Electron interaction-driven insulating ground state in Bi${}_2$Se${}_3$ topological insulators in the two-dimensional limit

We report a transport study of ultrathin Bi${}_2$Se${}_3$ topological insulators with thickness from one quintuple layer to six quintuple layers grown on sapphire by molecular beam epitaxy. At low temperatures, the film resistance increases logarithmically with decreasing temperature, revealing an insulating ground state. The insulating behavior becomes more pronounced in thinner films. The sharp increase of resistance with magnetic field, however, indicates the existence of weak antilocalization originated from the topological protection. We show that this unusual insulating ground state in the two-dimensional limit of topological insulators is induced by the combined effect of strong electron interaction and topological delocalization.

Figure 1

(a) An in situ STM image of a Bi${}_2$Se${}_3$ film with thickness $d$ $=$ 4 QL. The film is flat on macroscale, except for nanoscale islands and voids with 1 QL thickness. (b) Schematic structure of the Bi${}_2$Se${}_3$ ultrathin film for transport measurements (the thickness is not to scale).

Figure 2

The $R_{\square }$ vs $T$ curves for Bi${}_2$Se${}_3$ with thickness $d$ $=$ 1 to 6 QL. The resistance value decreases systematically with increasing film thickness. Films with thickness $d$ ⩾ 2 QL display metallic behavior at high temperatures but become insulating at sufficiently low temperatures.

Figure 3

(a) The normalized $R_{\square }$ shows a logarithmic increase with decreasing $T$ (the broken lines are guides to the eyes). Both the slope of the logarithmic upturn and the $T_{\min }$ increase with reducing $d$, indicating stronger insulating behavior in thinner films. (b) The thickness dependence of the resistivity minimum temperature $T_{\min }$.

Figure 4

The magnetoresistance of the five films with $d$ $=$ 2 to 6 QL all measured at $T$ $=$ 1.5 K. In the weak $H$ regime the MR shows a steep increase characteristic of WAL. For films with $d$ ⩾ 4 QL the contribution from the bulk states becomes pronounced in the high-field regime.

Figure 5

(a) The HLN fit of the weak-field δσ for films with different $d$ measured at $T$ $=$ 1.5 K. The thinner films have larger field scale, hence shorter phase coherence length, than the thicker films. (b) The thickness dependence of the phase coherence length $l_{\varphi }$.

Figure 6

The variation of conductance of the 3-QL film for field parallel (δσ${}_{\Vert }$, red) and perpendicular (δσ${}_{\perp }$, black) to the film measured at $T$ $=$ 1.5 K. Note that the field is in logarithmic scale. The broken line shows the logarithmic field dependence of parallel magnetoconductance, in agreement with the electron interaction picture.