Evolution of Topological Surface States in Tunable Topological Insulators

Bi$_{\mathrm{1-x}}$Sb$_{x}$ (0.07\textless $x$\textless 0.22) is the first generation of 3D topological insulators (TIs), possessing a bandgap and topological surface states (SSs) generated by spin-orbit coupling In fact, within the whole range of 0\textless $x$\textless 1 (i.e. from pure Bi to pure Sb), a topological phase transition has to occur as the system is twisted from topologically trivial to nontrivial phases, even though it becomes a semimetal hosting a negative indirect gap Therefore, taking advantage of Fourier-transform scanning tunneling spectroscopy (FT-STS) and \textit{ab initio} calculations, we investigate the progressive evolution of topological SSs in the tunable Bi$_{\mathrm{1-x}}$Sb$_{x}$ (0\textless $x$\textless 1) materials grown by means of molecular beam epitaxy In alloys with several representative compositions, quasiparticle interference (QPI) patterns of SSs exhibit dramatic dependence on $x$ values, indicating that intra-surface scatterings are ultimately determined by band structures and the associated spin textures. Additionally, the corresponding simulated QPI patterns are also revealed based on \textit{ab initio} calculations. Such systematic studies of the Bi$_{\mathrm{1-x}}$Sb$_{x}$ alloy family can be further explored to tailor surface energetic and transport properties for potential applications in quantum information, spintronics and many other topological quantum phenomena.