  $\alpha$-Sn is an elemental topological material, whose topological phases
can be tuned by strain and magnetic field. Such tunability offers a substantial
potential for topological electronics. However, InSb substrates, commonly used
to stabilize $\alpha$-Sn allotrope, suffer from parallel conduction,
restricting transport investigations and potential applications. Here, the
successful MBE growth of high-quality $\alpha$-Sn layers on insulating, hybrid
CdTe/GaAs(001) substrates, with bulk electron mobility approaching 20000
cm$^2$V$^{-1}$s$^{-1}$ is reported. The electronic properties of the samples
are systematically investigated by independent complementary techniques,
enabling thorough characterization of the 3D Dirac (DSM) and Weyl (WSM)
semimetal phases induced by the strains and magnetic field, respectively.
Magneto-optical experiments, corroborated with band structure modeling, provide
an exhaustive description of the bulk states in the DSM phase. The modeled
electronic structure is directly observed in angle-resolved photoemission
spectroscopy, which reveals linearly dispersing bands near the Fermi level. The
first detailed study of negative longitudinal magnetoresistance relates this
effect to the chiral anomaly and, consequently, to the presence of WSM.
Observation of the $\pi$ Berry phase in Shubnikov-de Haas oscillations agrees
with the topologically non-trivial nature of the investigated samples. Our
findings establish $\alpha$-Sn as an attractive topological material for
exploring relativistic physics and future applications.
