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1 Dirac electron states formed at the heterointerface between a topological insulator and a conventional semiconductor 1. Surface morphology of InP substrate and the device Figure S1(a) shows a 10-μm-square atomic force microscope (AFM) image of an InP substrate before film growth. An atomically flat surface spreads over a large area, as indicated by the root mean square of 0.17 nm. Figures S1(b) and S1(c) show AFM images on different scales after the growth of the topological insulator film. Triangular pyramids with a step-and-terrace structure are clearly apparent. The step height is close to 1 nm, corresponding to the height of one quintuple layer. a b c 2 μm 200 nm 2 μm 0 nm 2.1 nm 0 nm 11.4 nm 0 nm 11.4 nm Fig. S1 Atomic force microscope (AFM) images for substrate and device. (a) AFM image of InP substrate before growth. (b), (c) AFM images of device surface; (b) image scale at 1.5 μm and (c) 10 μm, respectively. 2. Electrical properties of (Bi 1 x Sb x ) 2 Te 3 films on semi-insulating InP substrates NATURE MATERIALS 1
2 In this study, the band parameters of each layer in the junctions, such as the Fermi energy of n-type InP and p-type (Bi 1 x Sb x ) 2 Te 3, should be tuned to allow the detection of interface states by tunneling spectroscopy. First, we investigated the dependence on the material composition (i.e. x dependence) of the electrical properties for (Bi 1 x Sb x ) 2 Te 3 films on semi-insulating InP to estimate the Fermi energy of (Bi 1 x Sb x ) 2 Te 3 without parasitic conduction. For 20-nm-thick (Bi 1 x Sb x ) 2 Te 3 on semi-insulating InP, we measured the longitudinal and Hall resistances by the conventional four probe method. Figures S2(a) and S2(b) display the dependences on x of the sheet resistance (R xx ) and charge-carrier density, respectively, estimated from the Hall resistance at temperature T = 2 K. As x decreases from x = 1, the resistance increases with decreasing p-type carrier density, which indicates that the Fermi level moves towards the energy gap. Around x = 0.87, where R xx is highest and the charge carrier changes sign, the Fermi level crosses the charge neutral point. Near this point, the bulk conduction is almost suppressed; therefore the conduction should be dominated by the surface transport of Dirac electrons. In addition, metallic or insulating states were observed for x > 0.90 or 0.90 > x > 0.80 films, respectively, indicating that p-type carriers are degenerate for x > In Fig. S2(c), we plot the carrier mobility calculated from these resistances and carrier densities as a function of the carrier density. The carrier mobility in the vicinity of the Dirac point reaches 1,000 cm 2 V 1 s 1, which is as high as that reported by previous studies on bulk and high-quality films [S1 S3]. By using these data from the (Bi 1 x Sb x ) 2 Te 3 films on semi-insulating InP substrates, we calculated the Fermi energy for p-type (Bi 1 x Sb x ) 2 Te 3 films. Finally, we drew the band alignment of p-type (Bi 1 x Sb x ) 2 Te 3 and n-type InP junctions as shown in Fig. 1 of the main text. 2 NATURE MATERIALS
3 SUPPLEMENTARY INFORMATION (Bi 1-x Sb x ) 2 Te 3 c T = 2 K 10 4 R xx (Ω) n (cm -2 ) a b μ (cm 2 /Vs) p (cm -2 ) T = 2 K x (Sb) n (cm -2 ) p (cm -2 ) Fig. S2 Transport properties of (Bi 1-x Sb x ) 2 Te 3 thin film. Sheet resistance (a) and charge carrier density (b) at 2 K for each composition of (Bi 1-x Sb x ) 2 Te 3 films on semi-insulating InP substrate. (c) Carrier mobility as a function of n- or p-type carrier density at T = 2 K. 3. Estimate of tunnel barrier width in the junction devices (Bi 1 x Sb x ) 2 Te 3 films used in this experiment were approximately 70-nm thick. As stated in the main text, carrier density in the n-type InP substrate was approximately cm 3. The estimate of the depletion-layer width needs to be carefully discussed. If NATURE MATERIALS 3
4 we assume a junction between two non degenerate semiconductors, the depletion-layer width between n-inp and p-sb 2 Te 3 is estimated from the Poisson equation to be approximately 35-nm-thick. In this calculation, we used a dielectric constant of 12 and 50 for InP and Sb 2 Te 3, respectively, and cm 3 and cm 3 as the electron and hole densities in InP and Sb 2 Te 3, respectively [S4]. However, a 35-nm depletion-layer width is very thick for electrons to tunnel through. In reality, because both InP and Sb 2 Te 3 in the device are degenerate semiconductors with a high density of charge carriers, we may have to consider the Thomas Fermi screening. The Thomas Fermi screening lengths for InP and Sb 2 Te 3 are 3.2 and 2.3 nm, respectively. In this case, the depletion-layer width is of the order of 5 