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Emergent gravity and chiral anomaly in Dirac semimetals in the presence of dislocations

We consider the recently discovered Dirac semimetals with two Dirac points $\pm{\bf K}$. In the presence of elastic deformations each fermion propagates in a curved space, whose metric is defined by the expansion of the effective Hamiltonian near the Dirac point. Besides, there is the emergent electromagnetic field that is defined by the shift of the Dirac point. We consider the case, when the deformations are caused by the dislocations. The dislocation carries singular torsion and the quantized flux of emergent magnetic field. Both torsion singularity and emergent magnetic flux may be observed in the scattering of quasiparticles on the dislocation due to Stodolsky and Aharonov - Bohm effects. We discuss quantum anomalies in the quasiparticle currents in the presence of emergent gauge and gravitational fields and the external electromagnetic field. In particular, it is demonstrated, that in the presence of external electric field the quasiparticles/holes are pumped from vacuum along the dislocation. The appeared chiral imbalance along the dislocation drives the analogue of chiral magnetic effect, that is the appearance of electric current along the dislocation.