Robust Gapless Surface State against Surface Magnetic Impurities on $({\mathrm{Bi}}_{0.5}{\mathrm{Sb}}_{0.5}{)}_2{\mathrm{Te}}_3$ Evidenced by In Situ Magnetotransport Measurements

Despite extensive experimental and theoretical efforts, the important issue of the effects of surface magnetic impurities on the topological surface state of a topological insulator (TI) remains unresolved. We elucidate the effects of Cr impurities on epitaxial thin films of $({\mathrm{Bi}}_{0.5}{\mathrm{Sb}}_{0.5}{)}_2{\mathrm{Te}}_3$: Cr adatoms are incrementally deposited onto the TI held in ultrahigh vacuum at low temperatures, and in situ magnetoconductivity and Hall effect measurements are performed at each increment with electrostatic gating. In the experimentally identified surface transport regime, the measured minimum electron density shows a nonmonotonic evolution with the Cr density ($n_{\text{Cr}}$): it first increases and then decreases with $n_{\text{Cr}}$. This unusual behavior is ascribed to the dual roles of the Cr as ionized impurities and electron donors, having competing effects of enhancing and decreasing the electronic inhomogeneities in the surface state at low and high $n_{\text{Cr}}$, respectively. The magnetoconductivity is obtained for different $n_{\text{Cr}}$ on one and the same sample, which yields clear evidence that the weak antilocalization effect persists and the surface state remains gapless up to the highest $n_{\text{Cr}}$, contrary to the expectation that the deposited Cr should break the time-reversal symmetry and induce a gap opening at the Dirac point.

Figure 1

Ambipolar field effect measured on a 15 nm thick $({\mathrm{Bi}}_{0.5}{\mathrm{Sb}}_{0.5}{)}_2{\mathrm{Te}}_3$ epitaxial film on ${\mathrm{SrTiO}}_3$ (111). The measurement temperature $T=500\mathrm{mK}$. (a) Hall resistivity curves at selected $V_G$’s. Inset: Optical image of the patterned TI device. The red scale bar measures $300\mu \mathrm{m}$. (b) Zero-field Hall coefficient $R_H(0)$ and (c) corresponding sheet resistance $R_{xx}$, with varying $V_G$.

Figure 2

(a)–(d) Two-band fittings of the Hall resistivity at $V_G=+200$, $+50$, $+30$, and $+10\mathrm{V}$, respectively. $R_{H,t}$, $R_{H,b}$ and $R_{xx,t}$, $R_{xx,b}$ denote the Hall coefficients and sheet resistances for the top and bottom SSs. At $V_G=+30\mathrm{V}$, the $R_{yx}$ curve is essentially linear, which precludes a meaningful two-band fitting. The resultant Hall coefficient from a linear fit is assigned to $R_{H,b}$ of the bottom surface, which dominates in this transport regime. (e),(f) Carrier densities, $n_t$ and $n_b$, and the corresponding mobilities ${\mu }_t$ and ${\mu }_b$ for the top and bottom SS at each $V_G$, respectively. Inset: Close-up view of $n_t$ at each $V_G$. (g),(h) Schematic band structures for the top and bottom SS at large positive and negative $V_G$’s, respectively.

Figure 3

(a) Magnetoconductivity for the same sample at selected gate voltages at $T=500\mathrm{mK}$. Magnetoresistance at higher magnetic fields is shown in Supplemental Material, S4 [49], which includes Refs. [54, 55]. The solid lines are fits to the HLN equation. Further details and remarks regarding the fitting can be found in the Supplemental Material, S5 [49]. (b),(c) Best-fit values of $\alpha$ and $B_{\varphi }$ from fittings to the HLN equation at each $V_G$.

Figure 4

(a) Electron densities at selected $V_G$’s with increasing Cr density for the same sample. $V_G=+10$, $+30$, and $+50\mathrm{V}$ are close to the surface transport regime. $V_G=+200\mathrm{V}$ serves as a reference showing the effect of electron doping by the Cr impurities. The black solid line marks the minimum electron density ($n_{\min }$) identified at each $n_{\text{Cr}}$. (b) $\alpha$ and (c) $B_{\varphi }$ from fittings of the MC data to the HLN equation at selected $V_G$’s as functions of Cr density.