Field-induced dissociation of two-dimensional excitons in transition metal dichalcogenides

Generation of photocurrents in semiconducting materials requires dissociation of excitons into free charge carriers. While thermal agitation is sufficient to induce dissociation in most bulk materials, an additional push is required to induce efficient dissociation of the strongly bound excitons in monolayer transition metal dichalcogenides (TMDs). Recently, static in-plane electric fields have proven to be a promising candidate. In the present paper, we introduce a numerical procedure, based on exterior complex scaling, capable of computing field-induced exciton dissociation rates for a wider range of field strengths than previously reported in the literature. We present both Stark shifts and dissociation rates for excitons in various TMDs calculated within the Mott-Wannier model. Here, we find that the field-induced dissociation rate is strongly dependent on the dielectric screening environment. Furthermore, applying weak-field asymptotic theory to the Keldysh potential, we are able to derive an analytical expression for exciton dissociation rates in the weak-field region.

Figure 1

Sketch of the two-dimensional exciton in the $xy$-plane with the radial coordinate rotated into the complex plane by an angle of $\varphi$ for $r>R$.

Figure 2

Exciton Stark shift and dissociation rate of the ground-state exciton for four important materials in various dielectric environments.

Figure 3

Stark shift and dissociation rates for excitons occupying either the $1s, 2s$, or $2p$ state in TMDs located in free space ($\kappa =1$).

Figure 4

Exciton dissociation rates for ${\mathrm{MoS}}_2$ (upper) and ${\mathrm{WSe}}_2$ (lower) encapsulated by various dielectric media. The circles are the numerically exact results obtained by the method in Appendix pp1 (same as those in Fig. 2). The solid lines correspond to the weak-field formula Eq. (9) with the parameters found in Table 1.

Figure 5

Exciton Stark shift for four important TMDs in various dielectric environments. The solid lines correspond to the real part of the resonance energy, while the dotted lines show the shift predicted by perturbation theory, $E-E_0\approx -\alpha {\varepsilon }^2/2$.