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 <!--[if gte msEquation 12]>N style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
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