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

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