Phonon helicity and Nieh-Yan Anomaly in the Kramers-Weyl semimetals of Chiral Crystals

Understand

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 in this condensed matter system.
• 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 at a finite phonon momentum and the phonon angular momentum reverses its sign for opposite momenta due to time reversal symmetry.