Abstract:Electrons in 2-dimensional crystals with a honeycomb lattice structure possess a new valley degree of freedom (DOF) in addition to charge and spin. Each valley is predicted to exhibit a Hall effect in the absence of a magnetic field whose sign depends on the valley index, but to date this effect has not been observed. Here we report the first observation of this new valley Hall effect (VHE). Monolayer MoS 2 transistors are illuminated by circularly polarized light which preferentially excites electrons into a specific valley, and a finite anomalous Hall voltage is observed whose sign is controlled by the helicity of the light. Its magnitude is consistent with theoretical predictions of the VHE, and no anomalous Hall effect is observed in bilayer devices due to the restoration of crystal inversion symmetry. Our observation of VHE opens up new possibilities for using the valley DOF as an information carrier in next-generation electronics and optoelectronics.The charge and spin degrees of freedom (DOF) of electrons are at the heart of modern electronics. They form the basis for a wide range of applications such as transistors, photodetectors and magnetic memory devices. Interestingly, electrons in 2-dimensional (2D) crystals that have a honeycomb lattice structure possess an extra valley DOF (1) in addition to charge and spin. This new DOF has the potential to be used as an information carrier in nextgeneration electronics (2-6). Valley-dependent electronics and optoelectronics based on semimetallic graphene, a representative 2D crystal, have been theoretically proposed (2-5), but the presence of inversion symmetry in the crystal structure of pristine graphene makes both optical and electrical control of the valley DOF very difficult.In contrast, monolayer molybdenum disulfide (MoS 2 ), a 2D direct band gap semiconductor (7, 8) that possesses a staggered honeycomb lattice structure, is inversion asymmetric. Its fundamental direct energy gaps are located at the K and K' valleys of the Brillouin zone as illustrated in figure 1A. Due to the broken inversion symmetry in its crystal structure, electrons in the two valleys experience effective magnetic fields (proportional to the Berry curvature (4)) with equal magnitudes but opposite signs (figure 1A). Such a magnetic field not only defines the optical selection rules (6) that allow optical pumping of valley-polarized carriers by circularly polarized photons (9-13), but also generates an anomalous velocity for the charge carriers (6, 14). Namely, when the semiconductor channel is biased, electrons from different valleys move in opposite directions perpendicular to the drift current, a phenomenon called the valley Hall effect (VHE) (4)(5)(6) 15). The VHE originates from the coupling of the valley DOF to the orbital motion of electrons (4, 9). This is closely analogous to the spin Hall effect with the spin-polarized electrons replaced by valley-polarized carriers.Under time reversal symmetry, equal amounts of Hall current from each valley flow in opposite direc...

Using polarization-resolved photoluminescence spectroscopy, we investigate breaking of valley degeneracy by out-of-plane magnetic field in back-gated monolayer MoSe2 devices. We observe a linear splitting of −0.22 meV T between luminescence peak energies in σ+ and σ− emission for both neutral and charged excitons. The optical selection rules of monolayer MoSe2 couple photon handedness to the exciton valley degree of freedom, so this splitting demonstrates valley degeneracy breaking. In addition, we find that the luminescence handedness can be controlled with magnetic field, to a degree that depends on the back-gate voltage. An applied magnetic field therefore provides effective strategies for control over the valley degree of freedom.

These authors contributed equally: Tingxin Li, Shengwei Jiang.Stacking order can significantly influence the physical properties of two-dimensional (2D) van der Waals materials 1 . The recent isolation of atomically thin magnetic materials 2-22 opens the door for control and design of magnetism via stacking order. Here we apply hydrostatic pressure up to 2 GPa to modify the stacking order in a prototype van der Waals magnetic insulator CrI3. We observe an irreversible interlayer antiferromagnetic (AF) to ferromagnetic (FM) transition in atomically thin CrI3 by magnetic circular dichroism and electron tunneling measurements. The effect is accompanied by a monoclinic to a rhombohedral stacking order change characterized by polarized Raman spectroscopy. Before the structural change, the interlayer AF coupling energy can be tuned up by nearly 100% by pressure. Our experiment reveals interlayer FM coupling, which is the established ground state in bulk CrI3, but never observed in native exfoliated thin films. The observed correlation between the magnetic ground state and the stacking order is in good agreement with first principles calculations 23-27 and suggests a route towards nanoscale magnetic textures by moiré engineering 28 .Intrinsic magnetism in 2D van der Waals materials has received growing attention 2-22 . Of particular interest is the thickness-dependent magnetic ground state in atomically thin CrI3. In these exfoliated thin films, the magnetic moments are aligned (in the out-of-plane direction) in each layer, but anti-aligned in adjacent layers 3,12-22 . They are FM (or AF) depending on whether there is (or isn't) an uncompensated layer. The relatively weak interlayer coupling compared to the intralayer coupling allows effective ways to control the interlayer magnetism, which have led to interesting spintronics applications including voltage switching 12-14 , spin filtering 16-20 and spin transistors 21 . The origin of interlayer AF coupling is, however, not well understood since interlayer FM order is the ground state in the bulk crystals. Recent ab initio calculations 23-27 and experiments 22,29,30 have suggested that stacking order could provide an explanation but a direct correlation between stacking order and interlayer magnetism is lacking.In bulk CrI3, the Cr atoms in each layer form a honeycomb structure, and each Cr atom is surrounded by six I atoms in an octahedral coordination (Fig. 1a). The bulk crystals undergo a structural phase transition from a monoclinic phase (space group C2/m) at room temperature to a

Monolayers of group-VI transition metal dichalcogenides (TMDs) of the hexagonal polytype consist of a single layer of transition metal atoms sandwiched between two layers of chalcogen atoms in a trigonal prismatic structure (Fig. 1a). Because of the absence of inversion symmetry, electrons in monolayer TMDs at the K and the K' valley of the Brillouin zone possess finite but opposite Berry curvatures 3,13

Recent experimental advances in atomically thin transition metal dichalcogenide (TMD) metals have unveiled a range of interesting phenomena including the coexistence of charge-density-wave (CDW) order and superconductivity down to the monolayer limit. The atomic thickness of two-dimensional (2D) TMD metals also opens up the possibility for control of these electronic phase transitions by electrostatic gating. Here, we demonstrate reversible tuning of superconductivity and CDW order in model 2D TMD metal NbSe_{2} by an ionic liquid gate. A variation up to ∼50% in the superconducting transition temperature has been observed. Both superconductivity and CDW order can be strengthened (weakened) by increasing (reducing) the carrier density in 2D NbSe_{2}. The doping dependence of these phase transitions can be understood as driven by a varying electron-phonon coupling strength induced by the gate-modulated carrier density and the electronic density of states near the Fermi surface.