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

Pallab Goswami, Sudip Chakravarty

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


The quantum phase transition between two clean, noninteracting topologically distinct gapped states in three dimensions is governed by a massless Dirac fermion fixed point, irrespective of the underlying symmetry class, and this constitutes a remarkably simple example of superuniversality. For a sufficiently weak disorder strength, we show that the massless Dirac fixed point is at the heart of the robustness of superuniversality. We establish this by considering both perturbative and nonperturbative effects of disorder. The superuniversality breaks down at a critical strength of disorder, beyond which the topologically distinct localized phases become separated by a delocalized diffusive phase. In the global phase diagram, the disorder controlled fixed point where superuniversality is lost, serves as a multicritical point, where the delocalized diffusive and two topologically distinct localized phases meet and the nature of the localization-delocalization transition depends on the underlying symmetry class. Based on these features, we construct the global phase diagrams of noninteracting, dirty topological systems in three dimensions. We also establish a similar structure of the phase diagram and the superuniversality for weak disorder in higher spatial dimensions. By noting that 1/r2 power-law correlated disorder acts as a marginal perturbation for massless Dirac fermions in any spatial dimension d, we have established a general renormalization group framework for addressing disorder driven critical phenomena for fixed spatial dimension d>2.

Original languageEnglish (US)
Article number075131
JournalPhysical Review B
Issue number7
StatePublished - Feb 16 2017

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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