LETTERS PUBLISHED ONLINE: 20 FEBRUARY 2014 | DOI: 10.1038/NMAT3885
Dirac electron states formed at the heterointerface between a topological insulator and a conventional semiconductor R. Yoshimi1*†, A. Tsukazaki1,2†‡, K. Kikutake1, J. G. Checkelsky1, K. S. Takahashi3, M. Kawasaki1,3 and Y. Tokura1,3 Topological insulators are a class of semiconductor exhibiting charge-gapped insulating behaviour in the bulk, but hosting a spin-polarized massless Dirac electron state at the surface1–4 . The presence of a topologically protected helical edge channel has been verified for the vacuum-facing surface of several topological insulators by means of angle-resolved photoemission spectroscopy5–7 and scanning tunnelling microscopy8–10 . By performing tunnelling spectroscopy on heterojunction devices composed of p-type topological insulator (Bi1−x Sbx )2 Te3 and n-type conventional semiconductor InP, we report the observation of such states at the solid-state interface. Under an applied magnetic field, we observe a resonance in the tunnelling conductance through the heterojunction due to the formation of Landau levels of two-dimensional Dirac electrons at the interface. Moreover, resonant tunnelling spectroscopy reveals a systematic dependence of the Fermi velocity and Dirac point energy on the composition x. The successful formation of robust non-trivial edge channels at a solid-state interface is an essential step towards functional junctions based on topological insulators11–13 . Modern semiconductor device technology is based on solidstate devices composed of various heterostructures such as p–n junctions, superlattices and transistors. Such heterointerface devices will also be necessary for future electronics based on topological insulators; emergent topological edge states on topological insulators may have great potential for spintronics and quantum computing due to their robustness and spin polarization ensured by the topological invariant. So far, however, most key experiments on boundary states have been performed on the surface of bulk topological insulators by spectroscopic techniques5–10 that can be applied only to vacuum-facing surfaces. To develop topological edge-state electrical circuits, it is indispensable to fabricate solid-state junction devices that maintain the Dirac edge state. Tunnelling spectroscopy applied to heterojunctions is a powerful tool for detecting the density of states at interfaces and in semiconductor quantum wells14–16 . In this study, the interfacestate density of topological insulator/non-topological insulator heterojunctions is examined on the basis of resonant tunnelling spectroscopy applied to samples in a magnetic field. By using molecular beam epitaxy, we fabricated a topological insulator/nontopological insulator p–n junction from the topological insulator
(Bi1−x Sbx )2 Te3 and the non-topological insulator InP (Fig. 1a; see Methods). InP used as the substrate is not a topological insulator; rather, it is a conventional III–V semiconductor with a bandgap Eg = 1.4 eV. To serve as a degenerate n-type layer, it was heavily doped with S so that its carrier density was 4 × 1018 cm−3 . (Bi1−x Sbx )2 Te3 is a well-known topological insulator and a narrowgap semiconductor (Eg ∼ 0.2–0.3 eV) whose carriers can be well controlled by tuning the material composition x (ref. 17). Here, we operated in the composition range 0.9 < x < 1 in (Bi1−x Sbx )2 Te3 to tune the degenerate hole density. The lattice of (111)-oriented InP matches well with that of (Bi1−x Sbx )2 Te3 ; therefore, our film quality was sufficient to form high-mobility surface states (see Supplementary Information) comparable to recent efforts in bulk crystals18–21 . After growing the film, 200-µm-square junction devices were fabricated by photolithography and ion milling with Ti/Au electrodes (see Methods). Using such a vertical device structure, the tunnelling conductance can be used to probe the Dirac states or quantized Landau levels at the interface forming the tunnelling barrier. (depicted by arrows in the band diagram shown in Fig. 1b). The tunnel barrier is implemented by a thin depletion layer (estimated to be approximately 5–30 nm from screening-length considerations; see Supplementary Information) that forms owing to conduction-band discontinuity in the InP side of the interface between these two semiconductors22,23 (Fig. 1b). Electrons that tunnel to (Bi1−x Sbx )2 Te3 dissipate to the bulk states (wavy arrow in Fig. 1b) and can be detected as current. This tunnelling conductance is proportional to the interface density of states, which in turn is modulated by Landau-level formation in intense magnetic fields. Figure 1c shows the current–voltage (I –V ) characteristics of Sb2 Te3 (x = 1)/InP heterostructures at 10 K, as measured with standard source measurement units. Under positive applied bias, the current slowly increases until an applied bias of V = 0.2 V, after which it rapidly increases, most likely because of an increase in excitation over the tunnel barrier. In contrast, the current under a negative applied bias is larger than that under a positive applied bias, in agreement with that observed for an Esaki-type tunnelling diode24 . To clarify the tunnelling processes in the junctions, we plot the differential conductance dI /dV for five junctions with varying Sb content (x = 1, 0.98, 0.95, 0.93 and 0.9) in Fig. 1d. The peaks and dips observed in the differential conductance at 0.048 < V < 0.12 are assigned on the basis of the schematic band diagrams (labelled
1 Department
of Applied Physics and Quantum-Phase Electronics Center (QPEC), University of Tokyo, Tokyo 113-8656, Japan, 2 Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba 277-8561, Japan, 3 RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan. †These authors equally contributed to this work. ‡Present address: Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan. *e-mail: [email protected] NATURE MATERIALS | VOL 13 | MARCH 2014 | www.nature.com/naturematerials
© 2014 Macmillan Publishers Limited. All rights reserved
253
NATURE MATERIALS DOI: 10.1038/NMAT3885
LETTERS a
c
40
V 20
p-(Bi1–xSb ) Te x 2 3
b
I (mA)
n-InP
p–(Bi1–xSbx)2Te3
n–InP
0
–20
–40 –0.3
d
0.5 eV
x = 1 (Sb2Te3) T = 10 K B=0T
–0.2
–0.1
0.0 V (V)
0.1
0.2
0.3
40
x = 0.90
20 nm
Vbias = 0.2 V 30
e
x = 0.93
InP
dI/dV (a.u.)
