Quantum transport properties of β-Bi4I4 near and well beyond the extreme quantum limit

We have investigated the magnetotransport properties of $\ensuremath{\beta}\text{-B}{\mathrm{i}}₄{\mathrm{I}}₄$ bulk crystal, which was recently theoretically proposed and experimentally demonstrated to be a topological insulator. At low temperature $T$ and magnetic field $B$ , a series of Shubnikov--De Haas (SdH) oscillations is observed on the magnetoresistivity (MR). Detailed analysis reveals a light cyclotron mass of $0.1\phantom{\rule{0.16em}{0ex}}{m}_e$, and the field angle dependence of MR reveals that the SdH oscillations originate from a convex Fermi surface. In the extreme quantum limit (EQL) region, there is a metal-insulator transition occurring soon after the EQL. We perform scaling analysis, and all the isotherms fall onto a universal scaling with a fitted critical exponent $\ensuremath{\zeta}\ensuremath{\approx}6.5$. The enormous value of critical exponent $\ensuremath{\zeta}$ implies this insulating quantum phase originated from strong electron-electron interactions in high fields. However, in the far end of EQL, both the longitudinal and Hall resistivity increase exponentially with $B$ , and the temperature dependence of the MR reveals an energy gap induced by the high magnetic field, signifying a magnetic freeze-out effect. Our findings indicate that bulk $\ensuremath{\beta}\text{-B}{\mathrm{i}}₄{\mathrm{I}}₄$ is an excellent candidate for a three-dimensional topological system for exploring EQL physics and relevant exotic quantum phases.