Gate-tunable quantum Hall effects in defect-suppressed $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ films

Despite many years of efforts, attempts to reach the quantum regime of topological surface states (TSS) on an electrically tunable topological insulator (TI) platform have so far failed on binary TI compounds such as $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ due to high density of interfacial defects. Here, utilizing an optimal buffer layer on a gatable substrate, we demonstrate the first electrically tunable quantum Hall effects (QHE) on TSS of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$. On the $n$ side, well-defined QHE shows up, but it diminishes near the charge neutrality point (CNP) and completely disappears on the $p$ side. Furthermore, around the CNP the system transitions from a metallic to a highly resistive state as the magnetic field is increased, whose temperature dependence indicates presence of an insulating ground state at high magnetic fields.

Figure 1

Gate-dependent magnetotransport data for $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ films. [(a)–(c)] Zero-field sheet resistance ($R_o$, top) and ${\left(ed{R}_H/dB\right)}^{-1}$ (bottom), which corresponds to sheet carrier density $\left(n_S\right)$ for single carrier species transport as a function of back-gate voltage $V_G$ for 8, 10, and 15 QL films, respectively. Solid black lines are a guide to the eye. The insets show magnetoresistance ($R_S$, top) and corresponding Hall resistance ($R_H$, bottom) as a function of magnetic field $B$, taken at several representative back-gate voltage values from which $R_o$ and $n_S$ were extracted. Note the different magnetic field range and temperature for 8 QL compared to 10 and 15 QL films. Ambipolar behavior is observed in (a) and (b).

Figure 2

QHE as a function of magnetic field at several gate voltage values for a 10 QL film. [(a)–(e)] Sheet resistance ($R_S$, top) and Hall resistance ($R_H$, bottom) up to $\left|B\right|=34.5\mathrm{T}$ at $V_G=0$, −30, −40, −70, and $-100\mathrm{V}$ respectively. Change in the sign of Hall effect and corresponding maxima in (f) zero-field sheet resistance $R_{\mathrm{o}}$ at $V_G\approx -70\mathrm{V}$ indicates that $p$-type carriers dominate the transport for $V_G<-70\mathrm{V}$. For $n$-type carriers, $v=1$ QHE is clearly observed at high magnetic fields. (g) Evolution of QHE with carrier density, where QHE disappears when carriers change from $n$ to $p$ type. $p$-type carrier density for $V_G=-100\mathrm{V}$ was estimated from the average slope of Hall effect in (e).

Figure 3

Gate voltage dependent transport properties of a 10 QL film at $T=0.35\mathrm{K}$ and $B$ field up to 44.5 T. (a) Sheet resistance $\left(R_S\right)$ and (b) Hall resistance $\left(R_H\right)$ at $T=0.35\mathrm{K}$ as a function of $V_G$ at several $B$ values from 0 to 44.5 T. Corresponding (c) sheet $\left({\sigma }_{XX}\right)$ and (d) Hall $\left({\sigma }_{XY}\right)$ conductance. $v=1$ QHE is observed at $V_G\approx -15\mathrm{V}$ to −20 V and nonsaturating magnetoresistance $\left(MR\right)=\frac{R_S\left(B\right)-R_S\left(0\right)}{R_S\left(0\right)}$ with $B$ is observed for $V_G\lesssim -21\mathrm{V}$ as plotted in inset of (a) for CNP and $V_G=-76\mathrm{V}$.

Figure 4

Temperature dependence of resistance at high magnetic field. Sheet resistance $\left(R_S\right)$ at (a) $B=0$, (b) 11.5, (c) 20, and (d) 44.5 T as a function of $V_G$ at several different temperatures. Note that the film was not measured at 9 K in (c). Inset in (a) shows semilogarithmic plot of $R_S$ vs $T$ at $V_G=0\mathrm{V}$ indicating a small upturn at low temperatures, which fits $log\left(T\right)$ dependence as indicated by the blue line. Insets in (b)–(d) show behavior of $R_S$ around $V_G=0\mathrm{V}$ in greater detail. (e) 2D plot of ratio $R_S\left(0.34\mathrm{K}\right)/R_S\left(1\mathrm{K}\right)$ plotted as a function of $V_G$ and $B$. Metallic-like behavior is observed for $V_G>-21\mathrm{V}$ while, for $V_G\lesssim -21\mathrm{V}$ insulating-like behavior is observed. (f) Semilogarithmic plot of temperature dependence of normalized $R_{\mathrm{CNP}}$ at $B=11.5$ and 44.5 T, where larger slope at 44.5 T indicates stronger insulating tendency: the solid lines are least-square fits using $R_{\mathrm{CNP}}\sim {log}_{10}\left(T\right)$.