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Keywords:

  • topological insulators;
  • Bi2Se3;
  • bulk quantum Hall effect;
  • transport

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and discussion
  5. Conclusion
  6. Acknowledgements
  7. References
  8. Supporting Information
Thumbnail image of graphical abstract

We present a study of the structural and electronic properties of highly doped topological insulator Bi2Se3 single crystals synthesized by the Bridgman method. Lattice structural characterizations by X-ray diffraction, scanning tunneling microscopy, and Raman spectroscopy confirmed the high quality of the as-grown single crystals. The topological surface states in the electronic band structure were directly re- vealed by angle-resolved photoemission spectroscopy. Transport measurements showed that the conduction was dominated by the bulk carriers and confirmed a previously observed bulk quantum Hall effect in such highly doped Bi2Se3 samples. We briefly discuss several possible strategies of reducing bulk conductance. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and discussion
  5. Conclusion
  6. Acknowledgements
  7. References
  8. Supporting Information

The electronic properties of Bi2Se3, a semiconductor made of van der Waals coupled stacking “quintuple layers” (QL), were thought to be well understood since it had been studied for decades in light of its excellent thermoelectric properties. However, recently, it has been revealed that Bi2Se3 belongs to a new class of quantum materials: three-dimensional (3D) topological insulators (TI) 1, 2. In a 3D TI, the bulk has a band gap (∼0.3 eV for Bi2Se3), and the surface has non-trivial topologically protected surface states (SS) 3–7, which give rise to 2D Dirac fermions with an odd number of Dirac cones (1 for Bi2Se3) and spin-momentum locking. Most as-grown Bi2Se3 samples have a significant amount of (uncontrolled) Se vacancies that cause unintentional n-type bulk doping. Previous well-documented magnetotransport studies 8–10 of Bi2Se3 with bulk carrier densities between ∼1017 and 1019 cm–3 show standard 3D transport behavior of a doped bulk semiconductor. Interestingly, recent measurements on Bi2Se3 in lower and higher carrier density regimes have both revealed novel magnetotransport behaviors. In very low bulk doping (with carrier density <1017 cm–3) samples (synthesized with compensating dopants, such as Sb), quantum oscillations of the 2D Dirac fermions attributed to TI SS have been observed 11. In very high bulk doping (carrier density *1019 cm–3) samples, a bulk quantum Hall effect (QHE) with a 2D-like transport behavior arising from parallel QLs in the 3D bulk has been observed 12. Here, we present comprehensive structural and electronic characterizations on such highly doped Bi2Se3. The structure of the crystals was analyzed by X-ray diffraction (XRD), scanning tunneling microscopy (STM), and Raman spectroscopy. The TI SS in our sample was directly revealed by angle-resolved photoemission spectroscopy (ARPES). On the other hand, our transport measurements show that the electronic conduction is dominated by the bulk. We present the temperature (T) dependent resistance data on samples with different thicknesses (from ∼60 nm to 310 nm), and magnetotransport data on one of the sample (“A”) confirming the previously observed bulk QHE 12 (up to higher magnetic field than that in Ref. 12). Our results underscore the challenge of accessing surface state electronic transport (due to high bulk conduction) in as-grown Bi2Se3 bulk crystals. At the end of this letter, we briefly discuss several possible strategies of reducing bulk doping or conduction.

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Figure 1. (a) Representative XRD pattern on single crystal Bi2Se3(001) surface. The peaks are labeled with (hkl) Miller indices. (b) Atomic resolution STM image of a cleaved surface of Bi2Se3 crystal. (c) Representative Raman spectrum measured on a Bi2Se3 crystal. Three characteristic Raman peaks are labeled. Inset: optical image of the Bi2Se3 single crystals. (d) High-resolution ARPES energy-momentum dispersion band mapping along a pair of time-reversal invariant points M–Γ–M on Bi2Se3.

