Pattern of indirect excitons in van der Waals heterostructure

Abstract

We studied photoluminescence of spatially indirect excitons (IXs) in a MoSe$_2$/WSe$_2$ van der Waals heterostructure. We observed a quasi-periodic triangular pattern of IXs with the characteristic wavelength of the pattern $\sim$ 2.6 $μ$m.

Figures (4)

• Figure 1: IX pattern. (a) Schematic energy-band diagram for the heterostructure. The oval indicates an indirect exciton (IX) composed of an electron ($-$) and a hole ($+$). (b) A microscope image showing the layers of the heterostructure. Scale bar is 10 $\mu$m. The red, green, cyan, and orange lines indicate the boundaries of MoSe$_2$ and WSe$_2$ monolayers and bottom and top hBN layers, respectively. (c,d) An image of IX PL intensity $I(x,y)$. (e,f) The pattern of $- \Delta I(x,y)$ highlighting the spatial modulation of $I(x,y)$. The cyan dots in (d,f) indicate the positions of local maxima in $- \Delta I(x,y)$. These maxima form a quasi-periodic triangular pattern. The yellow line in (c-f) shows the boundary of the MoSe$_2$/WSe$_2$ heterostructure. The laser excitation power $P_{\rm ex} = 0.2$ mW, temperature $T = 1.7$ K. The $\sim 2$$\mu$m laser excitation spot is centered at ($1.2, 3.2$).
• Figure 2: Characteristics of IX pattern. (a) A histogram of the distances between the local maxima in $- \Delta I(x,y)$. The characteristic wavelength $\lambda \sim 2.6$$\mu$m. (b) The Fourier transform of $- \Delta I(x,y)$ along the line connecting the local maxima. The broad peak on a noise background corresponds to a quasi-periodic modulation with the $\lambda$ lengthscale. (c) A histogram of the angles between the lines connecting the local maxima in $- \Delta I(x,y)$. The characteristic angle is $\sim 60^{\circ}$. (d) The Voronoi diagram for the local maxima in $- \Delta I(x,y)$ shown by cyan dots. The Voronoi cells are marked by red lines. The average coordination number for the full Voronoi cells, unbroken by the heterostructure edges, is six. The data correspond to the IX pattern in Fig. 1. These data characterize the IX pattern as a distorted triangular pattern.
• Figure 3: Density dependence. (a,b) Normalized profiles $I(x)$ (a) and $- \Delta I(x)$ (b) of IX PL showing the quasi-periodic modulation of $I(x)$ (a) and $- \Delta I(x)$ (b) along $x$ for different excitation densities $P_{\rm ex}$. The $\sim 2$$\mu$m laser excitation spot is centered at $x = 0$, $y = 0$. $T = 3.5$ K.
• Figure 4: Temperature dependence. (a,b) Normalized profiles $I(x)$ (a) and $- \Delta I(x)$ (b) of IX PL showing the quasi-periodic modulation of $I(x)$ (a) and $- \Delta I(x)$ (b) along $x$ for different temperatures $T$. The $\sim 2$$\mu$m laser excitation spot is centered at $x = 0$, $y = 0$. $P_{\rm ex} = 0.2$ mW.