Helicity-Selective Electron-Phonon Coupling Between $PT$-Partner States in $2H$-bilayer MoS$_2$

Rotational symmetry ($C_n$) constrains chiral phonons, but how other symmetries affect their interactions remains largely unexplored. We perform a theoretical and computational study of chiral phonon coupling to parity-time ($PT$)-degenerate electron doublets in $2H$-bilayer MoS$_2$. Although $PT$ suppresses phonon singlet chirality, chiral phonon doublets can helically interact with $PT$-partner electronic states via a mechanism similar to pseudospin. Selection rules are then analyzed with the interplay of $PT$ and $C_3$. Our computational results of $2H$-bilayer MoS$_2$ suggest chiral phonons may be used to resolve intravalley electronic states in $PT$ systems.