Fig. 2: Ab initio calculation of stacking-dependent band structure, wavefunctions and optical response.

a–c Band structure for different stacking orders. Spin orientation (∥ Z) of the individual bands is indicated by solid (spin up) and dashed (spin down) lines, respectively. The bands are colored corresponding to the dominant contribution of specific layers. The stacking of the band extrema at K follows the underlying ferroelectric potential. Due to mirror symmetry for the XM-XM-MX-MX case, some bands are (nearly) degenerate and cannot be attributed to an individual layer (indicated by different colors in f, i). d–i Absolute value of the lowest-energy spin-up conduction band (d–f) and highest-energy valence band (g–i) wavefunctions sorted according to their energies superimposed over the crystal structure. Colors indicate the dominant layer(s) for each wavefunction. Ellipses are used to indicate (near-)degenerate states. The wave functions are layer-localized for the fully polarized case (d, g). For XM-XM-MX-MX (f, i), the lowest-energy wave function is localized in the center layer, while the other wave functions have equal weight in the mirror-symmetric layers. j–l Oscillator strength for transitions from all spin-up K_{V B} to all K_CB with s⁺ polarization. The magnitude of these intralayer transitions is in good agreement with values for pristine monolayer MoS₂^56,57. m Calculated absorption spectra in the A excitonic region based on intralayer dipole matrix elements and layer-specific exciton binding energy, including a phenomenological Lorentzian line width of 20 meV.