Landau Quantization and the Thickness Limit of Topological Insulator Thin Films of ${\mathrm{Sb}}_2{\mathrm{Te}}_3$

We report the experimental observation of Landau quantization of molecular beam epitaxy grown ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ thin films by a low-temperature scanning tunneling microscope. Different from all the reported systems, the Landau quantization in a ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ topological insulator is not sensitive to the intrinsic substitutional defects in the films. As a result, a nearly perfect linear energy dispersion of surface states as a 2D massless Dirac fermion system is achieved. We demonstrate that four quintuple layers are the thickness limit for a ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ thin film being a 3D topological insulator. The mechanism of the Landau-level broadening is discussed in terms of enhanced quasiparticle lifetime.

Figure 1

(a) STM topographic image of 30 QL type-I sample prepared by MBE. Tunneling conditions are $V_{\mathrm{bias}}=5.0\mathrm{V}$, $I=50\mathrm{pA}$. The bias voltage is applied to the sample. The inset shows an atomic resolution image of ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ (111) surface (20 mV, 0.1 nA). The brighter spots correspond to Te atoms. (b) STM topographic image (1.0 V, 50 pA) showing the typical surface defects of the sample. (c) Bulk (setpoint: $V_{\mathrm{bias}}=0.3\mathrm{V}$, $I=50\mathrm{pA}$) and SS spectra (0.25 V, 0.2 nA) in the energy gap. Because of the much lower SS DOS compared with bulk DOS, a much closer tunneling gap is needed to reveal the detail of SS. (d) Landau quantization of topological SS at 7 T (curve), relation between LL energies and $\mathrm{sgn}(n)\sqrt{|n|B}$ (squares), and a linear fitting to the relation (line). The bias modulation was 1 mV at 987.5 Hz.

Figure 2

(a) STM topographic image (1.0 V, 50 pA) showing the surface defects of 7 QL type-II sample. (b) $dI/dV$ spectra (0.25 V, 0.2 nA) from 0 to 7 T. The dotted line indicates a field-independent $n=0$ LL at the Dirac point. Spectra under different fields are shifted vertically for clarity. (c) LL energies under various magnetic fields plotted versus $\mathrm{sgn}(n)\sqrt{|n|B}$. The line is a linear fitting to the data.

Figure 3

(a)–(d) $dI/dV$ spectra of 1–4 QL type-III ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ films. The bulk QWS are indicated by arrows. The corresponding SS spectrum for each thickness is displayed in the lower panel. The inset in (a) represents two sets of SS on the opposite surfaces. For 3 QL films, the SS spectrum at 7 T is also presented together with zero-field spectrum in the lower panel of (c), which were taken on type-II samples for better quality [35].

Figure 4

(a) $dI/dV$ spectra (0.2 V, $I=0.2\mathrm{nA}$) of a 4 QL type-II sample from 0 to 7 T. (b) The fitting of the LL energies versus $\mathrm{sgn}(n)\sqrt{|n|B}$ for magnetic fields from 2 to 7 T. (c) Full width at half maximum of LL peaks at different energies in (a) and Fig. 1d fitted by Lorentzian function. The hollow squares correspond to the LL peaks in type-I sample in Fig. 1d and have been shifted by the energy difference between the DPs of the two different samples.