Topological phase transition induced by random substitution

The transition from topologically nontrivial to a trivial state is studied by first-principles calculations on bulk zinc-blende type (Hg${}_{1-x}$Zn${}_x$)(Te${}_{1-x}$S${}_x$) disordered alloy series. The random chemical disorder was treated by means of the Coherent Potential Approximation. We found that although the phase transition occurs at the strongest disorder regime ($x\approx 0.5$), it is still manifested by well-defined Bloch states forming a clear Dirac cone at the Fermi energy of the bulk disordered material. The computed residual resistivity tensor confirm the topologically-nontrivial state of the HgTe-rich ($x<0.5$), and the trivial state of the ZnS-rich alloy series ($x>0.5$) by exhibiting the quantized behavior of the off-diagonal spin-projected component, independently on the concentration $x$.