Chiral phonons are the ones with nonzero polarization and can be observed only via a selective coupling with valley electrons and circularly polarized photons. In such process, a new physical quantity, i.e., pseudo-angular momentum (PAM), is required to meet the selection rule. However, phonon PAM was thought to be quantized and can be only defined in the symmorphic systems. In this work, we generalized the definition of PAM to three-dimensional non-symmorphic systems, which show distinct different properties compared with the one in symmorphic systems, e.g., PAM can be non-quantized and q-dependent but still be an observable quantity by experiments. Such new definitions and discoveries can help us to obtain chiral phonons in a broader class of systems with a nonzero group velocity and to convey information like chirality and angular momentum in solids as expected. Materials are also offered to understand the new definition and for further experimental detection.
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