Hydrodynamics of topological Dirac semi-metals with chiral and ℤ2 anomalies

Abstract

Abstract We consider the hydrodynamical model of topological Dirac semi-metal possessing two Dirac nodes separated in momentum space along a rotation axis. It has been argued that the system in question, except the chiral anomaly, is endowed with the other one ℤ2. In order to model such a system we introduce two U(1)-gauge fields. The presence of the additional ℤ2 anomaly leads to the non-trivial modifications of hydrodynamical equations and to the appearance of new kinetic coefficients bounded with the vorticity and the magnetic parts of Maxwell and auxiliary U(1)-gauge fields.