Evolution of topological surface states in antimony ultra-thin films

Abstract

Based on an inverted bulk band order, antimony thin films presumably could become topological insulators if quantum confinement effect opens up a gap in the bulk bands. Coupling between topological surface states (TSS) from opposite surfaces, however, tends to degrade or even destroy their novel characters. Here the evolution and coupling of TSS on Sb(111) thin films from 30 bilayers down to 4 bilayers was investigated using in-situ Fourier-transform scanning tunneling spectroscopy and density functional theory computations. On a 30-bilayer sample, quasi-particle interference patterns are generated by the scattering of TSS from the top surface only. As the thickness decreases, inter-surface coupling degrades spin polarisation of TSS and opens up new wavevector-dependent scattering channels, resulting in spin degenerate states in most part of the surface Brillouin zone, whereas the TSS near the zone centre exhibit little inter-surface coupling, so they remain spin-polarised without opening a gap at the Dirac point.

Figure 1. Atomic and electronic structures on Sb(111).

(a) STM image of 30 BL Sb(111) film grown on Si(111)-√3 × √3:Bi-β. Imaging conditions: V_b = −3 V, I = 50 pA. The inset shows the atomic-resolution image of Sb(111) surface (V_b = 1 V, I = 250 pA). The period is about 4.31 Å. (b) dI/dV_b spectrum taken on 30-BL Sb(111) surface. The inset shows the schematic SS bands forming a Dirac point at on Sb(111). By cutting the bands with vertical planes passing and axes, the dispersions lines of SS along these high symmetry directions can be obtained.

Figure 2. QPI patterns of TSS on 30-BL Sb(111).

(a) Real-space dI/dV_b map in an area of 20 nm × 20 nm taken at V_b = 40 mV, I = 120 pA. (b) Fourier transform of (a), consisting of six strong peaks along . The first SBZ (yellow hexagon) and high symmetry directions are marked. (c) FT-STS pattern around with three observable scattering vectors q_A, q_Band q_C. It was taken on a 40 nm × 40 nm area at V_b = 20 mV. (d) Schematic of CEC as well as the spin texture around , which has a central electron pocket and six hole pockets. The small grey arrows represent the spin directions. q_Aand q_B are allowed scattering vectors, while q_C is low in probability and q_D totally forbidden.

Figure 3. Scattering vectors in QPI patterns on 30-BL Sb(111).

(a) FT-STS maps of the same area taken at V_b from −40 mV to 150 mV are selected to extract the dispersion relationship. Each map shows two sets of scattering vectors corresponding to q_A and q_B, respectively. (b) The dispersions of q_A and q_B extracted from (a). Here the error bar corresponds to 0.05π Å⁻¹, which is determined by (2π/40) nm⁻¹. (c),(d) FT-STS mapping taken at 5 mV and the corresponding simulation pattern based on DFT computational data. (e),(f) Measured and simulated FT-STS patterns at 80 mV. q_Band q_Care marked for comparison with Fig. 2c–d.

Figure 4. QPI patterns reveal strongly inter-surface coupling of TSS in 9-BL Sb(111).

(a) A representative FT-STS mapping at 20 mV. Two cutoff vectors marked as q_Eand q_F are both shown as black dashed arrows. (b) q_Eand q_F in the calculated CEC at E_F. The grey arrows illustrate the spin directions of TSS on the top surface of a thick film. Intra-surface scatterings q_Aand q_B still exist and they correspond to the central green zone with high intensities in (a). (c) The corresponding simulated QPI pattern based on DFT calculations. (d) DFT-computation band structure of 9-BL Sb(111) along . The blue lines represent the SS band chosen for computing the spin separation. (e) Spin separation as a function of k, indicating strong k-dependent inter-surface coupling of SS. A, B and C are the intersection points of CEC at E_F with k axis along . (f) The real-space distributions of SS from near to obtained from DFT computations, showing that a well-defined localization of SS around but large penetration depth for states from 0.34 Å⁻¹ to .

Figure 5. Film thickness dependence of relative strength of intra- and inter-surface couplings of TSS.

(a–d) FT-STS patterns taken on 15, 12, 6, 5 BL Sb(111), respectively. The red and green arrows mark the position of I_B due to intra-surface coupling and I_E due to inter-surface coupling. (e) Plot of I_E/I_B as a function of film thckness.