Energy Symmetry Breaking of Dirac and Weyl Fermions in Magnetized Spinning Conical Geometries

Abstract

The dynamics of relativistic fermions are studied in the presence of an out-of-plane magnetic field and a spinning point-like defect, deriving exact solutions. These results show that the defect's spin (Pi$\varpi$) breaks the symmetry between fermion and antifermion energy levels around zero energy. This symmetry breaking is influenced by the magnetic field strength (B degrees$\mathcal {B}_{\circ }$) and the conical or anti-conical geometry. Energy levels are further modified by the fractionalized spin s similar to=s/alpha$\tilde{s} = s / \alpha$, where alpha$\alpha$ denotes the angular deficit or surplus, affecting conical or anti-conical backgrounds. While fractionalized spin has no effect when s similar to=-|s similar to|$\tilde{s} = -|\tilde{s}|$, it significantly alters energy levels when s similar to=+|s similar to|$\tilde{s} = +|\tilde{s}|$. The defect's spin impacts fermion energy levels, leaving antifermion levels unchanged. For large Pi similar to=Pi/alpha$\tilde{\varpi } = \varpi / \alpha$, the defect's spin dominates, minimizing internal quantum effects. In the case of Pi=0$\varpi = 0$ and alpha=1$\alpha = 1$, Landau levels are recovered. These findings suggest the potential to fine-tune charge carrier dynamics in magnetized monolayer materials with spinning defects or vortices.