GLYPH<s45> GLYPH<s52>GLYPH<s48> GLYPH<s45> GLYPH<s50>GLYPH<s48> GLYPH<s48> GLYPH<s50>GLYPH<s48> GLYPH<s40>GLYPH<s97>GLYPH<s41> GLYPH<s67> GLYPH<s50> GLYPH<s67> GLYPH<s50> GLYPH<s67> GLYPH<s51> GLYPH<s32> GLYPH<s121> GLYPH<s120> GLYPH<s40> GLYPH<s109> GLYPH<s32> GLYPH<s99> GLYPH<s109> GLYPH<s41> GLYPH<s45> GLYPH<s57>GLYPH<s48> GLYPH<s48> GLYPH<s57>GLYPH<s48> GLYPH<s48> GLYPH<s53> GLYPH<s49>GLYPH<s48> GLYPH<s32> GLYPH<s121> GLYPH<s120> GLYPH<s40> GLYPH<s109> GLYPH<s32> GLYPH<s99> GLYPH<s109> GLYPH<s41> GLYPH<s32>GLYPH<s32>GLYPH<s40>GLYPH<s100>GLYPH<s101> GLYPH<s103>GLYPH<s41> GLYPH<s45> GLYPH<s57>GLYPH<s48> GLYPH<s48> GLYPH<s57>GLYPH<s48> GLYPH<s48> GLYPH<s49>GLYPH<s48> GLYPH<s50>GLYPH<s48> GLYPH<s40>GLYPH<s98>GLYPH<s41> GLYPH<s52>GLYPH<s48> GLYPH<s50>GLYPH<s53> GLYPH<s49>GLYPH<s53> GLYPH<s55> GLYPH<s49>GLYPH<s46> GLYPH<s53>GLYPH<s32> GLYPH<s75> GLYPH<s32> GLYPH<s120> GLYPH<s120> GLYPH<s32> GLYPH<s40> GLYPH<s109> GLYPH<s32> GLYPH<s99> GLYPH<s109> GLYPH<s41> GLYPH<s32>GLYPH<s32>GLYPH<s40>GLYPH<s100>GLYPH<s101> GLYPH<s103>GLYPH<s41> FIG. 5: (Color online) (a) Angular-dependent oscillations of ρ yx within the C 3 - C 2 plane in the constant field B = 14 T measured at 1.5, 7, 15, 25, and 40 K. Inset shows oscilla- tions of Δ ρ yx after subtraction of the R H B cos θ term. (b) Angular-dependent oscillations of ρ xx within the C 3 - C 2 plane measured in the same conditions as in (a). work was supported by JSPS (KAKENHI 19674002 and 20030004) and AFOSR (AOARD 08-4099 and 10-4103). plane ( ⊥ C 3 ), where surface states are seen in photoe- mission [7–10] and tunneling [11] experiments. Another distinguishable feature of the “high-field” oscillations is that they survive up to rather high temperatures as can be seen in Fig. 5, where temperature dependences of both ρ$_{yx}$ ( θ ) and ρ$_{xx}$ ( θ ) are shown. Even at 40 K there are still visible traces of oscillations (see the inset of Fig. 5), while the “low-field” SdH and angular-dependent os- cillations disappear around 20 K. In spite of some simi- larities to the quasi-2D AMRO, the peak positions of the “high-field” oscillations apparently shift with the mag- netic field, which is not expected for the ordinary AMRO. Moreover, the existence of a finite coupling between con- duction planes is essential for the quasi-2D AMRO [25], but there is no such inter-plane coupling for the surface states as long as the crystal is thick enough. Therefore, the observed “high-field” angular oscillations are a new phenomenon apparently specific to topological insulators, and it is possible that they are associated with a coupling between the surface and the bulk states. In conclusion, we found two different types of oscilla- tory phenomena in the angular-dependent MR of a topo- logical insulator Bi $^{0}$.91 Sb $^{0}$.09 . One type is observed