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.
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