Investigation of topological nodal line phonons in rhenium-based alkali metal oxides (AReO4; A = Na, K, and Rb) using first principles methods.

Topological phonons in spinless systems have attracted considerable attention due to their symmetry-protected robustness and potential applications in phononic and quantum technologies. Here, we present a first-principles study of topological vibrational states in scheelite-type alkali-metal perrhenates AReO4 (A = Na, K, and Rb), which crystallize in the nonsymmorphic space group I41/a. All compounds are dynamically stable and exhibit host symmetry-enforced topological phonon features, including type-I nodal lines and quadratic nodal points. Notably, KReO4 exhibits an hourglass-like phonon dispersion along the Γ-X direction, induced by A-site-dependent vibrational coupling. Surface state calculations for phonons reveal a clear drumhead-like surface state confined within the projected nodal-line regions, appearing at 8.0-8.45 THz for NaReO4, 9.0-9.4 THz for KReO4, and 9.0-9.25 THz for RbReO4, respectively. Our results demonstrate that A-site cation variation enables a systematic comparative analysis of phonon topology in Re-based oxides, revealing how changes in ionic size, mass, and bonding modify vibrational band connectivity, thereby offering a simple strategy for engineering topological vibrational states in crystalline materials.