nm, which is possible for electrons to tunnel through. It is thus difficult to define the exact value of the depletion-layer width; nevertheless, the width can be crudely estimated to be in the range of 5 30 nm. 4. Dependence of observed extrema in ΔdI/dV on magnetic field We tried three ways of fitting the magnetic-field dependence of V ext observed in ΔdI/dV for observed V ext points (Fig. 2b). Figure S3(a) shows the results of a B-quadratic fit, and Fig. 3(b) shows the result of a B-linear fit. Fitting functions for the B-quadratic and B-linear cases are V ext = a B + V 0 and V ext = cb + V 0, respectively, where a, c and V 0 are fitting parameters and V 0 is common to four peak (dip) series. While the mean square error of the quadratic fit is V 2, that of the linear fit is much larger at V 2. The observed V ext points are well fit by the quadratic. (Of course, only the n = 0 LL, which is affected by the finite g-factor, should be well fit by the B-linear plot, as actually discerned in this comparison.) This result indicates that 4 NATURE MATERIALS
5 SUPPLEMENTARY INFORMATION Landau levels observed at the interface originate not from conventional electronic states but from Dirac states. In addition, we considered another scheme based on a B-linear plot for which we assumed arbitrarily different intersections (Fig. S3(c)). In this case, the fitting function was also V ext = cb + V 0, but V 0 depended on each peak (dip) series. However, such a linear fit with the different intersections can hardly be interpreted in terms of any rational model: States such as conventional electron states, midgap states and conduction-band states should basically have the two-fold spin degeneracy; each level shows a large shift but remains unsplit, whereas assigning the energy distance between the observed levels to Zeeman splitting would be unphysical in the light of the magnetic-field energy scale. a b c n = 1 n = 1 n = V ext (V) 0.15 n = 0 V ext (V) 0.15 n = 0 V ext (V) 0.15 n = n = n = n = B (T) B (T) B (T) Fig. S3 Three ways of fitting to observed V ext. (a) Dependence of V ext on magnetic field with quadratic fitting; (b), (c) two types of linear fits Tunneling spectroscopy for junctions with different compositions NATURE MATERIALS 5
6 Tunneling spectroscopy was performed for devices with compositions of x = 0.9, 0.93, 0.95, 0.98 and 1 in (Bi 1 x Sb x ) 2 Te 3. All (Bi 1 x Sb x ) 2 Te 3 alloys are p-type degenerate semiconductors; therefore, their interfaces form with similar band alignments with each Fermi energy in (Bi 1 x Sb x ) 2 Te 3 appearing as shown in Fig. 1b in the main text, but the depletion-layer widths differ. Figure S4(a) shows their tunneling spectra ΔdI/dV(B) at T = 10 K with vertical offsets proportional to B. The oscillations of tunneling conductance, which are due to Landau level (LL) formation, can be seen in all junctions. Figure S4(b) shows the applied voltage at the observed extrema in ΔdI/dV(B) as a function of B. The square-root magnetic-field dependence of n = ± 1 LL and the linear dependence of the n = 0 Zeeman shift is clearly observed for every junction as well as for as x = 1 (Sb 2 Te 3 ) (Fig. 2c). The convergence point of each LL at B = 0 T (the Dirac point) shifts to higher energy as x increases, as is summarized in Fig. 4b in the main text. 6 NATURE MATERIALS
7 SUPPLEMENTARY INFORMATION Fig. S4 Tunneling spectroscopy for different-composition junctions. (a) ΔdI/dV(B) spectra for x = 0.9, 0.93, 0.95, 0.98 and 1 in vertically applied magnetic fields from B = 1 T to 14 T. The traces are aligned with offset values proportional to B. The linear broken lines are to guide the eyes and trace the evolution of Landau level. The closed and open triangles indicate peaks and dips corresponding to the tunneling on/off LLs. (b) The applied bias (V ext ) of peaks and minima in ΔdI/dV(B) spectra for each NATURE MATERIALS 7
8 composition is plotted as a function of the square root of the magnetic field. Open and closed symbols show the dips and peaks, respectively (Fig. S4(a)). References S1. Ren, Z., Taskin, A. A., Sasaki, S., Segawa, K. & Ando, Y. Large bulk resistivity and surface quantum oscillations in the topological insulator Bi 2 Te 2 Se. Phys. Rev. B 82, (2010). S2. Analytis, J. G. et al. Two-dimensional surface state in the quantum limit of a topological insulator. Nature Phys. 6, (2010). S3. Zhang, J. et al. Band structure engineering in (Bi 1 x Sb x ) 2 Te 3 ternary topological insulators. Nature Commun. 2, 574 (2012). S4. R. Sehr et al. The optical properties of p-type Bi 2 Te 3 -Sb 2 Te 3 alloys between 2-15 microns J. Phys. Chem. Solids. 23, 1219 (1962) 8 NATURE MATERIALS
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