2016/03/31 by Pallab Goswami, Sudip Chakravarty · 21 citations
Mathematics · Physics and Astronomy · #Delocalized electron #Dirac fermion #Fermion #Massless particle #Mathematics #Multicritical point #Phase (matter) #Phase diagram #Phase transition #Physics #Quantum #Quantum and electron transport phenomena #Quantum critical point #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Quantum phases #Renormalization group #Topological Materials and Phenomena #Topological order #Topology (electrical circuits) #cond-mat.dis-nn #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.95.075131
published in Physical review. B./Physical review. B 95(7) (American Physical Society) · 25 pages, 6 figures; replaced with the version accepted by Phys. Rev. B
arxiv created 2017/01/26 · openalex publication_date 2017/02/16 · arxiv updated 2017/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.