Valley Zeeman e ect in elementary optical excitations of monolayerWSe 2

Amonolayer of a transitionmetal dichalcogenide such asWSe2 is a two-dimensional direct-bandgap valley-semiconductor1,2 having an e ective honeycomb lattice structure with broken inversion symmetry. The inequivalent valleys in the Brillouin zone could be selectively addressed using circularly polarized light fields3–5, suggesting the possibility for magneto-optical measurement and manipulation of the valley pseudospin degree of freedom6–8. Here we report such experiments that demonstrate the valley Zeeman e ect—strongly anisotropic lifting of the degeneracy of the valley pseudospin degree of freedom using an external magnetic field. The valley-splitting measured using the exciton transition deviates appreciably fromvalues calculatedusing a three-band tight-bindingmodel9 for an independent electron–hole pair at ±K valleys. We show, on the other hand, that a theoretical model taking into account the strongly bound nature of the exciton yields an excellent agreement with the experimentally observed splitting. In contrast to the exciton, the trion transition exhibits an unexpectedly large valley Zeeman e ect that cannot be understood within the same framework, hinting at a di erent contribution to the trion magnetic moment. Our results raise the possibility of controlling the valley degree of freedomusing magnetic fields in monolayer transition metal dichalcogenides or observing topological states of photons strongly coupled to elementary optical excitations in a microcavity10. Charge carriers in two-dimensional (2D) layered materials with a honeycomb lattice, such as graphene and transition metal dichalcogenides (TMDs), have a twofold valley degree of freedom labelled by ±K-points of the Brillouin zone, which are related to each other by time-reversal symmetry7. In TMDs, the low-energy physics takes place in the vicinity of ±K-points of the conduction and valence bands with Bloch states that are formed primarily from dz2 and dx2−y2 , dxy orbitals of the transition metal, respectively9. The magnetic moment of charged particles in a monolayer TMD arises from two distinct contributions: the intracellular component stems from the hybridization of the dx2−y2 and dxy orbitals as dx2−y2 ± idxy , which provide the Bloch electrons at ±K in the valence band an azimuthal angular momentum along z of lz=±2h̄ (Fig. 1a). The second—intercellular—contribution originates from the phase winding of the Bloch functions at ±K-points11–14. This latter contribution to orbital magnetic moment is different for conduction and valence bands owing to breakdown of electron– hole symmetry. Both contributions yield magnetic-field-induced splitting with an opposite sign in the two valleys. In a 2D material such as a monolayer TMD, the current circulation from the orbitals can only be within the plane; as a consequence, the corresponding orbital magnetic moment can only point out-of-plane. A magnetic field (B) along z distinguishes the sense of circulation in 2D, causing opposite energy shifts (−μ·B) in ±K valleys as a result of opposite magnetic moments. The lifting of degeneracy between the two valleys in the presence of B represents a valley analogue of the spin-Zeeman effect. Optical absorption or emission experiments would allow a direct determination of this valley Zeeman effect as the valley index (±K) for independent electron–hole pairs is linked to the helicity of light (σ) emitted normal to the monolayer3–5. On the other hand, it is well known that the optical excitation spectra of TMDs are strongly modified by Coulomb interactions, leading to strongly bound neutral and charged exciton (trion) resonances with non-hydrogenic excited states15–20. Moreover, it has been recently shown that the electron– hole exchange interaction couples the±Kvalleys21. It is therefore not a priori clear to what extent predictions about circular dichroism or orbital magnetic moments that are based on a non-interacting particle picture remain valid in optical measurements probing exciton or trion resonances. We perform polarization-resolved photoluminescence (PL) spectroscopy on monolayer WSe2 to identify the low-energy optical excitations (Methods). Figure 1b shows a typical polarizationresolved PL spectrum at zero field. A sizeable ‘valley coherence’ or linear dichroism (∼20%) of the exciton peak (X0) at ∼708 nm confirms its monolayer nature22. The peak at around 722 nm is identified as originating from trion (X) emission, consistent with the previous PL studies on WSe2 (ref. 22). Polarization-resolved PL measurements yielded a valley-contrasting circular dichroismof less than 20% for both X0 and X resonances in all the flakes that were measured. As we argue below, the electron–hole exchange-induced mixing of the two valleys is possibly responsible for reducing the degree of circular dichroism21,23. Figure 2a shows the behaviour of X0 at variousB up to 8.4 T in the Faraday geometry (B‖z). ThePL is analysed in a circularly polarized basis while the excitation of the laser is kept linearly polarized, detuned by over 200meV from the X0 resonance. A clear splitting of the X0 peak as a function of B is observed: the splitting increases linearly with B, with a slope of about 0.25meVT−1 (Fig. 2b). The magnitudes of B-dependent splitting in five different flakes are observed to be within ±10% of this value. We have also carried out resonant reflection measurements which showed a similar splitting for the exciton peak (Fig. 2c). The fact that we do not observe the trion peak in reflectionmeasurements indicates that our sample has a low doping density. The measurement of the magnetic-field dependence of PL in the Voigt geometry (B⊥ z) shows no observable splitting up to the highest B (Fig. 3a). This extreme anisotropy in the magnetic response of the monolayer is a direct consequence of the fact that