Spatial control of carrier capture in two-dimensional materials: Beyond energy selection rules

The carrier capture from a two-dimensional transition metal dichalcogenide monolayer into a quasi-zero-dimensional potential is a decisive process to exploit these remarkable materials as, e.g., single-photon sources. Here, we study theoretically the phonon-induced carrier capture in a ${\mathrm{MoSe}}_2$ monolayer using a Lindblad single-particle approach. Although one decisive control parameter of the capture efficiency is the energy selection rule, which links the energy of the incoming carriers to that of the final state via the emitted phonon, we show that additionally the spatiotemporal dynamics plays a crucial role. By varying the direction of the incoming carriers with respect to the orientation of the localized potential, we introduce a new control mechanism for the carrier capture: the spatial control.

Figure 1

(a) Sketch of the wave packet impinging on an asymmetric TMDC QD. The semiaxes of the QD are given by $a$ (long semiaxis) and $b$ (short semiaxis) [see Eq. (2)]. The angle $\theta$ defines the tilt between the propagation direction of the incoming wave packet and the long axis of the QD. (b) Square moduli of the bound-state wave functions for the potential in Eq. (2) with $\theta =0$ and (c) corresponding density of states (DOS) of the conduction band showing the energies of the four bound states with $\epsilon <0$.

Figure 2

Sketch of an experimental realization. A spherically symmetric wave packet is excited by optical excitation at $t=0$ and subsequently expands as a radially symmetric wave front for $t>0$. In the far field (black rectangle) close to the QD, the wave packet can be approximated as propagating only in $x$ direction.

Figure 3

Electronic density $n\left(\mathbf{r}\right)$ for the wave-packet impinging on the QD for $\theta =0$ without (left column) and with (right column) electron-phonon coupling. The charge has been normalized to the height of the initial wave packet. The black line marks the QD region (defined as where the potential has dropped to $10\%$ of its maximum). The three rows show snapshots of the spatiotemporal dynamics for the three phases: propagation towards the QD at $t=0.3\mathrm{ps}$, crossing of the QD at $t=0.5\mathrm{ps}$, and transmission at $t=1.0\mathrm{ps}$.

Figure 4

(a) Evolution of the occupations of the bound states for $\theta =0$ (top), $\pi /4$ (center), and $\pi /2$ (bottom). (b) Dependence of the final occupations ${\overline{f}}_i$ (upper panel) and the relative occupations ${\eta }_{ij}$ (lower panel) on the QD orientation $\theta$. All occupations are normalized to the density contained by the initial electronic distribution in a stripe of height $b/L$.

Figure 5

(a) Snapshots of the captured charge density $n_{\text{QD}}\left(\mathbf{r}\right)$ (see supplemental movie 1(a) in Ref. [71] for the full time evolution). (b) Spatiotemporal dynamics of the captured charge density along the $x$ axis [i.e., $n_{\text{QD}}(x,y=0,t)$]. (c) Temporal evolution of the $x$ and $y$ components of the center of mass of the trapped charge distribution (see also supplemental movie 1(b) in Ref. [71]). (d) Evolution of the normalized coherences. All figures are for the three QD orientations $\theta =0$ (upper row), $\pi /4$ (central row), and $\pi /2$ (lower row).