Probing and Manipulating Valley Coherence of Dark Excitons in Monolayer WSe2

Abstract

Monolayers of semiconducting transition metal dichalcogenides are two-dimensional direct-gap systems which host tightly-bound excitons with an internal degree of freedom corresponding to the valley of the constituting carriers. Strong spin-orbit interaction and the resulting ordering of the spin-split subbands in the valence and conduction bands makes the lowest-lying excitons in WX2 (X being S or Se) spin-forbidden and optically dark. With polarization-resolved photoluminescence experiments performed on a WSe2 monolayer encapsulated in a hexagonal boron nitride, we show how the intrinsic exchange interaction in combination with the applied in-plane and/or out-of-plane magnetic fields enables one to probe and manipulate the valley degree of freedom of the dark excitons.Monolayers of transition metal dichalcogenides (TMDs), such as MX 2 with M=Mo or W, and X=S, Se or Te, are two-dimensional direct-gap semiconductors 1 which attract a lot of interest due to their unique physical properties and potential applications in optoelectronics, photonics and the development of valleytronics 2-5,7,18 . The direct bandgap in semiconducting TMDs (S-TMDs) is located at the two inequivalent K ± points (valleys) of the first Brillouin zone, related by time reversal symmetry. In monolayers, the tightly bound and optically bright excitons 8-11 from K ± valley can efficiently couple to light with right/left circular polarization 12,13 , respectively.A unique feature of S-TMD monolayers is the so-called spin-valley locking 13 : strong spin-orbit interaction lifts the degeneracy between the two spin projections s =↑, ↓ in each valley, leaving only the Kramers degeneracy between the opposite valleys, K + , s ↔ K − , −s. While the valence band spin-orbit splitting ∆ v is very large (several hundred meV 13 ), its conduction band counterpart ∆ c is by an order of magnitude smaller 14-18 , thus allowing some degree of manipulation by an in-plane magnetic field. In tungsten-based S-TMDs, ∆ c has the same sign as ∆ v , leading to the spin subband ordering shown in Fig. 1(a). In each valley, the optically bright exciton has a higher energy than the dark exciton which is composed of the conduction and valence electronic states with opposite spin projections. This, among other things, results in a strong temperature dependence of the photoluminescence (PL) efficiency, as the bright states become more populated at higher temperatures 8,19,21 .Dark excitons can couple to light only via a residual spin-flip dipole matrix element d ⊥ , whose direction is perpendicular to the monolayer plane 22-24 . In consequence, the emission of dark excitons is directed predominantly along the monolayer plane, in contrast to the out-of-plane emission of bright excitons characterized by strong inplane optical dipoles, d , see Fig. 1(b). Notably, the valley degeneracy of dark excitons is lifted by the exchange interaction which mixes the valleys and produces two eigenstates with different energies. The higher energy component takes up the whole oscillator strength ...

Measurement of the spin-forbidden dark excitons in MoS2 and MoSe2 monolayers

“…An additional evidence for assigning the low-energy line observed for large in-plane magnetic field to spin-forbidden dark excitons is the measurements of its g -factor in an external field perpendicular to the monolayer. The measurements in the tilted field geometry presented below yield = −6.5; this large value is in good agreement with the predicted one in a simple model 27 (see Supplementary Note 9 ) and the measured one in WSe 2 MLs 22 , 28 (Table 1 ).…”

“…In Fig. 2b, we present the results of the fit for δ = 0.6 meV which corresponds to the value experimentally measured in WSe 2 22,28 . As δ is due to short range exchange interaction, which scales with the exciton binding energy, we do not expect the values to be strongly different between TMD materials as the exciton binding energies are roughly the same 29 .…”

“…The in-plane component of the field yields the mixing of the bright and dark exciton as already observed in the Voigt configuration and the out-of plane component leads to a Zeeman splitting of the states. While the energy splitting between the two spin/valley states for the bright exciton depends linearly with this z-component field (the slope given by effective g-factor), the field dependence of the dark states is more complicated since the two dark states at zero field are split by the exchange energy δ of the order of a few hundreds of µeV 22,28 (inset of Fig. 1c).…”

Inorganic 2D Luminescent Materials: Structure, Luminescence Modulation, and Applications

“…www.advopticalmat.de after optical excitation and exciton thermalization. Dark exciton emission can be efficiently brightened by application of a magnetic field, [120,124,125] near-field coupling to surface plasmon polaritons, [126] or coupling with phonons [127] or molecules. [128]…”

Long-lived populations of momentum- and spin-indirect excitons in monolayer WSe2

“…7 Long-lived dark excitons could also be useful as robust carriers of spin or valley information in spintronic or valleytronic devices through manipulating the helicity of the emitting photons. 11,12 The first step towards these applications is to understand the dynamics of dark excitons and the exciton-exciton interactions in tungsten-based h-TMDs.…”