Elemental topological Dirac semimetal {\alpha}-Sn with high quantum mobility

{\alpha}-Sn with a diamond-type crystal structure provides an ideal avenue to investigate novel topological properties owing to its rich diagram of topological phases and simple elemental material structure. Thus far, however, realisation of high-quality {\alpha}-Sn remains a challenge, which limits our understanding of its quantum transport properties and device applications. Here, we present epitaxial growth of {\alpha}-Sn on InSb (001) with the highest quality thus far and reveal that it is a topological Dirac semimetal (TDS) by quantum transport investigations together with first-principles calculations. We realise unprecedentedly high quantum mobilities of both the surface state (30000 cm^2/Vs), which is ten times higher than the previously reported values, and the bulk heavy-hole (HH) state (1700 cm^2/Vs), which has never been obtained experimentally. These excellent features allow us, for the first time, to quantitatively characterise the nontrivial interfacial and bulk band structure of {\alpha}-Sn via Shubnikov-de Haas oscillations at various temperatures and under various magnetic field directions. These results reveal the existence of a topological surface state (TSS) and a bulk HH band, both with nontrivial phase shifts, indicating that the TDS phase of {\alpha}-Sn is established. Furthermore, we demonstrate a crossover from the TDS to a two-dimensional topological insulator (2D-TI) and a subsequent phase transition to a trivial insulator when varying the thickness of {\alpha}-Sn. Our work indicates that {\alpha}-Sn is an excellent model system to study novel topological phases and a prominent material candidate for topological devices.