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

Abstract

The quantum phase transition between two clean, non interacting 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 $1/r^2$ power-law correlated disorder acts as a marginal perturbation for massless Dirac fermion in any spatial dimension $d$, we have established a general renormalization group framework for addressing disorder driven critical phenomena for fixed spatial dimension $d>2$.

25 pages, 6 figures; replaced with the version accepted by Phys. Rev. B

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Cited by in corpus (20)

• Topological superconductivity of spin-3/2 carriers in a three-dimensional doped Luttinger semimetal
• Global Phase Diagram of a Dirty Weyl Liquid and Emergent Superuniversality
• Dissolution of topological Fermi arcs in a dirty Weyl semimetal
• Unifying the Anderson Transitions in Hermitian and Non-Hermitian Systems
• Single particle excitations in disordered Weyl fluids
• Global phase diagram of a three dimensional dirty topological superconductor
• Nodal points of Weyl semimetals survive the presence of moderate disorder
• From weak to strong disorder in Weyl semimetals: Self-consistent Born approximation
• Topological and conventional phases of a three dimensional electron glass
• Dirty higher-order Dirac semimetal: Quantum criticality and bulk-boundary correspondence
• Two dimensional metallic phases from disordered QED${}_3$
• Non-Abelian bosonization and modular transformation approach to superuniversality
• Itinerant quantum multi-criticality of two dimensional Dirac fermions
• Quantum phases of disordered three-dimensional Majorana-Weyl fermions
• Two-dimensional conductors with interactions and disorder from particle-vortex duality
• Composite Fermion Nonlinear Sigma Models
• Precise determination of critical points of topological phase transitions via shift current in two-dimensional inversion asymmetric insulators
• Dynamic zero modes of Dirac fermions and competing singlet phases of antiferromagnetic order
• Superconductivity in doped planar Dirac insulators: A renormalization group study
• Can a quantum critical state represent a blackbody?