Thickness-dependent topological phase transition and Rashba-like preformed topological surface states of α-Sn(001) thin films on InSb(001)

Topological materials, possessing spin-momentum locked topological surface states (TSS), have attracted much interest due to their potential applications in spintronics. \ensuremath{\alpha}-phase Sn (\ensuremath{\alpha}-Sn), being one of them, displays enriched topological phases via band-gap engineering through a strain or confinement effect. In this work, we investigated the band evolution of in-plane compressively strained \ensuremath{\alpha}-Sn(001) thin films on InSb(001) in a wide range of thickness from 3 bilayers (BL) to 370 BL by combining angle-resolved photoemission spectra and first-principles calculations. Gapped surface states evolved to a linearly dispersive TSS at a critical thickness of 6 BL, indicating that the system undergoes a phase transition from topologically trivial to nontrivial. For films thicker than 30 BL, additional Rashba-like surface states (RSS) were identified. These RSS served as preformed TSS in another strain-induced topological phase transition. In thick films, 370-BL \ensuremath{\alpha}-Sn(001), so as to preclude the confinement effect in thin films, our results were consistent with a Dirac semimetal phase with Dirac nodes located along $\mathrm{\ensuremath{\Gamma}}--Z$. This thickness-dependent band-structure study deepens our understanding of topological phase transitions and the evolution of Dirac states. Furthermore, the coexistence of TSS and RSS in a Dirac semimetal \ensuremath{\alpha}-Sn might significantly enhance the potential for spintronic applications.