other materials. They also possess a large binding energy (~ 20 meV), rendering them significant even at room temperature. Our results open up new avenues both for fundamental studies of many-body interactions and for optoelectronic and valleytronic applications in 2D atomic crystals.The trion binding energy that we observe in monolayer MoS 2 is nearly an order of magnitude larger than that found in conventional quasi-2D systems, such as semiconductor quantum wells (QWs) [10][11][12][13] . This is a consequence of the greatly enhanced Coulomb interactions in monolayer MoS 2 , arising from reduced dielectric screening in gapped 2D crystals and the relatively heavy carrier band masses associated with the Mo d-manifolds 4,5,14 . For an electron density as high as n = 10 11 cm -2 , for instance, the dimensionless interaction parameter r s is ~60 in monolayer MoS 2 (Supplementary Information S1). This value is significantly larger than that for carriers in QWs even at very low doping levels 15 . Monolayer MoS 2 is a strongly interacting system even in the presence of relatively high carrier densities; it thus presents an ideal laboratory for exploring many-body phenomena, such as carrier multiplication and Wigner crystallization 16 .The atomic structure of MoS 2 consists of hexagonal planes of S and Mo atoms in a trigonal prismatic structure (Fig. 1a) 17 . The two sublattices of the hexagonal MoS 2 structure are occupied, respectively, by one Mo and two S atoms (Fig. 1b). Monolayer MoS 2 is a direct gap semiconductor with energy gaps located at the K and K' points of the Brillouin zone (Fig. 1c). Both the highest valence bands and the lowest conduction bands are formed primarily from the Mo d-orbitals 4,17 . The large spin-orbit interaction 2 splits the highest valence bands at the K (K') point by ~ 160 meV 2,3,7,14,18 . The valley and spin (VS) degrees are coupled because of the lack of inversion symmetry in monolayer MoS 2 . As has been recently shown experimentally, this allows optical pumping of a single valley (and spin) with circularly polarized light 7-9 .Here we investigate the optical response of monolayer MoS 2 as a function of carrier density by means of absorption and photoluminescence (PL) spectroscopy. In our investigations we have made use of MoS 2 monolayers p...

Exciton binding energy and excited states in monolayers of tungsten diselenide (WSe 2 ) are investigated using the combined linear absorption and two-photon photoluminescence excitation spectroscopy. The exciton binding energy is determined to be 0.37 eV, which is about an order of magnitude larger than that in III-V semiconductor quantum wells and renders the exciton excited states observable even at room temperature. The exciton excitation spectrum with both experimentally determined one-and two-photon active states is distinct from the simple two-dimensional (2D) hydrogenic model. This result reveals significantly reduced and nonlocal dielectric screening of Coulomb interactions in 2D semiconductors. The observed large exciton binding energy will also have a significant impact on next-generation photonics and optoelectronics applications based on 2D atomic crystals. DOI: 10.1103/PhysRevLett.113.026803 PACS numbers: 73.21.Fg, 71.35.Cc, 78.20.Ci, 78.55.Hx One of the most distinctive features of electrons in twodimensional (2D) semiconductors, such as single atomic layers of group VI transition metal dichalcogenides (TMDs) [1], is the significantly reduced dielectric screening of Coulomb interactions. An important consequence of strong Coulomb interactions is the formation of tightly bound excitons. Indeed, recent theoretical studies have predicted a large exciton binding energy between 0.5 and 1 eV in MoS 2 monolayers [2-10], a representative 2D direct gap semiconductor from the family of TMDs [11,12]. These values for the exciton binding energy are more than an order of magnitude larger than that in conventional III-V-based quasi-2D semiconductor quantum wells (QWs) [13,14]. Such tightly bound excitons are expected to not only dominate the optical response, but also to play a defining role in the optoelectronic processes, such as photoconduction and photocurrent generation in 2D semiconductors [1,15]. On the other hand, little is known about these tightly bound excitons from the experimental standpoint, except the energy of the lowest energy one-photon active exciton states [11] and an indirect evidence of large binding energies through recent studies on trions, quasiparticles of two electrons and a hole, or two holes and an electron [16][17][18]. Furthermore, a non-Rydberg series has been predicted for excitons in 2D semiconductors, arisen from the nonlocal character of screening of the Coulomb interactions [4,19]. While a Rydberg series for the exciton energy spectrum has been observed in bulk MoS 2 [20,21], similar experimental studies on monolayers of MoS 2 or other TMDs have not been reported [22].The challenge in experimental determination of the exciton binding energy in 2D TMDs by linear optical methods, commonly used for bulk semiconductors [23] or conventional semiconductor QWs [13], lies in the identification of the onset of band-to-band transitions in the optical absorption or emission spectrum. Such an onset of band-to-band transitions has not been observed in 2D TMDs presumably due to the sig...

We demonstrate the continuous tuning of the electronic structure of atomically thin MoS 2 on flexible substrates by applying a uniaxial tensile strain. A redshift at a rate of ~70 meV per percent applied strain for direct gap transitions, and at a rate 1.6 times larger for indirect gap transitions, have been determined by absorption and photoluminescence spectroscopy. Our result, in excellent agreement with first principles calculations, demonstrates the potential of twodimensional crystals for applications in flexible electronics and optoelectronics.

In nanomaterials, optical anisotropies reveal a fundamental relationship between structural and optical properties. Directional optical properties can be exploited to enhance the performance of optoelectronic devices, optomechanical actuators and metamaterials. In layered materials, optical anisotropies may result from in-plane and out-of-plane dipoles associated with intra- and interlayer excitations, respectively. Here, we resolve the orientation of luminescent excitons and isolate photoluminescence signatures arising from distinct intra- and interlayer optical transitions. Combining analytical calculations with energy- and momentum-resolved spectroscopy, we distinguish between in-plane and out-of-plane oriented excitons in materials with weak or strong interlayer coupling-MoS₂ and 3,4,9,10-perylene tetracarboxylic dianhydride (PTCDA), respectively. We demonstrate that photoluminescence from MoS₂ mono-, bi- and trilayers originates solely from in-plane excitons, whereas PTCDA supports distinct in-plane and out-of-plane exciton species with different spectra, dipole strengths and temporal dynamics. The insights provided by this work are important for understanding fundamental excitonic properties in nanomaterials and designing optical systems that efficiently excite and collect light from exciton species with different orientations.