  Using the self-consistent Born approximation, we study a topological phase
transition appearing in bulk HgCdTe crystals induced \emph{uncorrelated}
disorder due to both randomly distributed impurities and fluctuations in Cd
composition. By following the density-of-states evolution, we clearly
demonstrate the topological phase transition, which can be understood in terms
of the disorder-renormalized mass of Kane fermions. We find that the presence
of heavy-hole band in HgCdTe crystals leads to the topological phase transition
at much lower disorder strength than it is expected for conventional 3D
topological insulators. Our theoretical results can be also applied to other
narrow-gap zinc-blende semiconductors such as InAs, InSb and their ternary
alloys InAsSb.
