Anisotropic exciton transport in transition-metal dichalcogenides

In monolayer transitional metal dichalcogenides, the two excitonic states which are eigenstates of Coulomb interaction are coherent superposition of electron and holes in the two valleys. The exciton band which couples to the transverse electric mode of light has parabolic dispersion for the center-of-mass momentum, whereas the one which couples to the transverse magnetic mode has both parabolic and linear components. In this paper we show that the signatures of this band structure of excitons can be observed in exciton diffusion experiments. In particular, it is demonstrated that by pumping the system with linearly polarized light the exciton transport is anisotropic compared to circularly polarized pump and that such anisotropy is absent for the cases of two linearly or two quadratically dispersing bands. We show that the results persist for the moderate level of disorder present in realistic systems. Finally, we demonstrate that similar effects can be obtained for positively detuned exciton polaritons, in less stringent experimental requirements compared to the bare exciton case.

Figure 1

(a) Schematic drawing of the band structure of excitons in TMDs and (b) depiction of exciton transport when the system is pumped with linearly polarized light (left) and right circularly polarized light (right).

Figure 2

The dependence of two exciton branches resulting from (1) (a) and lower two EP branches from (2) for detunings $\mathrm{\Delta }=0\mathrm{meV}$ (b), $\mathrm{\Delta }=20\mathrm{meV}$ (c), and $\mathrm{\Delta }=60\mathrm{meV}$ (d) on absolute value of in plane momentum $\left|\mathbf{k}\right|$.

Figure 3

The dependence of the difference of group velocities of two branches of exciton and EP shown in Fig. 2 on absolute value of in-plane momentum $\left|\mathbf{k}\right|$.

Figure 4

Exciton transport when pumped with the $x$ polarized pump (a) and (c) and right circularly polarized (RCP) pump (b) and (d). (a) and (b) These correspond to the case without disorder, (c) and (d) for the case with disorder with correlation amplitude $\sigma =0.15\mathrm{meV}$.

Figure 5

EP transport when pumped with $x$-polarized pump (a) and (c), and right circularly polarized (RCP) pump (b) and (d). (a) and (b) Corresponding to the case without disorder, (c) and (d) for the case with disorder with correlation amplitude $\sigma =0.3\mathrm{meV}$. The detuning of EPs in the calculations is $\mathrm{\Delta }=60\mathrm{meV}$.