Chiral phonons in binary compounds $A$Bi ($A$ = K, Rb, Cs) with P2$_1$/c structure

Binary compounds $A$Bi ($A$ = K, Rb, Cs) crystallize in P2$_1$/c structure containing both clockwise and anticlockwise chiral chains of Bi atoms. Electronic band structure exhibits the insulating nature of these systems, with the band gap about $0.25$ eV. The presented study of dynamical properties confirm a stability of the system with P2$_1$/c symmetry. The crystal structure contains the quasi-one-dimensional Bi chains, exhibiting four-fold-like rotational ``local'' symmetry. Nevertheless, the system formally posses two-fold rotational symmetry. Independently of the absence of the three-fold (or higher) rotational symmetry axes for the whole crystal, the chiral modes propagate along the Bi atom chains in these systems. We discuss basic properties of these modes in monoatomic chiral chains. We show that the two-fold rotational symmetry axis affects the main properties of the chiral phonons, which are not realized at the high-symmetry points, but along some paths between them in the reciprocal space. In addition, in the doped system, the chiral phonons possess non-zero total angular momentum.