Interplay of Quasi-Quantum Hall Effect and Coulomb Disorder in Semimetals

Low carrier densities in topological semimetals (TSMs) enable the exploration of novel magnetotransport in the quantum limit (QL). Recent findings consistent with 3D quasi-quantum Hall effect (QQHE) have positioned TSMs as promising platforms for exploring 3D quantum Hall transport, but the lack of tunability in the Fermi level has thus far limited the ability to observe a QQHE signal. Here, we tune the defect concentrations in the Dirac semimetal Cd${}_3$As${}_2$ to achieve ultra-low carrier concentrations at 2 K around $2.9\times10^{16}$cm${}^{-3}$, giving way to QQHE signal at modest fields near 10 T. At low carrier densities, where QQHE is most accessible, we find that clear QQHE is obscured by a carrier density dependent background originating from Coulomb disorder from charged point defects and Landau level broadening. Our results highlight the interplay between QQHE and Coulomb disorder, demonstrating that clear observation of QQHE in TSMs intricately depends on Fermi level and disorder magnitudes. We find that Coulomb disorder, as theoretically predicted, is an essential ingredient for understanding the magnetoresistivity for a spectrum of Fermi levels in Cd${}_3$As${}_2$, anchoring the role of defects and charged disorder in TSM applications. We discuss future constraints and opportunities in exploring 3D QQHE and quantum Hall effects in TSMs.