Structural Alter-Phononics: Sublattice-Momentum Locking in Spinless Lattice Dynamics

The discovery of altermagnetism has shown that crystal symmetry can generate momentum-dependent internal polarization without net magnetization. Whether an analogous form of symmetry-organized momentum-space order can exist for spinless lattice vibrations remains unresolved. Here we identify a structural mechanism for $alter$-$phononics$, in which phonon eigenmodes formed from structurally equivalent sublattices acquire momentum-dependent sublattice polarization and frequency splitting in nonmagnetic crystals. The central quantity is the sublattice-resolved dynamical asymmetry $\Delta(\mathbf q)=D_{AA}(\mathbf q)-D_{BB}(\mathbf q)$, which controls the associated eigenvector polarization. We show that this effect requires an alter-generator that maps equivalent sublattices onto one another while rotating the wave vector, together with the absence of inversion exchange and little-group sublattice-exchange constraints that would otherwise enforce sublattice equipartition. These symmetry rules generate nematic $d$-wave, tetragonal $d/g$-wave, and tripartite six-lobe phonon textures. First-principles calculations demonstrate the mechanism in representative nonmagnetic crystals and show how a symmetry-preserving structural distortion can unlock a hidden $d_{x^2-y^2}$-type texture by removing glide-induced equipartition traps while retaining the screw-axis alter-generator. We further show that the eigenvector texture is inherited by sublattice-projected electron-phonon coupling and anharmonic response functions. Our results establish structural alter-phononics as a spinless counterpart to altermagnetic momentum-space order and provide experimentally testable signatures in finite-$\mathbf q$ phonon spectra and displacement patterns.