Abstract
In this study we present a theoretical investigation of the full-zone landscape of finite-momentum dark excitons in ${\mathrm{WSe}}_{2}$-MLs by solving the density-functional-theory (DFT)-based Bethe-Salpeter equation (BSE) under the guidance of symmetry analysis. The studies reveal the comprehensive valley-polarization landscape of finite-momentum exciton of ${\mathrm{WSe}}_{2}$ monolayer. Dictated by the crystal symmetry, the valley pseudospin texture over the extended exciton-momentum ${\mathbit{k}}_{\text{ex}}$ space exhibits rich structures, featured by the inherently full valley polarizations in the excitonic ${K}_{\text{ex}}$, ${K}_{\text{ex}}^{\ensuremath{'}}$, and ${Q}_{\text{ex},i}$ valleys and also by the contrasted valley depolarizations for the exciton states lying in the $\overline{{\mathrm{\ensuremath{\Gamma}}}_{\text{ex}}{M}_{\text{ex},i}}$ paths. Attractively, the superior valley polarizations of the intervalley dark excitons in ${\mathrm{WSe}}_{2}$-MLs are shown almost fully transferable to the optical polarization in the phonon-assisted photoluminescences because of the native suppression of exchange-induced depolarization in the second-order optical processes. The analysis of phonon-assisted photoluminescences accounts for the recently observed brightness, high degree of optical polarization, and long lifetime of the intervalley dark exciton states in tungsten-based TMD-MLs.
Highlights
Transition metal dichalcogenide monolayers (TMD-MLs) have drawn a broad interest in recent years because of the intriguing spin-valley-coupled characteristics in the electronic and excitonic structures [1,2,3,4,5,6]
It is known that the valley polarization of a bright exciton in a TMD-ML is very likely depolarized by the intrinsic electron-hole (e-h) exchange interaction that couples the interband excitations in the distinct valleys [4,9,10,11,12,13]
Under the effect of EHEI, the bright exciton (BX) states around the ex as well as the momentum-forbidden dark exciton (MFDX) ones along the exMex,i paths no longer remain degenerate and, as shown in Figs. 2(d) and 2(e), become valley split with +−(kex ) ≡ E+X,kex − E−X,kex ≈ 2| ̃ KK| = 0, where KK represents the e-h exchange interaction that intermixes the K and K valley components in the exciton states with kex
Summary
Transition metal dichalcogenide monolayers (TMD-MLs) have drawn a broad interest in recent years because of the intriguing spin-valley-coupled characteristics in the electronic and excitonic structures [1,2,3,4,5,6]. The latest cryogenic photoluminescence (PL) measurements on tungsten-based TMD-MLs have revealed the pronounced optical signatures of the intervalley MFDXs which are significantly bright [17], highly polarized [16,18], and long lived [30]. Such long-lived and optically accessible MFDXs are attractive for the quantum applications and realizing excitonic Bose-Einstein condensation (BEC) [31,32,33,34]. The theoretical analysis accounts for the recently observed spectral brightness [16,17,18], high degree of optical polarization [16,18], and long-lived dynamics of the intervalley MFDXs in tungstenbased TMD-MLs [30]
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