EV EC Sb2Te3 V=0V
20 x = 0.95
I x = 0.98 10 x=1
II I 0 0.00 II
III 0.05
III
0.10
0.15
0.20
0.25
V (V)
Figure 1 | Tunnelling spectroscopy in a topological insulator/non-topological insulator p–n junction. a, Schematic of device studied by tunnelling spectroscopy. Device contains p-(Bi1−x Sbx )2 Te3 /n-InP junctions. b, Band diagram of junctions under positive applied bias of 0.2 V. Straight and wavy arrows indicate electron tunnelling to the interface state and subsequent relaxation to the bulk, respectively. c, I–V characteristics for the composition x = 1 (Sb2 Te3 ) at 10 K. d, Differential conductance dI/dV as a function of bias voltage V for different compositions (x). Labels I, II and III indicate the positions of peak and dips in dI/dV curves, as shown by filled/open triangles. e, Band lineup for each typical bias condition at I, II, and III for x = 1 (Sb2 Te3 ). The conduction-band minimum and valence-band maximum are denoted by EC and EV , respectively.
I, II, and III), as shown in Fig. 1e. The dip at V = 0.048 V (labelled I) shows no dependence on material composition, which indicates that it corresponds to the Fermi energy in n-type InP. However, peaks II and dips III depend on the Sb concentration x, which reflects the variation in Fermi energy with x in p-type (Bi1−x Sbx )2 Te3 . Based on these trends, we expect that further increases in the bias beyond condition II would realize the detection of Dirac states in the bandgap of (Bi1−x Sbx )2 Te3 . An applied magnetic field influences the tunnelling conductance because of the formation of Landau levels in the Dirac interface states. Figure 2a shows a set of tunnelling conductance spectra dI /dV for an x = 1 (Sb2 Te3 ) junction at different magnetic fields B varying from 0 to 14 T at T = 10 K. The conductance clearly increases near V = 0.15 V. Although leakage current overlaps 254
with and blurs the conductance spectra, resonant tunnelling through Landau levels clearly plays a key role in this junction. To clarify such a process, we define the field-modulated components as 1dI /dV (B) = dI /dV (B) − dI /dV (B = 0) (Fig. 2b). Above 5 T, oscillatory spectral features due to Landau-level formation are clearly observed in 1dI /dV (B). To extract the extrema of 1dI /dV (B), we further differentiate 1dI /dV (B) with respect to V and adopt the zero-crossing points as the position of the extreme values of 1dI /dV ; these are plotted in Fig. 2c (peaks and valleys are denoted by filled and open circles, respectively). Except for the central peak, the magnetic-field √ dependence of the bias extrema (Vext ) is well fitted by using B curves with V = 0.15 V as the origin. Contrary to the linear behaviour of Landau levels in a conventional electronic system (see Supplementary Information), NATURE MATERIALS | VOL 13 | MARCH 2014 | www.nature.com/naturematerials
© 2014 Macmillan Publishers Limited. All rights reserved
NATURE MATERIALS DOI: 10.1038/NMAT3885 a
LETTERS c
3
0.24
dI/dV (a.u.)
x = 1 (Sb2Te3) T = 10 K
n
E
+1
2
0
14 T
n=1
–1 1 0.20 0
ΔdI/dV (B) (a.u.)
4
T = 10 K 14 T
3
Vext (V)
b
B=0T
2
0.16
n=0
1 B=1T
0
d
ΔdI/dV (B) (a.u.)
ΔdI/dV
4
30
10 K 20 K 40 K 80 K 120 K 160 K T = 200 K
0 0.00
0.12
1 0 0
20
10
V = 0.15 V B = 14 T
3 2
0.05
100 T (K)
n = –1
200
T = 10 K 0.08 0.10 0.15 V (V)
0.20
0.25
0
5
10
15
B (T)
Figure 2 | Landau-level formation observed in tunnelling spectra. a, dI/dV spectra of a sample in an applied magnetic field from B = 0 to 14 T in 1 T increments at 10 K. b, Dependence of 1dI/dV(B) = dI/dV(B) − dI/dV(0) on bias voltage V. Closed and open triangles indicate peaks and dips corresponding to the increase or decrease of tunnelling conductance in the presence or absence of Landau levels. The error bars are estimated from the standard deviation of extreme values of 1dI/dV.c, Bias extrema (Vext ) values observed in b as a function of magnetic field. Closed and open circles correspond to peaks and dips, respectively. The inset shows the band dispersion of the Dirac cone and its Landau-level formation in a magnetic field. d, 1dI/dV(B) at B = 14 T for various temperatures. The inset shows the temperature dependence of the n = 0 Landau-level peak height at the bias voltage of V = 0.15 V.
our observation can be explained by Landau-level formation within the Dirac-electron dispersion at the interface8–10 . On the basis of this identification, we assign the upper and lower peaks to n = +1 and −1 Landau levels, respectively. The strongest central peak corresponding to the n = 0 Landau level in 1dI /dV (B) spectra exhibits a slight shift that is linear with respect to the magnetic field. The fact that the n = 0 Landau level does not split but instead shifts with the Zeeman energy (g ∼ 11) demonstrates that the Dirac dispersion is spin polarized, as expected. As the Dirac electrons at the interface or surface of a topological insulator are subject to perfect spin-momentum locking, the spin degeneracy of each Landau level is fully lifted25 . In particular, the n = 0 Landau level is perfectly spin polarized along the applied field B and thus should have a Zeeman energy that depends linearly on B: g µB BSz , where µB is the Bohr magneton and Sz is the z component of the electron spin. The g value (∼11) of the Dirac state in Sb2 Te3 can be estimated by the field-induced shift of the n = 0 Landau level, which is significantly larger than that reported for the Bi-based topological insulators, Bi2 Se3 (ref. 8) and Bi2 Te2 Se (ref. 26). In addition, the temperature dependence of the Landau-level spectra at B = 14 T is shown in Fig. 2d. The observation of Landau levels at such a high temperature (up to T ∼100 K) indicates that Dirac states at
the interface are robust, a result attributable to the large energy gap between n = 0 and ±1 Landau levels. To confirm the dimensionality of the Landau states, we investigated the angular dependence of 1dI /dV (B) for x = 0.93 at 10 K. Figure 3a shows 1dI /dV (B) measured at three different angles (θ = 0◦ , 45◦ and 75◦ with respect to the surface normal; see the schematic of the measurement configuration in the inset of the left panel). By rigidly √ offsetting 1dI /dV (B) spectra by an increment proportional√ to B, the peak and dip structures can be aligned, indicating the B-like evolution of Landau levels. As the magnetic field is tilted from the normal towards the plane (left to right panels), the peak amplitude decreases and the Landau-level splitting decreases, as shown for B = 9 T. Figure 3b shows Vext plotted as a function of the√ square root of the perpendicular component of the magnetic field ( B cos θ ) at five different angles θ . The resulting scaling relation Vext versus B cos θ further demonstrates that Landau levels observed in this study originate from the two-dimensional Dirac electron states at the interface between a topological insulator and a trivial insulator. The enhancement of tunnelling conductance through the formation of Landau levels was observed systematically in other compositions of topological insulator films (see Supplementary
NATURE MATERIALS | VOL 13 | MARCH 2014 | www.nature.com/naturematerials
© 2014 Macmillan Publishers Limited. All rights reserved
255
NATURE MATERIALS DOI: 10.1038/NMAT3885
LETTERS a
15
θ = 0°
15
x = 0.93 T = 10 K
15
45°
b
75°
0.18
0.16
9T
n=1 0.14
5
B=1T
ΔdI/dV (B) (a.u.)
