Supplementary information: Topological Properties Determined by Atomic Buckling in Self-Assembled Ultrathin Bi (110)

Transcription

1 Supplementary information: Topological Properties Determined by Atomic Buckling in Self-Assembled Ultrathin Bi (110) Yunhao Lu, *,, Wentao Xu, Mingang Zeng, Guanggeng Yao, Lei Shen, Ming Yang, Ziyu Luo, Feng Pan, Ke Wu, Tanmoy Das, Pimo He, Jianzhong Jiang,, Jens Martin, Yuan Ping Feng, Hsin Lin, *, and Xue-sen Wang *, Department of Materials Science and Engineering, Zhejiang University, Hangzhou , China Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore , Singapore Department of Chemistry, National University of Singapore, 3 Science Drive 3, Singapore , Singapore Department of Physics and State Key Laboratory of Silicon Materials, Zhejiang University, Hangzhou , China Y.L. and W.X. contributed equally to this work. 1

2 1. Formation energy and stability of Bi(110) slabs The formation energy of an N-ML Bi(110) slab is defined as: E E ( N) 2N ( N) slab Ebulk (1) where E slab (N) is the total energy of the slab with an area of one Bi(110) surface unit cell, 2N is the number of Bi atoms in such a unit-cell-area slab, and E bulk is energy of one Bi atom in the bulk. In order to discuss the relative stability of the slab, we define the second difference of E(N) as: 2 E( N) E( N 1) E( N 1) 2E( N) (2) 2 If E ( N) 0, the N-ML slab is stable, otherwise the film is unstable against breaking into segments of neighbouring thicknesses. The following results are for the BP structure and it is similar for DBP structure. 2

3 Figure S1: (a) Thickness-dependent formation energy E(N). (b) The 2 second-difference energy E( N). (c) STM image of Bi(110) ultra-thin films on HOPG (V s = 3 V, I = 0.03 na). The inset shows the atomic-resolution STM image of the film surface (V s = -200 mv, I = 0.11 na). The surface unit cell is indicated by the black rectangle with lattice constants indicated in Å. 3

4 2. Optimized DBP structure of 2-ML Bi(110) film, doping-level dependent stability and band obtained by hybrid functional. Figure S2: (a) & (b) Side and top view of optimized DBP structure of 2-ML Bi(110) film with buckled structure and unit cell indicated. Green and blue circles represent two different layers. (c) The dependence of 4

5 energy difference between the BP and DBP structures of 2-ML Bi(110) film on the electron doping-level. (d) Band structure of 2-ML BP-structured Bi(110) film obtained by hybrid functional (HSE06). Fermi level is set to zero. (e) & (f) Density of states of BP and DBP structures with doping level e/å 2 5

6 3. The h-dependent energy gap(δ) at Dirac point of 4-ML Bi(110) film and its doping-level dependent stability Figure S3: (a) Band structure of 4-ML BP-structured Bi(110) including SOC with energy gap at Dirac point indicated. (b) The h-dependent energy gap (Δ) at Dirac point of 4-ML Bi(110) film. (c) The dependence of energy difference between the BP and DBP structures of 4-ML Bi(110) film on the electron doping-level. 6

7 4. Band structures of BP-structured 6-ML and 8-ML Bi(110) films Figure S4: Band structures of BP-structured 6-ML and 8-ML Bi(110) films. The Fermi level is set to E = 0. 7

8 5. Geometrical structures and stability of 2-ML Bi(110) nanoribbon 2-ML Bi(110) nanoribbon can be classified as even- and odd-edge types as shown in the upper panel of Fig. S5. Each edge atom of the even- and odd-edge nanoribbon has one and two dangling bonds, respectively. As the central part of the ribbon remains to be bulk structure on substrate, only the edge atoms are allowed to relax while other atoms are fixed to their bulk positions. Upon structural optimization, the out-most atoms on the edges form additional bonds with inner atoms to saturate dangling bonds. Reconstruction involving more atoms is found at the odd edges because more dangling bonds need to be saturated than at the even edges. To evaluate the relative stability of 2-ML Bi(110) nanoribbons as a function of ribbon width, we evaluated the per-atom formation energy defined as: Eribbon( N) E formation E 2N BL (3) where E ribbon (N) is the total energy of a Bi nanoribbon of N atomic units in width, 2N is the number of Bi atoms in the studied supercell, and E BL is the energy per atom in a infinite wide 2-ML Bi(110). As shown in the lower panel of Fig. S5, the formation energy of odd-edge ribbons is always higher than neighboring even-edge ribbons, so odd-edge ribbons are less stable than the even ones. 8

9 Figure S5:Side view of symmetric 2-ML Bi(110) nanoribbon models with even-edge and odd-edge structures before structural relaxation. (b) Width-dependent formation energy of 2-ML Bi(110) ribbon with even-odd oscillation. The fitted exponential lines are colored in red and green colors as guides to the eye. 9

