Extended Data Fig. 7: Calculated valley shifts vs. U for AA stacking.

Calculated shifts of the optical transition energies in the K and \({K}^{{\prime} }\) valleys as a function of U for AA stacked MoSe₂/CrBr₃. Dashed horizontal lines show experimentally measured values. As the effective Hubbard U on the chromium atomic sites is increased from 0 to 2 eV the optical transition energies in the K and \({K}^{{\prime} }\) valleys (solid lines with dots) display a non-monotonic evolution for both \(+\hat{z}\) and \(-\hat{z}\) chromium spin polarizations. Since the relative band alignment between CrBr₃ and MoSe₂ states changes with increased U, the resulting resonant avoided crossing phenomena produces a blue or red shift in the optical transition energies. A U = 0.9 eV (denoted by vertical dotted line) is found to simultaneously reproduce the experimental band gap of CrBr₃ and qualitatively capture the 1−3 meV magnitude of the asymmetric exciton shifts in the two valleys.