Fig. 1: Chiral and topological phonons in quantum materials.
From: Weyl phonons: the connection of topology and chirality
Topological phonons are characterized by nontrivial topological invariants, associated with nontrivial pseudospin texture around the band degeneracies and topological surface states2,3. Chiral phonons are described by phonon modes with finite AM, associated with circular atomic motions in the real space, thus also referred to as circularly polarized phonons. These two concepts are fundamentally connected in 3D non-centrosymmetric materials. The left panels show the spiral surface state, the pseudospin texture, and the band dispersion of the twofold quadruple Weyl phonon with C = +4. Right panels show that in the vicinity of twofold quadruple Weyl point, the corresponding lattice motion is chiral with finite AM3,4. The general relation between Weyl and chiral phonons are highlighted in the middle panel. In non-centrosymmetric materials, Weyl phonons are a special type of chiral phonons. Chiral phonons are, however, not necessarily topological. The coupling between chiral and topological phonons with electronic and magnetic excitations can give rise to unusual quantum phenomena, such as chiral superconductivity, chiral density waves, magnetism, and unconventional transport properties.