4T
10
ΔdI/dV (B) (a.u.)
ΔdI/dV (B) (a.u.)
10
5
0.12
Vext (V)
10
75° 60° 45° 30° 15° 0° 0.10
n=0
5 0.08 n = –1
B
0.06
θ 0 0.04
0.10 V (V)
0.20
0 0.04
0.10 V (V)
0.20
0 0.04
0.10 V (V)
0.20
0.04
0
1
2
3
(B cos θ )1/2 (T1/2)
Figure 3 | Angular dependence of Landau-level formation. a, 1dI/dV (B) measured at different angles (θ = 0◦ , 45◦ and 75◦ ) with applied √ magnetic fields at 10 K. The inset of the left-most panel shows the measurement configuration. The data are vertically offset by an amount proportional to B. Linear dashed lines guide the eyes for the evolution of Landau levels. Filled and open circles show the positions of peaks and dips plotted in b. b, Peaks and dips of the applied bias (Vext ) for each angle as a function of the square root of the perpendicular component of the magnetic field (B cos θ)1/2 . The error bars are estimated from the standard deviation of extreme values of 1dI/dV. a
7
6
n=1
(105 m s–1)
Exp.
F
5
4 ARPES 3 0.88
n = –1 0.92
0.96
1.00
x (Sb)
b 0.14
V (V)
DP 0.10
0.06
0.02 0.88
VB
0.92
0.96
1.00
x (Sb)
Figure 4 | Composition dependence of Fermi velocity and energy of Dirac point in (Bi1 − xSbx )2 Te3 . a, Fermi velocity νF for each composition of (Bi1−x Sbx )2 Te3 , calculated from the field evolution at n = ±1. Grey circles show the νF data evaluated by angle-resolved photoemission spectroscopy (ARPES) experiments17 . The error bars indicate the standard deviation of fitting analysis shown in Fig. 2c. b, Bias voltage for Dirac point (DP) compared with valence-band maximum (VB) as estimated from the bias condition labelled II in Fig. 1d and carrier density. 256
Information). From the evolution of the Landau levels, we derived the band parameters of the Dirac interface states. √ Figure 4a shows the Fermi velocity vF calculated from 1En = vF 2eh¯ Bn. The vF for n = +1 is greater than that for n = −1, which we attribute to the asymmetry of the Dirac cone above and below the Dirac point. Such a convex shape of the Dirac dispersion was also observed in angle-resolved photoemission spectroscopy7 (ARPES). In fact, the curvature of Dirac dispersion and vF calculated from the surface Dirac states found by ARPES17 is very close to that deduced from the n = −1 Landau level in the present tunnelling spectroscopy measurement. Finally, we show the energy of the Dirac point obtained from the Landau-level convergence point at B = 0 T (Fig. 2c or Fig. 3b) relative to the valence-band maximum estimated from the peak bias labelled II in Fig. 1d. The Dirac point approaches the valence-band maximum on decreasing the Sb composition; a behaviour that also agrees well with the ARPES result for the surface state17 . In conclusion, by applying tunnelling spectroscopy to a p–n junction composed of a topological insulator and a trivial band insulator, we have detected Landau-level formation in the twodimensional Dirac electron state at a solid interface. Such a state would be difficult to probe √ with other surface-sensitive spectroscopies. In particular, the B behaviour of the peak bias clearly demonstrates that a Dirac dispersion is present at such an interface. Detailed band parameters such as the Fermi velocity and energy of the Dirac point are readily derived from these experimental results and agree with those of surface states measured by ARPES. These observations clearly show that the Dirac state of the topological insulator is maintained, despite the connection to another non-topological material. In particular, the result shows that Esaki-type tunnelling occurs in a junction based on a conventional narrow-gap semiconductor, thus ensuring the compatibility of topological insulator thin films with the accumulated knowledge of semiconductor technology. Further studies examining the vertical transport across interface states should shed new light on the spin–orbit interaction and related physics in comparison with previous studies on the weak antilocalization effect on low-field magnetoresistance27 . The NATURE MATERIALS | VOL 13 | MARCH 2014 | www.nature.com/naturematerials
© 2014 Macmillan Publishers Limited. All rights reserved
NATURE MATERIALS DOI: 10.1038/NMAT3885 robustness of topological Dirac electron states at a solid/solid interface may be observable in different types of material such as superconductors11 and ferromagnets12 , which should open the door towards the implementation of exotic dissipationless phenomena and applications.
