Tunable resonant s-p mixing of excitons in van der Waals heterostructures

Abstract

Excitonic states of tightly-bound electron-hole pairs dominate the optical response in a growing class of two-dimensional (2D) materials and their van der Waals (vdW) heterostructures. In transition metal dichalcogenides (TMDs) a useful guidance for the excitonic spectrum is the analogy with the states in the 2D hydrogen atom. From our symmetry analysis and solving the Bethe-Salpeter equations we find a much richer picture for excitons and predict their tunable resonant s-p mixing. The resonance is attained when the subband splitting matches the energy difference between the 1s and 2p+ (or 2p-) excitons, resulting in the anticrossing of the spectral lines in the absorption as a function of the subband splitting. By focusing on TMDs modified by magnetic proximity, and gated 3R-stacked bilayer TMD, we corroborate the feasibility of such tunable spin splitting. The resulting tunable and bright s-p excitons provide unexplored opportunities for their manipulation and enable optical detection of Rashba or interlayer coupling in vdW heterostructures.

Figures (3)

• Figure 1: (a) Spin-forbidden and spin-allowed optical transitions in the $K$ valley of proximitized ML TMDs, with valence ($v$) and conduction ($c$) band splitting, $2\Delta_v \gg 2\Delta_c$. The mixing is introduced by a broken mirror symmetry. (b) The evolution of the optical absorption and exciton energies, $\Omega_\pm$, as $2\Delta_c$ is tuned by the proximity-induced exchange coupling $J$, obtained from the Bethe-Salpeter equation. (c) Exciton energy levels before and after "turning on" of the mixing. $\Delta_{sp}=\Omega_{2p_+\uparrow\downarrow}-\Omega_{1s_+\uparrow\downarrow}$. Yellow (green) lines: bright (dark) excitons. The $s-p$ resonance condition $\Omega_{\uparrow\uparrow1s}=\Omega _{\downarrow\uparrow2p_+}$ or, equivalently, $2\Delta_c=\Delta_{sp}$ is demonstrated.
• Figure 2: BSE results for ML TMD: (a) Brightening of the $|2p_+{\uparrow\downarrow}\rangle$ and $|2p_-{\downarrow\uparrow}\rangle$ excitons with different $J$. Anticrossings appear in bottom-left [its enhanced view, white rectangle, in Fig. \ref{['fig:sp2']}(b)] and top-right region. (b) Mixing of the $|1s{\uparrow\uparrow}\rangle$ and $|2p_+{\uparrow\downarrow}\rangle$ excitonic states. (c), (d) The absorption spectra at two $s-p$ resonances. Marked as vertical white dashed lines in (a). (e), (f) Phases of dominant components of $\vec{\mathcal{A}}^{s,a}(\bm{k})$, see Eq. (\ref{['eq:A_ML']}). The direction (length) of an arrow denotes the phase and (the magnitude). Exciton energies at the resonance and their evolution with $J$ are marked in (c) and Fig. \ref{['fig:sp1']}(b).
• Figure 3: BSE results for 3R stacked BL TMD: (a) Evolution of the absorption as the subband splitting $2\Delta_{c(v)}$ is tuned through out-of-plane gate voltage $V_g$. Here, $J_0$ is the magnitude of $J$ realizing the exact $s-p$ resonance. (b) Mixing of the intralayer $1s$ excitons and the interlayer $|2p_+{\uparrow\downarrow}\rangle$ exciton. The $|{\uparrow}({\downarrow)}\rangle$ pseudospin denotes the t(b) layer index. (c) The absorption at the resonance, as marked by the white dashed line in (a). (d)-(f). Phases of the dominant components of $\vec{\mathcal{A}}^{s,a}(\bm{k})$ and $\vec{\mathcal{A}}^{1s-}(\bm{k})$. Corresponding exciton energies at the resonance and evolution with $V_g$ are marked in (c) and (a).