Extended Spatial Coherence of Interlayer Excitons in ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ Heterobilayers

We report on the spatial coherence of interlayer exciton ensembles as formed in ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ heterostructures and characterized by point-inversion Michelson-Morley interferometry. Below 10 K, the measured spatial coherence length of the interlayer excitons reaches values equivalent to the lateral expansion of the exciton ensembles. In this regime, the light emission of the excitons turns out to be homogeneously broadened in energy with a high temporal coherence. At higher temperatures, both the spatial coherence length and the temporal coherence time decrease, most likely because of thermal processes. The presented findings point towards a spatially extended, coherent many-body state of interlayer excitons at low temperature.

Figure 1

(a) Sketch of a ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ heterobilayer encapsulated in hBN. (b) Photoluminescence spectrum of corresponding interlayer excitons (IXs) with an emission energy of $E_{\mathrm{IX}}=1.389\mathrm{eV}$ (${\lambda }_{\mathrm{IX}}=892.6\mathrm{nm}$) at $T_{\mathrm{bath}}=1.7\mathrm{K}$ ($E_{\text{laser}}=1.94\mathrm{eV}$ and $P_{\text{laser}}=2\mathrm{\mu }\mathrm{W}$). Inset: spatially resolved photoluminescence image of the sample at $P_{\text{laser}}=3\mathrm{\mu }\mathrm{W}$. Scale bar, $1\mathrm{\mu }\mathrm{m}$. Dotted circle: measured point spread function (PSF) of the optical circuitry at ${\lambda }_{\mathrm{IX}}$. (c) Concept of the point-inversion Michelson-Morley interferometry. (d) Four exemplary interference images of the photoluminescence image as in the inset of (a) vs the path difference $s=2\mathrm{\Delta }$. (e) Corresponding spatially resolved coherence image $|g^{(1)}(x,y)|$.

Figure 2

Normalized first order correlation function $|g^{(1)}(\tau )|=|g^{(1)}(\tau ,x=0,y=0)|$ as in Fig. 1 for $x=0$, $y=0$, as a function of $s$ and therefore, $\tau =s/c$, with $c$ the speed of light. The full width at half maximum (FWHM) of $|g^{(1)}(\tau )|$ gives the temporal coherence time ${\tau }_c=(223\pm 6)\mathrm{fs}$. The exponential curves fit the data as expected for a purely homogeneously broadened light emission. All experimental parameters as in Fig. 1.

Figure 3

(a) Time-resolved photoluminescence of IXs at $E_{\mathrm{IX}}=1.389\mathrm{eV}$. After the laser is turned off, the photoluminescence decays exponentially with a lifetime of $(20.3\pm 1.3)\mathrm{ns}$ (dashed line). For the interference experiments, the signal is detected during a time window of 22.4 ns at a time delay of 6.4 ns after the laser is turned off. (b) $|g^{(1)}(x)|$ of the signal within the detection window of (a) for several laser powers vs the spatial coordinate $x$, i.e., $|g^{(1)}(x)|=|g^{(1)}(\tau =0,x,y=0)|$ as highlighted by the dashed line in Fig. 1. Dashed lines are Gaussian fits to the data to extract the FWHM of the spatial distributions, which is the spatial coherence length $x_c$. (c) Dependence of $x_c$ on $P_{\text{laser}}$. At lowest power, $x_c$ exceeds the PSF of the optical circuitry, while for high powers, $x_c$ is consistent with the PSF. Dotted (dotted-dashed) line: PSF at ${\lambda }_{\mathrm{IX}}$ (at the excitation wavelength). Inset: ratio of $x_c$ to the FWHM $l_D$ of the overall spatial photoluminescence images [cf. inset of Fig. 1].

Figure 4

(a) Photoluminescence spectra of IXs for $T_{\text{bath}}=1.7,4,\dots ,14\mathrm{K}$. (b) Normalized $|g^{(1)}(\tau )|$ for $T_{\mathrm{bath}}=14$ (gray) and 1.7 K (black). (c) Temporal coherence time ${\tau }_c$ vs $T_{\mathrm{bath}}$. Gray dashed line is a guide to the eye. (d) Spatial coherence length $x_c$ vs $T_{\mathrm{bath}}$. Time delay: 19.2 ns and time window of 16 ns. Dotted line (dotted-dashed line) is the PSF at ${\lambda }_{\mathrm{IX}}$ (at the excitation wavelength). Experimental parameters are $E_{\text{laser}}=1.94\mathrm{eV}$ and $P_{\text{laser}}=400\mathrm{nW}$.