Emergence and suppression of phonon vortices in two-dimensional crystals: Interplay of lattice symmetry, heavy impurities, and shear

Abstract

Phonon vortices are vortex-like displacement fields that appear in the vibrational modes of two- dimensional materials. Here, we demonstrate that these vortices arise as symmetry-adapted linear combinations of degenerate planar phonon modes, with the superposition coefficients uniquely de- termined by the lattice point group. This symmetry principle establishes that vortices are intrinsic standing-wave solutions in perfect crystals, requiring neither impurities nor disorder. A heavy mass impurity favors vortex modes over planar modes through stronger resonance-induced frequency soft- ening, whereas shear deformation suppresses vortex modes by breaking rotational symmetry. The competition between these two effects gives rise to a precisely predictable strain threshold. The proposed framework, grounded in symmetry and energy-minimization, provides a useful basis for understanding vibrational topological defects induced by other types of impurities or defects. This study further suggests that defect and shear engineering constitutes an effective tuning strategy for controlling vibrational modes and the associated thermal and mechanical properties of crystals.