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Results and discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and discussion
  5. Conclusion
  6. Acknowledgements
  7. References
  8. Supporting Information

High-quality Bi2Se3 single crystals (optical images shown in the inset of Fig. 1c) were synthesized by the Bridgman technique (see Supporting Information, online at: www.pss-rapid.com). Figure 1a shows an XRD pattern measured on Bi2Se3(001) surface. The XRD reflections are attributed to Bi2Se3 (0,0,6) (0,0,9) (0,0,12) (0,0,15) planes, confirming the sample's single crystalline structure. From powder XRD data (not shown), we extract two lattice constants, a = 4.137 Å and c = 28.679 Å, which are consistent with the previously reported values 13, 14. The atomic resolution STM image (Fig. 1b) of a cleaved Bi2Se3(001) surface was measured in ultrahigh vacuum, showing a lattice constant a = 4.2 Å, confirming the XRD result. The lattice structure of our samples was further investigated by Raman spectroscopy. A representative Raman spectrum is shown in Fig. 1c. Three Raman peaks at proximately 72 cm–1, 131.8 cm–1, and 174.9 cm–1 agree well with the characteristic lattice vibration modes A1g1, Eg2 and A1g2 observed in a previous study 15. The topological SS of our samples were directly revealed by ARPES as shown in Fig. 1d. The Fermi level is located at 150 meV above the bulk conduction band minimum (CBM) in this sample. The Fermi wave vector and Fermi velocity of the SS are found to be kF = 0.1 Å–1 and vF = 5 × 105 m/s, similar to previous APRES measurements 1 on Bi2Se3 (see Supporting Information for more analysis on the ARPES data).

Figure 2a shows the four-terminal longitudinal resistance (Rxx) of a 150 nm thick exfoliated flake (sample A) measured from room temperature down to 5 K, displaying a metallic behavior, as qualitatively expected for the highly doped bulk. The T dependence of Rxx can be fitted to a simplified phenomenological model developed for doped Bi2Te3 bulk crystals 16 (which shows generally similar transport properties as doped Bi2Se3):

  • Rxx = R0 + α eθ/T + β T2.((1))

R0, a low-T residual resistance, corresponds to the contributions of impurity scattering. Phonon scattering and electron–electron (e–e) scattering give rise to the exponential and the quadratic terms, respectively. We found R0 = 22.46 Ω, α = 13.5 Ω, θ = 217 K and β = 0.00009 Ω/K2 give the best fit (as shown by the red line in Fig. 2a) to the experimental data (circles in Fig. 2a). The T dependence is dominated by the phonon scattering 16 and the fitting parameter θ corresponds to an effective phonon frequency ω = kBθ /ħ = 3.1 × 1013 rad/s. The very small value of β indicates that the e–e scattering effect is negligible in our sample. We measured the T dependence resistivity on six samples with different thicknesses. As an indicator of the metallic behavior, we take the high-T (270 K) resistance normalized by the respective low-T (15 K) value, and plot the ratio against the sample thickness (Fig. 2b). Interestingly, the thinner samples appear to be “less metallic” as measured by this ratio. Figure 2b suggests that thinning down the crystal thickness can be an effective means to reduce the metallic bulk conduction of Bi2Se3 (even for samples with high bulk doping) that may help bring out the SS transport signatures that are often overwhelmed by the bulk conduction.

Figure 3a shows Rxx and Hall resistance Rxy for sample A as functions of perpendicular magnetic field (B) applied along the c-axis at 340 mK. The carrier (n-type) density and mobility extracted from the low-B measurements are 4.7 × 1019 cm–3 and ∼400 cm2/Vs respectively. At higher B, Rxx oscillates periodically in 1/B (with a period BF), which can be interpreted as Shubnikov–de Haas oscillations due to the formation of Landau levels (LL). The N- th minimum of Rxx, counting from B = BF (which defines N = 1), corresponds to the N- th LL (labeled in Fig. 3a). We plot the assigned LL index N against the inverse of the magnetic field (B) positions of the observed minima in Rxx (B) in the inset of Fig 3a. The black solid line is a linear fit with N-axis intercept 0 ± 0.02 and slope BF = 163 T, corresponding to a bulk carrier Fermi wave vector kF = 0.07 Å–1. Furthermore, accompanying the minima in Rxx, Rxy shows developing quantized plateaus. In Fig. 3b, we plot normalized quantized Hall step size Δ(1/Rxy) and ΔRxy (difference between two adjacent plateaus in 1/Rxy and Rxy, respectively, then normalized by their own values at N = 6) as functions of LL index N. It clearly shows that Δ(1/Rxy) is largely independent with increasing LL index, while ΔRxy decreases. The approximately constant value of Δ(1/Rxy) for different LLs is ∼1.2e2/h per QL (the number of QLs is determined by sample's thickness, where the scaling of Δ(1/Rxy) with the thickness as observed previously 12 further confirms that the transport is dominated by the bulk). The quantization in Rxy can be interpreted as a “bulk QHE” 12 attributed to parallel 2D electron gas arising from the stacking QLs in highly doped Bi2Se3 crystals (carrier density *1019 cm–3, where the Se vacancies may help reduce the electronic couplings between the QLs), and not caused by SS or any other surface conduction channels. The quantized Hall step size in 1/Rxy was examined down to lower LLs compared to our previous study 12, and confirmed to remain approximately constant for different LLs. Our results (here and in Ref. 12), along with those from earlier experiments 10, 11, 17–19 on less-doped Bi2Se3, demonstrate the rich physics in the magnetotransport of Bi2Se3 in different regimes of bulk carrier densities.