Methods The (Bi1−x Sbx )2 Te3 films were fabricated on n-type and semi-insulating InP (111) substrates by molecular beam epitaxy. The epi-ready InP substrates were vacuum annealed at 380 ◦ C, and 70-nm-thick (Bi1−x Sbx )2 Te3 films were deposited with the substrate at 300 ◦ C. The beam flux ratio of Te per Bi and Sb was set to approximately 15 to prevent Te deficiency in the films. Sb concentration x in the (Bi1−x Sbx )2 Te3 films was defined by the ratio of beam equivalent pressures of Bi and Sb measured by the beam-flux monitor before the film deposition. The growth rate for the films was approximately 0.34 quintuple layer per minute. The junction devices were fabricated by the following procedures. First, to form ohmic electrical contacts, the top and bottom contact electrodes of Ti/Au were deposited on both sides of the film surface and on the InP substrate. The top Ti/Au layer plays an important role in preventing degradation of the topological insulator by photoresist or water attachment. Second, the sample was spin-coated with photoresist, and then baked at 90 ◦ C for 10 min. Third, the mesa structure comprising a 200-µm-square pattern was formed by etching using photolithography and ion milling. After washing off the photoresist with acetone, silver paint was used to make contact to both sides by hand to Au wires, after which the devices were baked in air at 150 ◦ C for 1 h. The samples were placed in a magnetic field and studied by tunnelling spectroscopy with a standard set-up (Quantum Design, PPMS) and a semiconductor parameter analyser (Agilent).
Received 2 July 2013; accepted 13 January 2014; published online 20 February 2014
References 1. Kane, C. L. & Mele, E. J. Z2 topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005). 2. Fu, L., Kane, C. L. & Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007). 3. Moore, J. E. & Balents, L. Topological invariants of time-reversal-invariant band structures. Phys. Rev. B 75, 121306(R) (2007). 4. Hasan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010). 5. Hsieh, D. et al. A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970–974 (2008). 6. Chen, Y. L. et al. Experimental realization of a three-dimensional topological insulator, Bi2 Te3 . Science 325, 178–181 (2009). 7. Hsieh, D. et al. A tunable topological insulator in the spin helical Dirac transport regime. Nature 460, 1101–1105 (2009). 8. Cheng, P. et al. Landau quantization of topological surface states in Bi2 Se3 . Phys. Rev. Lett. 105, 076801 (2010). 9. Hanaguri, T., Igarashi, K., Kawamura, M., Takagi, H. & Sasagawa, T. Momentum-resolved Landau-level spectroscopy of Dirac surface state in Bi2 Se3 . Phys. Rev. B 82, 081305(R) (2010). 10. Jiang, Y. et al. Landau quantization and the thickness limit of topological insulator thin films of Sb2 Te3 . Phys. Rev. Lett. 108, 016401 (2012). 11. Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008). 12. Qi, X. L., Hughes, T. L. & Zhang, S. C. Topological field theory of time-reversal invariant insulators. Phys. Rev. B 78, 195424 (2008).
LETTERS 13. Seradjeh, B., Moore, J. E. & Franz, M. Exciton condensation and charge fractionalization in a topological insulator film. Phys. Rev. Lett. 103, 066402 (2009). 14. Klein, J., Leger, A., Belin, M., Defourneau, D. & Sangster, M. J. L. Inelasticelectron-tunneling spectroscopy of metal–insulator–metal junctions. Phys. Rev. B 7, 2336–2348 (1973). 15. Bockenhoff, E., Klitzing, K. V. & Ploog, K. Tunneling from accumulation layers in high magnetic fields. Phys. Rev. B 38, 10120–10123 (1988). 16. Yang, C. H., Yang, M. J. & Kao, Y. C. Magnetotunneling spectroscopy in a double-barrier heterostructure: Observation of incoherent resonant-tunneling processes. Phys. Rev. B 40, 6272–6276 (1989). 17. Zhang, J. et al. Band structure engineering in (Bi1−x Sbx )2 Te3 ternary topological insulators. Nature Commun. 2, 574 (2011). 18. Qu, D. X., Hor, Y. S., Xiong, J., Cava, R. J. & Ong, N. P. Quantum oscillations and Hall anomaly of surface states in the topological insulator Bi2 Te3 . Science 329, 821 (2010). 19. Analytis, J. G. et al. Two-dimensional surface state in the quantum limit of a topological insulator. Nature Phys. 6, 960–964 (2010). 20. Taskin, A. A., Ren, Z., Sasaki, S., Segawa, K. & Ando, Y. Observation of Dirac holes and electrons in a topological insulator. Phys. Rev. Lett. 107, 016801 (2011). 21. Sacepe, B. et al. Gate-tuned normal and superconducting transport at the surface of a topological insulator. Nature Commun. 2, 575 (2011). 22. Levinstein, M., Rumyantsev, S. & Shur, M. Handbook Series on Semiconductor Parameters (World Scientific, 1996). 23. Hao, G. et al. Synthesis and characterization of few-layer Sb2 Te3 nanoplates with electrostatic properties. RSC Advances 2, 10694–10699 (2012). 24. Esaki, L. New phenomenon in narrow germanium p–n junctions. Phys. Rev. 109, 603–604 (1958). 25. Winkler, R. Spin–Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems (Springer, 2003). 26. Xiong, J. et al. High-field Shubnikov–de Haas oscillations in the topological insulator Bi2 Te2 Se. Phys. Rev. B 86, 045314 (2012). 27. Chen, J. et al. Gate-voltage control of chemical potential and weak antilocalization in Bi2 Se3 . Phys. Rev. Lett. 105, 176602 (2010).
Acknowledgements This research was supported by the Japan Society for the Promotion of Science through the Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program) on ‘Quantum Science on Strong Correlation’ initiated by the Council for Science and Technology Policy and by JSPS Grant-in-Aid for Scientific Research(S) No. 24224009 and No. 24226002.
Author contributions Y.T. conceived the project. R.Y. and K.K. grew the thin films, made the devices and performed the tunnelling spectroscopy measurements. R.Y. analysed the data and wrote the manuscript with contributions from all authors. A.T., J.G.C., K.S.T., M.K. and Y.T. jointly discussed the results.
Additional information Supplementary information is available in the online version of the paper. Reprints and permissions information is available online at www.nature.com/reprints. Correspondence and requests for materials should be addressed to R.Y.
Competing financial interests The authors declare no competing financial interests.
