Crossover between Weak Antilocalization and Weak Localization in a Magnetically Doped Topological Insulator

We report transport studies on magnetically doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ topological insulator ultrathin films grown by molecular beam epitaxy. The magnetotransport behavior exhibits a systematic crossover between weak antilocalization and weak localization with the change of magnetic impurity concentration, temperature, and magnetic field. We show that the localization property is closely related to the magnetization of the sample, and the complex crossover is due to the transformation of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ from a topological insulator to a topologically trivial dilute magnetic semiconductor driven by magnetic impurities. This work demonstrates an effective way to manipulate the quantum transport properties of the topological insulators by breaking time-reversal symmetry.

Figure 1

(a) Schematic structure of the 3QL ${\mathrm{Bi}}_{2-x}{\mathrm{Cr}}_x{\mathrm{Se}}_3$ film on sapphire for transport studies. The thickness is not to scale. (b) The $R_{\square }-T$ curves of the five ${\mathrm{Bi}}_{2-x}{\mathrm{Cr}}_x{\mathrm{Se}}_3$ films all show metallic behavior at high $T$ but becomes insulating at low $T$. (c) Both the minimum resistance value ($R_{\min }$) and the onset temperature ($T_{\mathrm{onset}}$) for the insulating behavior increases with $x$.

Figure 2

(a) Pure ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ film shows linear Hall effect up to 5 T. (b) to (e) Hall traces in Cr doped ${\mathrm{Bi}}_{2-x}{\mathrm{Cr}}_x{\mathrm{Se}}_3$ films show more pronounced nonlinearity with increasing $x$. (f) and (g) Pure ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and the $x=0.04$ films show negative MC characteristic of WAL. (h) The $x=0.07$ film shows a nonmonotonic MC at $T=1.5\mathrm{K}$ and WAL at higher $T$. (i) and (j) The $x=0.13$ and $x=0.23$ films show sharp WL-like MC at $T=1.5\mathrm{K}$. At higher $T$, WAL dominates at low $H$ while WL is recovered at high $H$.

Figure 3

(a) Red solid squares show the $T=1.5\mathrm{K}$ $R_{yx}{}^0$ as a function of $x$. Black open circles show the $\alpha$ values in the HLN fit. (b) Red solid squares show $T$-dependent $R_{yx}{}^0$ for the $x=0.23$ film. Black open circles show the $\alpha$ values. (c) Black symbols are the $T=1.5\mathrm{K}$ MC for all five ${\mathrm{Bi}}_{2-x}{\mathrm{Cr}}_x{\mathrm{Se}}_3$ films showing the crossover from WAL to WL. Red lines are the fits using the HLN formula. (d) Black symbols show the MC curves at representative $T$ for the $x=0.23$ film and red curves are HLN fits at the low $T$ and high $T$ limits.

Figure 4

(a) ARPES spectrum of pure ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ shows well-resolved Dirac-like surface states. The surface states (SS), bulk conduction band (BCB), and bulk valence band (BVB) are marked by arrows. The $\Delta \sim 100\mathrm{meV}$ gap near the Dirac point is induced by the hybridization between the two surfaces [32]. In the $x=0.07$ (b) and $x=0.13$ films (c) the surface states become weaker and the gap becomes larger. (d) In the ARPES spectrum of the strongly magnetic $x=0.23$ film the surface states totally disappear.