Probing Nieh-Yan Anomaly through phonon dynamics in the Kramers-Weyl semimetals of Chiral Crystals

Nieh-Yan anomaly describes the non-conservation of chiral charges induced by the coupling between Dirac fermions and torsion fields. Since the torsion field is beyond general relativity, this effect remains hypothetical and its relevance to our universe is unclear in the context of high-energy physics. In this work, we propose that the phonons can induce a torsion field for the Kramers-Weyl fermions through electron-phonon interaction in a non-magnetic chiral crystal, thus leading to the occurrence of the Nieh-Yan anomaly. As a consequence, the Nieh-Yan term can strongly influence the phonon dynamics and lead to the helicity of acoustic phonons, namely, two transverse phonon modes mix with each other to form a circular polarization with a non-zero angular momentum and the phonon angular momentum forms a hedgehog texture in the momentum space. The phonon helicity can be probed through measuring the total phonon angular momentum driven by a temperature gradient.