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 material, the MoS 2 monolayer emits light strongly. The freestanding monolayer exhibits an increase in luminescence quantum efficiency by more than a factor of 1000 compared with the bulk material.

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...

Graphene's success has shown that it is possible to create stable, single and few-atom-thick layers of van der Waals materials, and also that these materials can exhibit fascinating and technologically useful properties. Here we review the state-of-the-art of 2D materials beyond graphene. Initially, we will outline the different chemical classes of 2D materials and discuss the various strategies to prepare single-layer, few-layer, and multilayer assembly materials in solution, on substrates, and on the wafer scale. Additionally, we present an experimental guide for identifying and characterizing single-layer-thick materials, as well as outlining emerging techniques that yield both local and global information. We describe the differences that occur in the electronic structure between the bulk and the single layer and discuss various methods of tuning their electronic properties by manipulating the surface. Finally, we highlight the properties and advantages of single-, few-, and many-layer 2D materials in field-effect transistors, spin- and valley-tronics, thermoelectrics, and topological insulators, among many other applications.

Single-layer transition metal dichalcogenides (TMDs) provide a promising material system to explore the electron's valley degree of freedom as a quantum information carrier 1-3 . The valley degree of freedom in single-layer TMDs can be directly accessed by means of optical excitation 4-6 . The rapid valley relaxation of optically excited electron-hole pairs (excitons) 7-9 through the long-range electron-hole exchange interaction 10,11 , however, has been a major roadblock. Theoretically such a valley relaxation does not occur for the recently discovered dark excitons [12][13][14][15][16] , suggesting a potential route for long valley lifetimes 10 . Here we investigate the valley dynamics of dark excitons in single-layer WSe 2 by time-resolved photoluminescence spectroscopy. We develop a waveguide-based method to enable the detection of the dark exciton emission, which involves spin-forbidden optical transitions with an out-of-plane dipole moment. The valley degree of freedom of dark excitons is accessed through the valley-dependent Zeeman effect under an out-of-plane magnetic field. We find a short valley lifetime for the dark neutral exciton, likely due to the short-range electron-hole exchange 17,18 , but long valley lifetimes exceeding several nanoseconds for dark charged excitons.Single-layer transition metal dichalcogenides (TMDs, MX 2 : M=Mo, W; X=S, Se) are direct band-gap semiconductors with direct gaps located at the K and K' valleys of the Brillouin zone 19,20 . Both valence and conduction bands are spin-split at the two valleys by the strong spinorbit coupling. The exciton formed by Coulomb interaction from electron and hole of antiparallel spins is a bright exciton (optically active), and from electron and hole of parallel spins, a dark exciton (optically inactive). The bright exciton exhibits strong valley circular dichroism (i.e. each handedness of circularly polarized light couples only to one of the two valleys), which provides an effective means to access the valley degree of freedom 4-6 . However, the valley relaxation is very fast (order of 10 ps) for the bright neutral 7-9 and charged excitons 21-23 . The fast valley relaxation is attributed to the long-range electron-hole exchange interaction 10,11 , which mixes the two valley exciton states. On the other hand, intervalley scattering of the dark exciton would require a spin flip, which does not occur through the longrange exchange interaction 10 . A long-lived valley polarization of the dark exciton is thus possible. In tungsten-based TMDs the dark exciton has a lower energy than the bright exciton and has recently been shown long-lived 13,24 . Direct measurement of the valley lifetime of the dark exciton, however, remains challenging. This spin-forbidden exciton has an out-of-plane (OP) transition dipole moment 12,14,25 , making its detection difficult with conventional far-field optical techniques. In addition, unlike for the bright exciton, there are no valley-dependent optical selection rules for the dark exciton that can be utilized ...

Two-dimensional transition metal dichalcogenides with strong spin-orbit interactions and valley-dependentBerry curvature effects have attracted tremendous recent interests 1-7 . Although novel single-particle and excitonic phenomena related to spin-valley coupling have been extensively studied 1,3-6 , effects of spin-momentum locking on collective quantum phenomena remain unexplored. Here we report an observation of superconducting monolayer NbSe2 with an inplane upper critical field over six times of the Pauli paramagnetic limit by magnetotransport measurements. The effect can be understood in terms of the competing Zeeman effect and large intrinsic spin-orbit interactions in non-centrosymmetric NbSe2 monolayers, where the electronic spin is locked to the out-of-plane direction. Our results provide a strong evidence of unconventional Ising pairing protected by spin-momentum locking and open up a new avenue for studies of noncentrosymmetric superconductivity with unique spin and valley degrees of freedom in the exact two-dimensional limit.Monolayer transition metal dichalcogenide (TMD) of the hexagonal structure consists of a layer of transition metal atoms sandwiched between two layers of chalcogen atoms in the trigonal prismatic structure 8 (Fig. 1a). It possesses out-of-plane mirror symmetry and in-plane inversion asymmetry. The presence of the transition metal also gives rise to large spin-orbit interactions (SOIs). The mirror symmetry restricts the crystal field ( ⃗) to the plane. The SOIs split the spin states at finite momentum ⃗⃗ in the absence of inversion symmetry. They manifest as an effective magnetic field along the direction of ⃗⃗ × ⃗ , which is out-of-plane for the restricted two-dimensional (2D) motion of electrons in the plane. The electronic spin is thus oriented in the out-of-plane direction and in opposite directions for electrons of opposite momenta 1-3 (Fig. 1a). Such spinmomentum locking is destroyed in the bulk where inversion symmetry and spin degeneracy are restored 1,2,7 (Fig. 1b). Novel valley-and spin-dependent phenomena including optical orientation of the valley polarization 3,4 and the valley Hall effect 5 arisen from spin-momentum locking have been recently demonstrated in group-VI TMD

Time-resolved, pulsed terahertz spectroscopy has developed into a powerful tool to study charge carrier dynamics in semiconductors and semiconductor structures over the past decades. Covering the energy range from a few to about 100 meV, terahertz radiation is sensitive to the response of charge quasiparticles, e.g., free carriers, polarons, and excitons. The distinct spectral signatures of these different quasiparticles in the THz range allow their discrimination and characterization using pulsed THz radiation. This frequency region is also well suited for the study of phonon resonances and intraband transitions in low-dimensional systems. Moreover, using a pump-probe scheme, it is possible to monitor the nonequilibrium time evolution of carriers and low-energy excitations with sub-ps time resolution. Being an all-optical technique, terahertz time-domain spectroscopy is contact-free and noninvasive and hence suited to probe the conductivity of, particularly, nanostructured materials that are difficult or impossible to access with other methods. The latest developments in the application of terahertz time-domain spectroscopy to bulk and nanostructured semiconductors are reviewed.

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...