NATURE MATERIALS | VOL 13 | MARCH 2014 | www.nature.com/naturematerials
© 2014 Macmillan Publishers Limited. All rights reserved
257
Dirac electron states formed at the heterointerface between a topological insulator and a conventional semiconductor R. Yoshimi1*†, A. Tsukazaki1,2†‡, K. Kikutake1, J. G. Checkelsky1, K. S. Takahashi3, M. Kawasaki1,3 and Y. Tokura1,3 Topological insulators are a class of semiconductor exhibiting charge-gapped insulating behaviour in the bulk, but hosting a spin-polarized massless Dirac electron state at the surface1–4 . The presence of a topologically protected helical edge channel has been verified for the vacuum-facing surface of several topological insulators by means of angle-resolved photoemission spectroscopy5–7 and scanning tunnelling microscopy8–10 . By performing tunnelling spectroscopy on heterojunction devices composed of p-type topological insulator (Bi1−x Sbx )2 Te3 and n-type conventional semiconductor InP, we report the observation of such states at the solid-state interface. Under an applied magnetic field, we observe a resonance in the tunnelling conductance through the heterojunction due to the formation of Landau levels of two-dimensional Dirac electrons at the interface. Moreover, resonant tunnelling spectroscopy reveals a systematic dependence of the Fermi velocity and Dirac point energy on the composition x. The successful formation of robust non-trivial edge channels at a solid-state interface is an essential step towards functional junctions based on topological insulators11–13 . Modern semiconductor device technology is based on solidstate devices composed of various heterostructures such as p–n junctions, superlattices and transistors. Such heterointerface devices will also be necessary for future electronics based on topological insulators; emergent topological edge states on topological insulators may have great potential for spintronics and quantum computing due to their robustness and spin polarization ensured by the topological invariant. So far, however, most key experiments on boundary states have been performed on the surface of bulk topological insulators by spectroscopic techniques5–10 that can be applied only to vacuum-facing surfaces. To develop topological edge-state electrical circuits, it is indispensable to fabricate solid-state junction devices that maintain the Dirac edge state. Tunnelling spectroscopy applied to heterojunctions is a powerful tool for detecting the density of states at interfaces and in semiconductor quantum wells14–16 . In this study, the interfacestate density of topological insulator/non-topological insulator heterojunctions is examined on the basis of resonant tunnelling spectroscopy applied to samples in a magnetic field. By using molecular beam epitaxy, we fabricated a topological insulator/nontopological insulator p–n junction from the topological insulator
(Bi1−x Sbx )2 Te3 and the non-topological insulator InP (Fig. 1a; see Methods). InP used as the substrate is not a topological insulator; rather, it is a conventional III–V semiconductor with a bandgap Eg = 1.4 eV. To serve as a degenerate n-type layer, it was heavily doped with S so that its carrier density was 4 × 1018 cm−3 . (Bi1−x Sbx )2 Te3 is a well-known topological insulator and a narrowgap semiconductor (Eg ∼ 0.2–0.3 eV) whose carriers can be well controlled by tuning the material composition x (ref. 17). Here, we operated in the composition range 0.9 < x < 1 in (Bi1−x Sbx )2 Te3 to tune the degenerate hole density. The lattice of (111)-oriented InP matches well with that of (Bi1−x Sbx )2 Te3 ; therefore, our film quality was sufficient to form high-mobility surface states (see Supplementary Information) comparable to recent efforts in bulk crystals18–21 . After growing the film, 200-µm-square junction devices were fabricated by photolithography and ion milling with Ti/Au electrodes (see Methods). Using such a vertical device structure, the tunnelling conductance can be used to probe the Dirac states or quantized Landau levels at the interface forming the tunnelling barrier. (depicted by arrows in the band diagram shown in Fig. 1b). The tunnel barrier is implemented by a thin depletion layer (estimated to be approximately 5–30 nm from screening-length considerations; see Supplementary Information) that forms owing to conduction-band discontinuity in the InP side of the interface between these two semiconductors22,23 (Fig. 1b). Electrons that tunnel to (Bi1−x Sbx )2 Te3 dissipate to the bulk states (wavy arrow in Fig. 1b) and can be detected as current. This tunnelling conductance is proportional to the interface density of states, which in turn is modulated by Landau-level formation in intense magnetic fields. Figure 1c shows the current–voltage (I –V ) characteristics of Sb2 Te3 (x = 1)/InP heterostructures at 10 K, as measured with standard source measurement units. Under positive applied bias, the current slowly increases until an applied bias of V = 0.2 V, after which it rapidly increases, most likely because of an increase in excitation over the tunnel barrier. In contrast, the current under a negative applied bias is larger than that under a positive applied bias, in agreement with that observed for an Esaki-type tunnelling diode24 . To clarify the tunnelling processes in the junctions, we plot the differential conductance dI /dV for five junctions with varying Sb content (x = 1, 0.98, 0.95, 0.93 and 0.9) in Fig. 1d. The peaks and dips observed in the differential conductance at 0.048 < V < 0.12 are assigned on the basis of the schematic band diagrams (labelled
1 Department
of Applied Physics and Quantum-Phase Electronics Center (QPEC), University of Tokyo, Tokyo 113-8656, Japan, 2 Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba 277-8561, Japan, 3 RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan. †These authors equally contributed to this work. ‡Present address: Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan. *e-mail: [email protected] NATURE MATERIALS | VOL 13 | MARCH 2014 | www.nature.com/naturematerials
© 2014 Macmillan Publishers Limited. All rights reserved
253
NATURE MATERIALS DOI: 10.1038/NMAT3885
LETTERS a
c
40
V 20
p-(Bi1–xSb ) Te x 2 3
b
I (mA)
n-InP
p–(Bi1–xSbx)2Te3
n–InP
0
–20
–40 –0.3
d
0.5 eV
x = 1 (Sb2Te3) T = 10 K B=0T
–0.2
–0.1
0.0 V (V)
0.1
0.2
0.3
40
x = 0.90
20 nm
Vbias = 0.2 V 30
e
x = 0.93
InP
dI/dV (a.u.)
