Fig. 4: Higher-index transition and brightening of dark excitons.

a The normalized photocurrent spectra of a 10-layer BP device measured at \(77.5\ {{{{{\rm{K}}}}}}\) under a series of external fields. The unit of the numerical labels for the field in the figure is \({{{{{\rm{V}}}}}}\ {{{{{{\rm{nm}}}}}}}^{-1}\). The red dashed frame highlights the emerging \({E}_{21}\) and \({E}_{12}\) transitions. The peak marked by a magenta dashed circle is an artifact from ice. The black dashed line indicates the evolution of the \({E}_{11}\) peak. Spectra are vertically shifted for clarity. b The peak positions extracted from Fig. 4a as a function of external field. The inset is a schematic illustration for the forbidden optical transitions \({E}_{21}\) and \({E}_{12}\). c The conduction and valence band splittings extracted from our 8- to 10-layer photocurrent spectra shown in Supplementary Fig. 18, Supplementary Fig. 19 and Fig. 4a respectively. The black and red curves are the fitting results based on Eqs. (2) and (3) respectively. d The intensity ratio of \({E}_{12}\) to \({E}_{11}\) transitions as a function of field extracted from Fig. 4a. The intensities were extracted by Lorentz fitting of the peaks in the spectra. e Numerical calculation of the corresponding intensity ratio.