Fig. 2: Stochastic interlayer exciton hybridization.
From: Optical signatures of interlayer electron coherence in a bilayer semiconductor
a–c, The simulated absorption map exhibits a simple crossing (a) as in Fig. 1c when the two excitons are uncoupled (\({{\mathcal{W}}}_{0}=0,\,\sigma =0\) in equation (2)), an avoided crossing (b) with asymmetry in the intensities of the two branches when the excitons are hybridized (\({{\mathcal{W}}}_{0}=-20\,\,\text{meV}\,,\,\sigma =0\)) and a stochastic crossing (c) reminiscent of Fig. 1e when the exciton coupling has a static, random character (\({{\mathcal{W}}}_{0}=0,\,\sigma =20\,\text{meV}\)). d, The measured reflectance contrast spectra are analysed using a few-parameter fit based on the model of stochastic coupling in equation (2); shown are two linecuts at n ≈ 1.2 × 1012 cm−2 corresponding to zero (blue curve) and non-zero electric fields (red curve), respectively. Such a fit (dashed lines) quantitatively captures both the linear Stark effect and the stochasticity of the interlayer exciton hybridization. Here, Sbkg is the fitted reflectance encoding background effects, while Rno-TMD is the measured reflectance at an optical spot away from the bilayer (Supplementary Section IX). e,f, The evolution of \({{\mathcal{W}}}_{0}\) and σ with the electron density n at T ≈ 8 K (e) and temperature T at n ≈ 1.3 × 1012 cm−2 (f). We find that both \(| {{\mathcal{W}}}_{0}|\) and σ increase (decrease) with increasing n (T), indicating a stronger hybridization between excitons at higher electron densities and lower temperatures. The dashed lines in e and f represent mean-field trends for the stochastic variance σ (Supplementary Section X). The error bars represent combined experimental and fitting uncertainties, as detailed in Supplementary Section IX.