EV EC Sb2Te3 V=0V
20 x = 0.95
I x = 0.98 10 x=1
II I 0 0.00 II
III 0.05
III
0.10
0.15
0.20
0.25
V (V)
Figure 1 | Tunnelling spectroscopy in a topological insulator/non-topological insulator p–n junction. a, Schematic of device studied by tunnelling spectroscopy. Device contains p-(Bi1−x Sbx )2 Te3 /n-InP junctions. b, Band diagram of junctions under positive applied bias of 0.2 V. Straight and wavy arrows indicate electron tunnelling to the interface state and subsequent relaxation to the bulk, respectively. c, I–V characteristics for the composition x = 1 (Sb2 Te3 ) at 10 K. d, Differential conductance dI/dV as a function of bias voltage V for different compositions (x). Labels I, II and III indicate the positions of peak and dips in dI/dV curves, as shown by filled/open triangles. e, Band lineup for each typical bias condition at I, II, and III for x = 1 (Sb2 Te3 ). The conduction-band minimum and valence-band maximum are denoted by EC and EV , respectively.
I, II, and III), as shown in Fig. 1e. The dip at V = 0.048 V (labelled I) shows no dependence on material composition, which indicates that it corresponds to the Fermi energy in n-type InP. However, peaks II and dips III depend on the Sb concentration x, which reflects the variation in Fermi energy with x in p-type (Bi1−x Sbx )2 Te3 . Based on these trends, we expect that further increases in the bias beyond condition II would realize the detection of Dirac states in the bandgap of (Bi1−x Sbx )2 Te3 . An applied magnetic field influences the tunnelling conductance because of the formation of Landau levels in the Dirac interface states. Figure 2a shows a set of tunnelling conductance spectra dI /dV for an x = 1 (Sb2 Te3 ) junction at different magnetic fields B varying from 0 to 14 T at T = 10 K. The conductance clearly increases near V = 0.15 V. Although leakage current overlaps 254
with and blurs the conductance spectra, resonant tunnelling through Landau levels clearly plays a key role in this junction. To clarify such a process, we define the field-modulated components as 1dI /dV (B) = dI /dV (B) − dI /dV (B = 0) (Fig. 2b). Above 5 T, oscillatory spectral features due to Landau-level formation are clearly observed in 1dI /dV (B). To extract the extrema of 1dI /dV (B), we further differentiate 1dI /dV (B) with respect to V and adopt the zero-crossing points as the position of the extreme values of 1dI /dV ; these are plotted in Fig. 2c (peaks and valleys are denoted by filled and open circles, respectively). Except for the central peak, the magnetic-field √ dependence of the bias extrema (Vext ) is well fitted by using B curves with V = 0.15 V as the origin. Contrary to the linear behaviour of Landau levels in a conventional electronic system (see Supplementary Information), NATURE MATERIALS | VOL 13 | MARCH 2014 | www.nature.com/naturematerials
© 2014 Macmillan Publishers Limited. All rights reserved
NATURE MATERIALS DOI: 10.1038/NMAT3885 a
LETTERS c
3
0.24
dI/dV (a.u.)
x = 1 (Sb2Te3) T = 10 K
n
E
+1
2
0
14 T
n=1
–1 1 0.20 0
ΔdI/dV (B) (a.u.)
4
T = 10 K 14 T
3
Vext (V)
b
B=0T
2
0.16
n=0
1 B=1T
0
d
ΔdI/dV (B) (a.u.)
ΔdI/dV
4
30
10 K 20 K 40 K 80 K 120 K 160 K T = 200 K
0 0.00
0.12
1 0 0
20
10
V = 0.15 V B = 14 T
3 2
0.05
100 T (K)
n = –1
200
T = 10 K 0.08 0.10 0.15 V (V)
0.20
0.25
0
5
10
15
B (T)
Figure 2 | Landau-level formation observed in tunnelling spectra. a, dI/dV spectra of a sample in an applied magnetic field from B = 0 to 14 T in 1 T increments at 10 K. b, Dependence of 1dI/dV(B) = dI/dV(B) − dI/dV(0) on bias voltage V. Closed and open triangles indicate peaks and dips corresponding to the increase or decrease of tunnelling conductance in the presence or absence of Landau levels. The error bars are estimated from the standard deviation of extreme values of 1dI/dV.c, Bias extrema (Vext ) values observed in b as a function of magnetic field. Closed and open circles correspond to peaks and dips, respectively. The inset shows the band dispersion of the Dirac cone and its Landau-level formation in a magnetic field. d, 1dI/dV(B) at B = 14 T for various temperatures. The inset shows the temperature dependence of the n = 0 Landau-level peak height at the bias voltage of V = 0.15 V.
our observation can be explained by Landau-level formation within the Dirac-electron dispersion at the interface8–10 . On the basis of this identification, we assign the upper and lower peaks to n = +1 and −1 Landau levels, respectively. The strongest central peak corresponding to the n = 0 Landau level in 1dI /dV (B) spectra exhibits a slight shift that is linear with respect to the magnetic field. The fact that the n = 0 Landau level does not split but instead shifts with the Zeeman energy (g ∼ 11) demonstrates that the Dirac dispersion is spin polarized, as expected. As the Dirac electrons at the interface or surface of a topological insulator are subject to perfect spin-momentum locking, the spin degeneracy of each Landau level is fully lifted25 . In particular, the n = 0 Landau level is perfectly spin polarized along the applied field B and thus should have a Zeeman energy that depends linearly on B: g µB BSz , where µB is the Bohr magneton and Sz is the z component of the electron spin. The g value (∼11) of the Dirac state in Sb2 Te3 can be estimated by the field-induced shift of the n = 0 Landau level, which is significantly larger than that reported for the Bi-based topological insulators, Bi2 Se3 (ref. 8) and Bi2 Te2 Se (ref. 26). In addition, the temperature dependence of the Landau-level spectra at B = 14 T is shown in Fig. 2d. The observation of Landau levels at such a high temperature (up to T ∼100 K) indicates that Dirac states at
the interface are robust, a result attributable to the large energy gap between n = 0 and ±1 Landau levels. To confirm the dimensionality of the Landau states, we investigated the angular dependence of 1dI /dV (B) for x = 0.93 at 10 K. Figure 3a shows 1dI /dV (B) measured at three different angles (θ = 0◦ , 45◦ and 75◦ with respect to the surface normal; see the schematic of the measurement configuration in the inset of the left panel). By rigidly √ offsetting 1dI /dV (B) spectra by an increment proportional√ to B, the peak and dip structures can be aligned, indicating the B-like evolution of Landau levels. As the magnetic field is tilted from the normal towards the plane (left to right panels), the peak amplitude decreases and the Landau-level splitting decreases, as shown for B = 9 T. Figure 3b shows Vext plotted as a function of the√ square root of the perpendicular component of the magnetic field ( B cos θ ) at five different angles θ . The resulting scaling relation Vext versus B cos θ further demonstrates that Landau levels observed in this study originate from the two-dimensional Dirac electron states at the interface between a topological insulator and a trivial insulator. The enhancement of tunnelling conductance through the formation of Landau levels was observed systematically in other compositions of topological insulator films (see Supplementary
NATURE MATERIALS | VOL 13 | MARCH 2014 | www.nature.com/naturematerials
© 2014 Macmillan Publishers Limited. All rights reserved
255
NATURE MATERIALS DOI: 10.1038/NMAT3885
LETTERS a
15
θ = 0°
15
x = 0.93 T = 10 K
15
45°
b
75°
0.18
0.16
9T
n=1 0.14
5
B=1T
ΔdI/dV (B) (a.u.)
