Valley axion field and surface phonon modes in 3D time reversal invariant Dirac materials

Axion electrodynamics can emerge in 3D topological materials and plays an essential role in a variety of physical phenomena, including surface half quantum Hall effect, topological magneto-optical response, chiral/helical fermions along dislocations, magnon-polariton, etc. In this work, we consider a thin film of a 3D time reversal invariant Dirac semi metal Na₃Bi and find that the effective action of the phonon degrees of freedom due to a strain-induced pseudo gauge field (valley dependent) takes the form of axion electrodynamics. The axion field mainly influences the surface phonon modes with no significant contribution in the bulk. In the presence of a surface thermal gradient, the axion field gives rise to additional non-vanishing angular momentum response coefficients. We calculate numerically the angular momentum response coefficients as a function of the axion field.