Chiral effective dynamo and torsion time loops holonomy on dislocated Dirac materials

Chiral torsional anomalies have recently been applied in condensed matter and models of gravitation and quantum field theory, in particular in Dirac and Weyl materials. Moreover, Einstein–Cartan space–time elastic gauge spaces with vanishing spin connection have appeared in the teleparallelism framework. Recently, Ciappina et al. (PRD (2020)) have investigated torsion in quantum field theory through time loops on Dirac materials endowed with torsion in (2 + 1)-dimensional space–time where the third dimension is replaced by time dimension. They considered Riemann-flat spaces graphenes for example. In this paper, a space–time teleparallel geometry is used where we encoded physical information of Burgers vectors on Dirac curved materials (GdA, CQG 38 (2021)). It is shown that when the magnetic or pseudo-magnetic field is encoded in this metric one obtains an interesting (2 + 1)-dimensional space–time is shown to lead to pseudo-Maxwell equations. We also show that a Riemann-flat grapheno, for example, imposes a vanishing Nieh–Yan (NY) torsional anomaly, whereas a curved Dirac material presents a non-vanishing NY anomaly. Torsion-induced holonomy on Dirac materials is investigated. Signatures of chiral dynamo effects in Dirac materials from the chiral chemical potential encoded into the covariant derivative are found. It is shown that in the absence of chiral effect the magnetic field torsion contribution decays, whereas in the chiral dynamo case, a dynamo effect is found. It is shown that from the interaction of chiral chemical potential with torsion an effective chiral chemical potential is found, which depends on the zero-component of Cartan torsion.