4T
10
ΔdI/dV (B) (a.u.)
ΔdI/dV (B) (a.u.)
10
5
0.12
Vext (V)
10
75° 60° 45° 30° 15° 0° 0.10
n=0
5 0.08 n = –1
B
0.06
θ 0 0.04
0.10 V (V)
0.20
0 0.04
0.10 V (V)
0.20
0 0.04
0.10 V (V)
0.20
0.04
0
1
2
3
(B cos θ )1/2 (T1/2)
Figure 3 | Angular dependence of Landau-level formation. a, 1dI/dV (B) measured at different angles (θ = 0◦ , 45◦ and 75◦ ) with applied √ magnetic fields at 10 K. The inset of the left-most panel shows the measurement configuration. The data are vertically offset by an amount proportional to B. Linear dashed lines guide the eyes for the evolution of Landau levels. Filled and open circles show the positions of peaks and dips plotted in b. b, Peaks and dips of the applied bias (Vext ) for each angle as a function of the square root of the perpendicular component of the magnetic field (B cos θ)1/2 . The error bars are estimated from the standard deviation of extreme values of 1dI/dV. a
7
6
n=1
(105 m s–1)
Exp.
F
5
4 ARPES 3 0.88
n = –1 0.92
0.96
1.00
x (Sb)
b 0.14
V (V)
DP 0.10
0.06
0.02 0.88
VB
0.92
0.96
1.00
x (Sb)
Figure 4 | Composition dependence of Fermi velocity and energy of Dirac point in (Bi1 − xSbx )2 Te3 . a, Fermi velocity νF for each composition of (Bi1−x Sbx )2 Te3 , calculated from the field evolution at n = ±1. Grey circles show the νF data evaluated by angle-resolved photoemission spectroscopy (ARPES) experiments17 . The error bars indicate the standard deviation of fitting analysis shown in Fig. 2c. b, Bias voltage for Dirac point (DP) compared with valence-band maximum (VB) as estimated from the bias condition labelled II in Fig. 1d and carrier density. 256
Information). From the evolution of the Landau levels, we derived the band parameters of the Dirac interface states. √ Figure 4a shows the Fermi velocity vF calculated from 1En = vF 2eh¯ Bn. The vF for n = +1 is greater than that for n = −1, which we attribute to the asymmetry of the Dirac cone above and below the Dirac point. Such a convex shape of the Dirac dispersion was also observed in angle-resolved photoemission spectroscopy7 (ARPES). In fact, the curvature of Dirac dispersion and vF calculated from the surface Dirac states found by ARPES17 is very close to that deduced from the n = −1 Landau level in the present tunnelling spectroscopy measurement. Finally, we show the energy of the Dirac point obtained from the Landau-level convergence point at B = 0 T (Fig. 2c or Fig. 3b) relative to the valence-band maximum estimated from the peak bias labelled II in Fig. 1d. The Dirac point approaches the valence-band maximum on decreasing the Sb composition; a behaviour that also agrees well with the ARPES result for the surface state17 . In conclusion, by applying tunnelling spectroscopy to a p–n junction composed of a topological insulator and a trivial band insulator, we have detected Landau-level formation in the twodimensional Dirac electron state at a solid interface. Such a state would be difficult to probe √ with other surface-sensitive spectroscopies. In particular, the B behaviour of the peak bias clearly demonstrates that a Dirac dispersion is present at such an interface. Detailed band parameters such as the Fermi velocity and energy of the Dirac point are readily derived from these experimental results and agree with those of surface states measured by ARPES. These observations clearly show that the Dirac state of the topological insulator is maintained, despite the connection to another non-topological material. In particular, the result shows that Esaki-type tunnelling occurs in a junction based on a conventional narrow-gap semiconductor, thus ensuring the compatibility of topological insulator thin films with the accumulated knowledge of semiconductor technology. Further studies examining the vertical transport across interface states should shed new light on the spin–orbit interaction and related physics in comparison with previous studies on the weak antilocalization effect on low-field magnetoresistance27 . The NATURE MATERIALS | VOL 13 | MARCH 2014 | www.nature.com/naturematerials
© 2014 Macmillan Publishers Limited. All rights reserved
NATURE MATERIALS DOI: 10.1038/NMAT3885 robustness of topological Dirac electron states at a solid/solid interface may be observable in different types of material such as superconductors11 and ferromagnets12 , which should open the door towards the implementation of exotic dissipationless phenomena and applications.
