Magnetic field independent shape of the zero-energy landau levels in a disordered T₃ model

Using the Lanczos recursion method, we exactly determine the shape of the zero-energy Landau level (LL) in a disordered T ₃ lattice under a strong magnetic field. We discover that the shape of the zero-energy LL depends on the distribution of disorder, but is independent of magnetic field strength. Our analytical study attributes this intriguing behavior to the macroscopic and magnetic field independent degeneracy owing to the existence of the flat band. Moreover, our simulations unravel that the density of states obeys an unconventional scaling law, leading to the fact that the relation between the magnetoconductivity and the carrier density is independent of the disorder strength. (paper)