Layer and orbital interference effects in photoemission from transition metal dichalcogenides

In this work, we provide an effective model to evaluate the one-electron dipole matrix elements governing optical excitations and the photoemission process of single-layer (SL) and bilayer (BL) transition metal dichalcogenides. By utilizing a $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ Hamiltonian, we calculate the photoemission intensity as observed in angle-resolved photoemission from the valence bands around the $\overline{K}$ valley of ${\mathrm{MoS}}₂$. In SL ${\mathrm{MoS}}₂$, we find a significant masking of intensity outside the first Brillouin zone, which originates from an in-plane interference effect between photoelectrons emitted from the Mo $d$ orbitals. In BL ${\mathrm{MoS}}₂$, an additional interlayer interference effect leads to a distinctive modulation of intensity with photon energy. Finally, we use the semiconductor Bloch equations to model the optical excitation in a time- and angle-resolved pump-probe photoemission experiment. We find that the momentum dependence of an optically excited population in the conduction band leads to an observable dichroism in both SL and BL ${\mathrm{MoS}}₂$.