Electric-Field Tuning of the Surface Band Structure of Topological Insulator ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ Thin Films

We measured the response of the surface state spectrum of epitaxial ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ thin films to applied gate electric fields by low temperature scanning tunneling microscopy. The gate dependent shift of the Fermi level and the screening effect from bulk carriers vary as a function of film thickness. We observed a gap opening at the Dirac point for films thinner than four quintuple layers, due to the coupling of the top and bottom surfaces. Moreover, the top surface state band gap of the three quintuple layer films was found to be tunable by a back gate, indicating the possibility of observing a topological phase transition in this system. Our results are well explained by an effective model of 3D topological insulator thin films with structure inversion asymmetry, indicating that three quintuple layer ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ films are topologically nontrivial and belong to the quantum spin Hall insulator class.

Figure 1

Characterization of ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ thin films. (a) STM topographic image, $150\mathrm{nm}\times 150\mathrm{nm}$, of nominally 5 QL ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ film grown by molecular beam epitaxy (MBE) on ${\mathrm{SrTiO}}_3(111)$. (b) Atomic resolution STM image, $10\mathrm{nm}\times 10\mathrm{nm}$. The STM topographic height is shown in a color scale covering a range of 5 nm for (a) and 0.14 nm for (b). Tunneling parameters are $I=30\mathrm{pA}$, $V_B=1.5\mathrm{V}$, for (a) and $V_B=0.2\mathrm{V}$ for (b). (c),(d) $dI/dV$ spectra as a function of ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ film thickness for $V_G=0\mathrm{V}$, for wide (c) and narrow (d) energy ranges. The narrow energy range spectra are obtained with lower tunneling impedance. The curves are offset vertically for clarity. The red dashed line in (d) indicates the shift of the midgap position toward the Fermi level with increased thickness. (e) Total charge density and displacement field versus gate voltage for a 3 QL ${\mathrm{Sb}}_2{\mathrm{Te}}_3/{\mathrm{SrTiO}}_3$ device obtained by charging the device. (f) 3 QL ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ film two-terminal resistance versus gate voltage. (inset) Schematic of band bending through the TI film at different $V_G$. The diagrams shows the conduction and valence bands going through the film, and the surface state dispersions at the STO interface (left), and vacuum interface (right). At $V_G=0$ there is initial $p$-type band bending which increases with negative gate voltage.

Figure 2

In situ measurement of electric field gating of MBE grown ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ thin films. $dI/dV$ versus $V_B$ spectra as a function of the indicated back gate voltage for a (a) 2 QL thick film, and (b) 3 QL thick film. A shift of the QW peaks to higher energy is seen with increased gate potential, as indicated by the dashed lines. (c) The relative shift of the QW peak positions versus displacement field for 2–4 QL films. Error bars are 1 standard deviation uncertainties in determining the QW peak positions. The solid lines are linear fits to the data points. (d) The gating tunability versus film thickness obtained from the slopes of the linear fits in (c). The error bars are 1 standard deviation uncertainties from the linear fits. The solid line is a polynomial fit to the data points.

Figure 3

Electric field effect of surface state band gaps in MBE grown ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ thin films. $dI/dV$ versus $V_B$ spectra of the surface state gap as a function of the indicated back gate voltage for (a) 2 QL ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ film, and (b) 3 QL ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ film. The curves are offset for clarity. (c) Calculated surface state DOS using the dispersions in Eqs. (1, 2) as a function of applied potential. See text for model parameters. (d) Measured surface state band gap from the spectra in (b) of 3 QL ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ thin films as a function of displacement field (blue round symbols), and surface state band gap from the model DOS calculation in (c) versus $\gamma U$ (red square symbols). The band gaps are determined from the peak minimum and maximum in the second derivative spectra [see green dashed curve in (a) and tic marks in (a)–(c)] for both the experiment and model calculation. The error bars are 1 standard deviation uncertainty determined from peak fitting. The solid line is a linear fit to the data with a slope of $17.3\pm 2.5\mathrm{meV}/\mathrm{V}{\AA }^{-1}$. The error is 1 standard deviation uncertainty determined from the linear fit. (e)–(g) Energy versus momentum dispersion calculated using Eqs. (1, 2) showing the variation of the band gap as a function of increasing structure inversion asymmetry potential. See text for model parameters. At the potential $\gamma U=0.18\mathrm{eV}=\gamma U_C$ the gap closes, indicating a topological phase transition. (h) Surface state band gaps calculated from the 3D TI model using Eqs. (1, 2) with $\Delta =0.16\mathrm{eV}$, $D=-5\mathrm{eV}{\AA }^2$, $v_F=2.5\mathrm{eV}\AA$, and $\Delta /B>0$ (blue; $B=15\mathrm{eV}{\AA }^2$), and $\Delta /B<0$ (red; $B=-15\mathrm{eV}{\AA }^2$).