Thickness-Independent Transport Channels in Topological Insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ Thin Films

With high quality topological insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin films, we report thickness-independent transport properties over wide thickness ranges. Conductance remained nominally constant as the sample thickness changed from 256 to $\sim 8\mathrm{QL}$ (where QL refers to quintuple layer, $1\mathrm{QL}\approx 1\mathrm{nm}$). Two surface channels of very different behaviors were identified. The sheet carrier density of one channel remained constant at $\sim 3.0\times {10}^{13}{\mathrm{cm}}^{-2}$ down to 2 QL, while the other, which exhibited quantum oscillations, remained constant at $\sim 8\times {10}^{12}{\mathrm{cm}}^{-2}$ only down to $\sim 8\mathrm{QL}$. The weak antilocalization parameters also exhibited similar thickness independence. These two channels are most consistent with the topological surface states and the surface accumulation layers, respectively.

Figure 1

Molecular beam epitaxy growth of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ films. (a) Reflection high energy electron diffraction pattern of a typical ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ film grown on an ${\mathrm{Al}}_2{\mathrm{O}}_3(0001)$ substrate by MBE. The sharp streaky pattern accompanied by the bright specular spot and Kikuchi lines is indicative of a high quality single crystalline growth. (b) $1.5\times 1.5\mu {\mathrm{m}}^2$ scanned atomic force microscopy image of a 300 QL thick ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ film grown on ${\mathrm{Al}}_2{\mathrm{O}}_3(0001)$. Large terraces (largest ever reported for ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin films) are observed, further verifying the high quality of the grown films.

Figure 2

Transport properties of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ films. (a) Resistance vs temperature for each thickness. (b) Conductance at 1.5 K as a function of thickness. (c) Hall resistance vs magnetic field for a 16 QL sample plotted together with the two-carrier model fitting curve described in the text. (d) and (e) Sheet carrier densities and mobilities vs thickness. For 2 and 3 QL films (shown by a diamond in the inset), the sheet carrier density was directly read off from the linear $R_{xy}$ vs $B$ curve. In (b), (d), and (e), the horizontal straight lines are guides for illustration, and data for films thinner than 16 QL are plotted in the insets. (f) Conduction band minimum ($C{B}_{\min }$) and valence band maximum ($V{B}_{\max }$) along the depth of the sample, showing the downward band bending toward the surface. (g) Schematic surface band diagrams, depicting how the surface bands change through the critical thickness (6 QL) when the surface Fermi level is high: CB and SS stand for the bulk conduction band and the topological surface state, respectively.

Figure 3

Weak antilocalization effect. (a) Normalized resistance change as a function of the magnetic field, measured at 1.5 K, where $\Delta R(B)\equiv R(B)-R(0)$. The deep cusp in low field regime is characteristic of the WAL effect. (b) Conductance change vs magnetic field in the low field regime: 8–128 QL curves are almost overlapping. The theoretical WAL fitting curves are plotted together for each data set. (c) and (d) The WAL fitting parameters, $A$ and $l_{\phi }$, vs the thickness, respectively. The horizontal lines are a guide for illustration.