Defect-Induced Modification of Low-Lying Excitons and Valley Selectivity in Monolayer Transition Metal Dichalcogenides

We study the effect of point-defect chalcogen vacancies on the optical properties of monolayer transition metal dichalcogenides using ab initio $GW$ and Bethe-Salpeter equation calculations. We find that chalcogen vacancies introduce unoccupied in-gap states and occupied resonant defect states within the quasiparticle continuum of the valence band. These defect states give rise to a number of strongly bound defect excitons and hybridize with excitons of the pristine system, reducing the valley-selective circular dichroism. Our results suggest a pathway to tune spin-valley polarization and other optical properties through defect engineering.

Figure 1

(a) Top and side views of $5\times 5$ TMD supercells with one chalcogen vacancy. Vacancy sites are circled by a black dotted line. (b) Left: Isosurfaces of the occupied (bottom) and unoccupied (top) wave functions associated with the defect states in a $5\times 5$ supercell of ${\mathrm{MoSe}}_2$. Right: The quasiparticle band structure of ${\mathrm{MoSe}}_2$, along the $\overline{\mathrm{\Gamma }}$-to-$\overline{K}$ line in the supercell BZ (inset), calculated using $G_0{W}_0@\mathrm{LDA}$, including SOC corrections. Defect (D) or pristinelike (Pr) states are labeled as $v_{\mathrm{D}/\mathrm{Pr}}$ ($c_{\mathrm{D}/\mathrm{Pr}}$) for occupied (unoccupied) states. The inset shows a schematic (not to scale) of the supercell BZ compared to the BZ of a single unit cell of a pristine TMD. (c) Defect-state energy levels, calculated within DFT (LDA) and $G_0{W}_0$ for ${\mathrm{MoSe}}_2$ (left) and ${\mathrm{WS}}_2$ (right). Defect states are shown by black dashed lines, and the bulk states are shown in red and blue shaded regions for the spin-up and spin-down spin-orbit split bands.

Figure 2

(a) Absorbance spectrum of $5\times 5$ supercells of ${\mathrm{MoSe}}_2$ with a single chalcogen vacancy. (b) Contributions of each band to each exciton state, plotted with respect to the exciton excitation energy (Only the $A$ series of spin-orbit split excitons is included for clarity). The bands are labeled as either bulklike dispersive bands relative to the valence band maximum (VBM) and conduction band minimum (CBM) or as flat defect bands $v_{\mathrm{D}}$, $c_{\mathrm{D}1}$, and $c_{\mathrm{D}2}$, with the occupied band contributions in red and unoccupied band contributions in blue. The size of each dot is proportional to square of the $k$-space electron-hole amplitude of the contribution from each band weighted by the oscillator strength of the exciton state.

Figure 3

Absorbance spectra of ${\mathrm{MoSe}}_2$ computed for different defect densities. 2.0% defect density corresponds to the explicitly calculated $5\times 5$ supercell (black line), and 0.0% corresponds to the pristine monolayer (yellow line). Other densities are evaluated following Eq. (5) in the Supplemental Material.

Figure 4

Schematic of band-to-band transition near $\overline{K}$ (top panel) and degree of circular dichroism in the supercell BZ (bottom panel) for the band-to-band transitions (a) VBM to $c_{\mathrm{D}1}$, (b) VBM to $c_{\mathrm{D}2}$, and (c) VBM to CBM of the monolayer ${\mathrm{MoSe}}_2$ $5\times 5$ supercell with the chalcogen vacancy. The selected band-to-band transition is in black, with other bands in gray.

Figure 5

Intensity (arbitrary units) of the instantaneous emission of left-hand circularly polarized light (${\sigma }_L$, red) or right-hand circularly polarized light (${\sigma }_R$, blue) from an exciton state excited by right-hand circularly polarized light, in a $5\times 5$ unit cell of ${\mathrm{MoSe}}_2$ with a single chalcogen vacancy.