Methods The (Bi1−x Sbx )2 Te3 films were fabricated on n-type and semi-insulating InP (111) substrates by molecular beam epitaxy. The epi-ready InP substrates were vacuum annealed at 380 ◦ C, and 70-nm-thick (Bi1−x Sbx )2 Te3 films were deposited with the substrate at 300 ◦ C. The beam flux ratio of Te per Bi and Sb was set to approximately 15 to prevent Te deficiency in the films. Sb concentration x in the (Bi1−x Sbx )2 Te3 films was defined by the ratio of beam equivalent pressures of Bi and Sb measured by the beam-flux monitor before the film deposition. The growth rate for the films was approximately 0.34 quintuple layer per minute. The junction devices were fabricated by the following procedures. First, to form ohmic electrical contacts, the top and bottom contact electrodes of Ti/Au were deposited on both sides of the film surface and on the InP substrate. The top Ti/Au layer plays an important role in preventing degradation of the topological insulator by photoresist or water attachment. Second, the sample was spin-coated with photoresist, and then baked at 90 ◦ C for 10 min. Third, the mesa structure comprising a 200-µm-square pattern was formed by etching using photolithography and ion milling. After washing off the photoresist with acetone, silver paint was used to make contact to both sides by hand to Au wires, after which the devices were baked in air at 150 ◦ C for 1 h. The samples were placed in a magnetic field and studied by tunnelling spectroscopy with a standard set-up (Quantum Design, PPMS) and a semiconductor parameter analyser (Agilent).
Received 2 July 2013; accepted 13 January 2014; published online 20 February 2014
References 1. Kane, C. L. & Mele, E. J. Z2 topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005). 2. Fu, L., Kane, C. L. & Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007). 3. Moore, J. E. & Balents, L. Topological invariants of time-reversal-invariant band structures. Phys. Rev. B 75, 121306(R) (2007). 4. Hasan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010). 5. Hsieh, D. et al. A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970–974 (2008). 6. Chen, Y. L. et al. Experimental realization of a three-dimensional topological insulator, Bi2 Te3 . Science 325, 178–181 (2009). 7. Hsieh, D. et al. A tunable topological insulator in the spin helical Dirac transport regime. Nature 460, 1101–1105 (2009). 8. Cheng, P. et al. Landau quantization of topological surface states in Bi2 Se3 . Phys. Rev. Lett. 105, 076801 (2010). 9. Hanaguri, T., Igarashi, K., Kawamura, M., Takagi, H. & Sasagawa, T. Momentum-resolved Landau-level spectroscopy of Dirac surface state in Bi2 Se3 . Phys. Rev. B 82, 081305(R) (2010). 10. Jiang, Y. et al. Landau quantization and the thickness limit of topological insulator thin films of Sb2 Te3 . Phys. Rev. Lett. 108, 016401 (2012). 11. Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008). 12. Qi, X. L., Hughes, T. L. & Zhang, S. C. Topological field theory of time-reversal invariant insulators. Phys. Rev. B 78, 195424 (2008).
LETTERS 13. Seradjeh, B., Moore, J. E. & Franz, M. Exciton condensation and charge fractionalization in a topological insulator film. Phys. Rev. Lett. 103, 066402 (2009). 14. Klein, J., Leger, A., Belin, M., Defourneau, D. & Sangster, M. J. L. Inelasticelectron-tunneling spectroscopy of metal–insulator–metal junctions. Phys. Rev. B 7, 2336–2348 (1973). 15. Bockenhoff, E., Klitzing, K. V. & Ploog, K. Tunneling from accumulation layers in high magnetic fields. Phys. Rev. B 38, 10120–10123 (1988). 16. Yang, C. H., Yang, M. J. & Kao, Y. C. Magnetotunneling spectroscopy in a double-barrier heterostructure: Observation of incoherent resonant-tunneling processes. Phys. Rev. B 40, 6272–6276 (1989). 17. Zhang, J. et al. Band structure engineering in (Bi1−x Sbx )2 Te3 ternary topological insulators. Nature Commun. 2, 574 (2011). 18. Qu, D. X., Hor, Y. S., Xiong, J., Cava, R. J. & Ong, N. P. Quantum oscillations and Hall anomaly of surface states in the topological insulator Bi2 Te3 . Science 329, 821 (2010). 19. Analytis, J. G. et al. Two-dimensional surface state in the quantum limit of a topological insulator. Nature Phys. 6, 960–964 (2010). 20. Taskin, A. A., Ren, Z., Sasaki, S., Segawa, K. & Ando, Y. Observation of Dirac holes and electrons in a topological insulator. Phys. Rev. Lett. 107, 016801 (2011). 21. Sacepe, B. et al. Gate-tuned normal and superconducting transport at the surface of a topological insulator. Nature Commun. 2, 575 (2011). 22. Levinstein, M., Rumyantsev, S. & Shur, M. Handbook Series on Semiconductor Parameters (World Scientific, 1996). 23. Hao, G. et al. Synthesis and characterization of few-layer Sb2 Te3 nanoplates with electrostatic properties. RSC Advances 2, 10694–10699 (2012). 24. Esaki, L. New phenomenon in narrow germanium p–n junctions. Phys. Rev. 109, 603–604 (1958). 25. Winkler, R. Spin–Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems (Springer, 2003). 26. Xiong, J. et al. High-field Shubnikov–de Haas oscillations in the topological insulator Bi2 Te2 Se. Phys. Rev. B 86, 045314 (2012). 27. Chen, J. et al. Gate-voltage control of chemical potential and weak antilocalization in Bi2 Se3 . Phys. Rev. Lett. 105, 176602 (2010).
Acknowledgements This research was supported by the Japan Society for the Promotion of Science through the Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program) on ‘Quantum Science on Strong Correlation’ initiated by the Council for Science and Technology Policy and by JSPS Grant-in-Aid for Scientific Research(S) No. 24224009 and No. 24226002.
Author contributions Y.T. conceived the project. R.Y. and K.K. grew the thin films, made the devices and performed the tunnelling spectroscopy measurements. R.Y. analysed the data and wrote the manuscript with contributions from all authors. A.T., J.G.C., K.S.T., M.K. and Y.T. jointly discussed the results.
Additional information Supplementary information is available in the online version of the paper. Reprints and permissions information is available online at www.nature.com/reprints. Correspondence and requests for materials should be addressed to R.Y.
Competing financial interests The authors declare no competing financial interests.
NATURE MATERIALS | VOL 13 | MARCH 2014 | www.nature.com/naturematerials
© 2014 Macmillan Publishers Limited. All rights reserved
257