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Figure 2. (a) Temperature dependence of four-terminal longitudinal resistance (Rxx) in sample A. The red line shows the fitting to Eq. (1). (b) R (T = 270 K)/ R (T = 15 K) plotted against sample thicknesses.

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Figure 3. (a) Hall resistance (Rxy) and Rxx of sample A as functions of magnetic field (B, perpendicular to the QLs) measured at T = 340 mK. The minima in Rxx corresponding to a series of Landau Level indices are labeled with arrows. Inset: LL fan diagram. (b) Normalized step size in 1/Rxy and Rxy plotted against LL index (N).

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Conclusion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and discussion
  5. Conclusion
  6. Acknowledgements
  7. References
  8. Supporting Information

High quality Bi2Se3 single crystals were synthesized by Bridgman techniques. The lattice structure is characterized by XRD, STM and Raman spectroscopy that confirmed the excellent crystalline quality. Our as-grown crystals are found to have high bulk carrier density (>1019 cm–3, presumably due to substantial n-type doping by Se vacancies). The temperature dependence of resistance confirms the metallic behavior, which is weaker for thinner samples. We conducted magnetotransport measurements in a higher B field to reach lower LL compared to our previous study 12 and confirmed the bulk QHE previously observed. Accessing SS transport in as-grown Bi2Se3 remains challenging. There are several possible strategies to reduce the bulk conduction: for example, (i) thinning down the thickness of the crystal 20, 21; (ii) adding more Se during growth to reduce Se vacancies (see Fig. S1 in Supporting Information); (iii) growing mixed crystals such as Bi2Te2Se which has been shown to have a large bulk resistivity (low bulk carrier density) 22, 23; (iv) growing crystals with compensating dopants (e.g., Sb 11 or Ca 24) to reduce bulk doping. Employing one or more of such strategies will likely be important to prepare TI materials for transport studies and device applications of TI SS.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and discussion
  5. Conclusion
  6. Acknowledgements
  7. References
  8. Supporting Information

We acknowledge support from DARPA MESO program (Grant N66001-11-1-4107). STM measurements and part of the transport measurements were carried out at Argonne National Laboratory Center for Nanoscale Materials (CNM) under the auspices of CNM user research program (CNM-998). Part of the magnetotransport measurements were performed at the National High Magnetic Field Laboratory (NHMFL). The Princeton-led synchrotron X-ray-based measurements are supported by the Office of Basic Energy Sciences, U.S. Department of Energy (grants DE-FG-02-05ER46200, and AC03-76SF00098). M.Z.H. acknowledges visiting-scientist support from Lawrence Berkeley National Laboratory (LBNL) and additional support from the A. P. Sloan Foundation. The ARPES measurements using synchrotron X-ray facilities are supported by the Advanced Light Source in the LBNL. We thank E. Palm (NHMFL), L. Engel (NHMFL), J. J. Jaroszynski (NHMFL), N. P. Guisinger (ANL), B. Fisher (ANL) and P. Metcalf (Purdue) for experimental assistance.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and discussion
  5. Conclusion
  6. Acknowledgements
  7. References
  8. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and discussion
  5. Conclusion
  6. Acknowledgements
  7. References
  8. Supporting Information

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