SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION Aharonov-Bohm interference in topological insulator nanoribbons Hailin Peng 1,2, Keji Lai 3,4, Desheng Kong 1, Stefan Meister 1, Yulin Chen 3,4,5, Xiao-Liang Qi 4,5, Shou- Cheng Zhang 4,5, Zhi-Xun Shen 3,4,5, Yi Cui 1,* 1 Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA. 2 College of Chemistry and Molecular Engineering, Peking University, Beijing , P. R. China. 3 Department of Applied Physics, Stanford University, Stanford, California 94305, USA. 4 Department of Physics, Stanford University, Stanford, California 94305, USA. 5 Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA. These authors contributed equally to the work. *To whom correspondence should be addressed. yicui@stanford.edu. nature materials 1

2 Figure S1. a, TEM image of a intrinsic Bi 2 Se 3 nanoribbon with a gold catalyst at the tip. b and c, EDX data of the Bi 2 Se 3 nanoribbon and tip, respectively. The Cu peaks come from the Cu TEM grid. Quantitative analysis shows a 2 : 3 atomic ratio for Bi and Se stoichiometry (Bi 40%, Se 60%) of the nanoribbon. 2 nature MATERIALS

3 Figure S2. TEM of intrinsic, Sn-doped, and Se-doped Bi 2 Se 3 nanoribbons. a, TEM of a wide Bi 2 Se 3 nanoribbon supported on a holey carbon film. b, High-resolution TEM image of the Bi 2 Se 3 nanoribbon. The edge of the nanoribbon was atomically sharp and no amorphous phase was observed. Inset is the corresponding selected area diffraction (SAED) pattern. c, TEM image of Sn-doped Bi 2 Se 3 nanoribbons. d, higher-magnification TEM image showing a particle at the end of the Sn-doped Bi 2 Se 3 nanoribbon. e, High-resolution TEM image of the Sn-doped Bi 2 Se 3 nanoribbon showing hexagonal lattice planes with lattice spacing of nm, corresponding to the (11-20) plane of the rhombohedral Bi 2 Se 3 looking along the [0001] zone axis. Inset is the corresponding SAED pattern. f, TEM image of a Se-doped Bi 2 Se 3 nanoribbon. g, High-resolution TEM image and the corresponding SAED pattern of the Se-doped Bi 2 Se 3 nanoribbon showing the single-crystalline rhombohedral phase. nature materials 3

4 Figure S3. Hall effect of several Bi 2 Se 3 nanoribbons under different growth conditions. By controlling the growth conditions, we have obtained Bi 2 Se 3 nanoribbons with different carrier densities. The intrinsic material can show either high (black) or low (blue) carrier density, depending on the amount of Se vacancy during the growth. The carrier density can be further reduced by introducing hole doping, such as Sn/Au catalyst (magenta) or excess Se vapor post annealing (red). The density calculated from the Hall slopes ranges from to cm -2 at 2 K. Note that for the low density samples, the R xy traces deviate from strange lines at high fields, which will be discussed in Figure S4. 4 nature MATERIALS

5 Figure S4. Estimation of transport properties of the surface and bulk electrons. a. SEM image of a wide nanoribbon with electrodes patterned in a Hall-bar shape. Perpendicular magnetic fields are applied for the Hall measurement. b. Hall trace of the device in a measured at 2 K. The Hall slope at low fields (red dashed line) is larger than that at high fields (blue dashed line). c. The oscillatory part of the longitudinal resistance ΔR xx as a function of the inverse B-field. Inset, FFT power spectrum of ΔR xx. Both the Hall trace and the quantum oscillation indicate that multiple channels of carriers participate in the transport. Although we cannot rule out completely other effects such as several electric sub-bands, it is highly possible that the observed phenomenon results from surface (n 1, μ 1 ) and bulk (n 2, μ 2 ) conduction nature materials 5

6 with distinct electron mobility. Note that n 1 = 2n s due to the presence of up and down surfaces. At low fields (μb << 1), the Hall slope corresponds to an effective density n eff = 1/eR H = (n 1 μ 1 + n 2 μ 2 ) 2 / (n 1 μ n 2 μ 2 2 ), while n eff = n 1 + n 2 at high fields (μb >> 1). The sheet resistance in this device is R = 1/(en 1 μ 1 + en 2 μ 2 ) = 117 Ω / sq. Since both the theory and ARPES data suggest a bigger Fermi surface area A F for the surface states, we assign the larger FFT period at 110 (1/T) -1 to the surface states Δ(1/B) = (4π 2 e/h)/a F. Solving the equations above, we obtain the surface density n s ~ cm -2 and mobility μ s ~ cm 2 /Vs, bulk density n b ~ cm -3 (thickness ~ 50nm) and μ b ~ cm 2 /Vs. Note that the bulk density and mobility determined here are consistent with the values reported in Bi 2 Se 3 single crystals. 21 The mean free path of the surface electrons is l e = ħk F μ/e ~ 80 nm. Using the theoretically predicted 3 Fermi velocity v F ~ m/s, the phase coherent diffusion length L φ = (l e v F τ φ ) 1/2 is estimated as ~ 0.5 μm. Further experiments, including careful angular and temperature dependences, are needed to justify the naive assignment of surface and bulk states, as well as the order-of-magnitude estimation of the parameters. 6 nature MATERIALS