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The quantum phase transition between two clean, non interacting topologicallydistinct gapped states in three dimensions is governed by a massless Diracfermion fixed point, irrespective of the underlying symmetry class, and thisconstitutes a remarkably simple example of superuniversality. For asufficiently weak disorder strength, we show that the massless Dirac fixedpoint is at the heart of the robustness of superuniversality. We establish thisby considering both perturbative and nonperturbative effects of disorder. Thesuperuniversality breaks down at a critical strength of disorder, beyond whichthe topologically distinct localized phases become separated by a delocalizeddiffusive phase. In the global phase diagram, the disorder controlled fixedpoint where superuniversality is lost, serves as a multicritical point, wherethe delocalized diffusive and two topologically distinct localized phases meetand the nature of the localization-delocalization transition depends on theunderlying symmetry class. Based on these features we construct the globalphase diagrams of noninteracting, dirty topological systems in threedimensions. We also establish a similar structure of the phase diagram and thesuperuniversality for weak disorder in higher spatial dimensions. By notingthat $1/r^2$ power-law correlated disorder acts as a marginal perturbation formassless Dirac fermion in any spatial dimension $d$, we have established ageneral renormalization group framework for addressing disorder driven criticalphenomena for fixed spatial dimension $d > 2$.

Superuniversality of topological quantum phase transition and global phase diagram of dirty topological systems in three dimensions