Van Hove singularity-driven Hall plateau transitions in Dirac semimetals

We investigate the influence of a van Hove singularity (VHS) on the quantum Hall effect (QHE) in Dirac semimetals, and show that the presence of a VHS induces a splitting of the Landau levels (LLs), which progressively shifts from higher to lower energies as the VHS energy decreases. Within the WKB approximation, we obtain an analytical expression for the LL spectrum that exhibits excellent agreement with numerical calculations, thereby identifying the LL splitting as originating from the LL crossing of an effective potential barrier generated by the VHS. This LL splitting gives rise to quantum Hall-plateau transitions, whose combination with the intersections of LLs associated with different subbands due to finite-size confinement produces a characteristic irregular and nonuniform plateau structure in the Hall conductivity. Furthermore, the interplay of Dirac-cone tilting and spin-orbit coupling can strongly deform the band structure, producing hole-pocket-like states that cause a nonmonotonic dependence of the Hall conductivity on the Fermi energy. Our results may provide an explanation for the experimentally observed irregular evolution of Hall plateaus with increasing magnetic field.