at lower fields and provides a new way to distinguish the 2D FS. The other one, which becomes prominent at higher fields, probably comes from the (111) plane and points to new physics in transport properties of topological in- sulators. We thank V. M. Yakovenko for discussions. This [33] Y. Zhang et al. , Nature 438 , 201 (2005). [32] G. P. Mikitik and Yu. V. Sharlai, Phys. Rev. Lett. 82 , 2147 (1999). [31] The SdH frequency of the 2D FS is 0.57 T when B is perpendicular to the 2D plane, but it becomes 0.65 T when B is 30 ◦ tilted, as is the case for two of the three equivalent 2D FSs in B ‖ C 2 . [30] V. P. Gusynin and S. G. Sharapov, Phys. Rev. B 71 , 125124 (2005). [29] S. G. Sharapov, V. P. Gusynin, and H. Beck, Phys. Rev. B 69 , 075104 (2004). [28] The scattering time τ (= ℏ / 2 πk B T D ) and the Fermi ve- locity v F (= ℏ k F /m c ) gives the mean free path ℓ = v F τ . In the present sample, v 3 D F ≈ 7.6 × 10 6 cm/s is an order of magnitude smaller than v 2 D F ≈ 8.4 × 10 7 cm/s. [27] D. Schoenberg, Magnetic Oscillations in Metals (Cam- bridge University Press, 1984). [26] We observed weaker oscillations in the same sample be- fore etching, corroborating their surface origin. [25] B. K. Cooper and V. M. Yakovenko, Phys. Rev. Lett. 96 , 037001 (2006). [24] G. M. Danner, W. Kang, and P. M. Chaikin, Phys. Rev. Lett. 72 , 3714 (1994). [23] K. Yamaji, JPSJ 58 , 1520 (1989). [22] K. Kajita et al. , Solid St. Comm. 70 , 1189 (1989). [21] M. V. Kartsovnik et al. , JETP Lett. 48 , 541 (1988). [20] D.-H. Lee, Phys. Rev. Lett. 103 , 196804 (2009). [19] Y. Ran, Y. Zhang, and A. Vishwanath, Nat. Phys. 5 , 298 (2009). [18] Y. Tanaka, T. Yokoyama, and N. Nagaosa, Phys. Rev. Lett. 103 , 107002 (2009). [17] A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Lud- wig, Phys. Rev. B 78 , 195125 (2008). [16] R. Shindou and S. Murakami, Phys. Rev. B 79 , 045321 (2009). [15] J. G. Checkelsky et al. , Phys. Rev. Lett. 103 , 246601 (2009). [14] H. Peng et al. , Nature Materials, doi:10.1038/nmat2609. [13] A. A. Taskin and Y. Ando, Phys. Rev. B 80 , 085303 (2009). [12] T. Zhang et al. , Phys. Rev. Lett. 103 , 266803 (2009). [11] P. Roushan et al. , Nature 460 , 1106 (2009). [10] A. Nishide et al. , Phys. Rev. B 81 , 041309(R) (2010). [9] D. Hsieh et al. , Nature 460 , 460 (2009). [8] D. Hsieh et al. , Science 323 , 919 (2009). [7] D. Hsieh et al. , Nature 452 , 970 (2008). [6] H.-J. Zhang et al. , Phys. Rev. B. 80 , 085307 (2009). [5] J. C. Y. Teo, L. Fu, and C. L. Kane, Phys. Rev. B. 78 , 045426 (2008). [4] X-L. Qi, T. L. Hughes, and S.-C. Zhang, Phys. Rev. B 78 , 195424 (2008). [3] J. E. Moore and L. Balents, Phys. Rev. B 75 , 121306(R) (2007). [2] L. Fu and C. L. Kane, Phys. Rev. B 76 , 045302 (2007). [1] L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 98 , 106803 (2007). 4