10 6. The band structure of ribbon and energy gap of two edge bands at X as a function of the ribbon width (a) [110] Top view Side view (d) Figure S6: (a) Optimized geometrical structure of 2-ML BP-structured Bi(110) ribbon with top and side views. The orientation of the ribbons is indicated by arrow. (b) Band structure of the ribbon shown in (a). (c) Energy gap at X of edge bands indicated by red circle in (b) as a function 10

11 of the ribbon width. (d) Calculated band structure of the ribbon (~ 6 nm in width) with all atoms fixed in their bulk positions. Bulk states are shaded by green color and Fermi level is set at zero. 7. The band structure of DBP ribbon Figure S7:Calculated band structure of the DBP ribbon with a width of 6 nm. The states localized at the edges of the ribbon are visualized by red circles. The Fermi level E F is set at E = 0. Note that a parabolic-like band from bulk appears around Fermi level. 11

12 8. Fermi level estimation It is not easy to estimate Fermi level shift accurately from STS measurement for 2D systems with low electron density. Work function difference may induce charge transfer between the tip and sample. Fig.S8(a) shows the schematic potential barrier between non-interacting tip and sample. In our situation, tip and sample are PtIr and Bi(110). Measured with respect to the same reference point, the Fermi level E F of the materials differ by an amount equal to the work function (W PtIr and W Bi ) difference. If tip and sample are connected with bias voltage = 0 (Fig.S8(b)), electrical equilibrium requires that the Fermi energy is the same on both sides, i.e. Fermi levels are aligned. In order to establish this situation electrons flow from the side with lower work function to the other side with higher work function. Knowing the work function for Bi (4.22 ev), Pt (5.65 ev) and Ir (5.27 ev), and assuming that the work function of PtIr is an average of the individual work functions of Pt and Ir, respectively, one can estimate the amount of charge flowing from Bi(110) to the tip. Please note that the above mentioned work function value is a theoretical estimate and that the real work function maybe depend on surface orientation and other details. Nevertheless, the work function difference between tip and Bi(110) film (eф = W PtIr - W Bi ) is expected to be in the order of 1 ev. 12

13 The density of locally induced positive charge on Bi(110) is roughly given by ε 0 Ф/d, where ε 0 is the dielectric constant and d is the tip-sample separation. With Ф ~ 1 V and d ~ 1 Å, the density of locally induced positive charge is in the order of 10-2 e/å 2, which is comparable in size, but opposite in sign, to the estimated doping carrier density in the Bi(110) films on HOPG without the influence of the tunneling tip. Consequently, the apparent Fermi level in STS measurements should be near zero bias voltage. Figure S8:Schematic potential barrier between tip and sample. (a) Non-interacting tip and sample. (b) Tip and sample are connected with sample bias = 0. 13

14 9. Edge states of 4-ML Bi(110) (a) (b) Figure S9: (a) STM image of 4-ML Bi(110) film on HOPG (V s = 0.3 V, I = 0.02 na). The inset is a zoom-in STM image of the blue rectangle (V s = 0.3 V, I = 0.16 na). (b) STS taken along four different lines 1, 2, 3 and 4 as indicated in panel (a). Each series of the eight spectra from bottom to top are taken from equally spaced locations along the corresponding line from side A to side B. The reconstruction quite near the edge affect the STS, for example at V (STS along line 1 and 2), but the edge states near the Fermi level are always present (STS along line 1, 2 and 3), which indicate that the edge reconstructions have no obvious effect on the states. 14

15 10. Edge states of 2-ML and 4-ML Bi(110) perpendicular to the edges 15

16 Figure S10:(a) STM image of 2-ML Bi(110) island on HOPG (V s = 2 V, I = 0.03). The insert is a zoom-in STM image of the blue rectangle (V s = 400 mv, I = 0.12 na). (b) STS spectra from the edge to interior of the island along the red line in (a). (c) STM image of 2-ML Bi(110) island on HOPG (V s = 2 V, I = 0.03). The insert is a zoom-in STM image of the blue rectangle (V s = 400 mv, I = 0.06 na). (d) STS spectra from the edge to interior of the island along the red line in (c). (e) STM image of 4-ML Bi(110) island on HOPG (V s = 2 V, I = 0.02). The insert is a zoom-in STM image of the blue rectangle (V s = 100 mv, I = 0.05 na). (f) STS spectra from the edge to interior of the island along the red line in (e). (g) STM image of 4-ML Bi(110) island on HOPG (V s = 2 V, I = 0.03). The insert is a zoom-in STM image of the blue rectangle (V s = 400 mv, I = 0.16 na). (h) STS spectra from the edge to interior of the island along the red line in (g). All measurements are performed at 4.2 K. 16