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

TL;DR

This paper demonstrates the superuniversality of topological quantum phase transitions in three-dimensional disordered systems, showing robustness at weak disorder and a breakdown at critical disorder strength, with implications for phase diagrams in various dimensions.

Contribution

It establishes the superuniversality of topological phase transitions in 3D disordered systems and constructs their global phase diagrams, including effects of disorder and higher dimensions.

Findings

Superuniversality holds at weak disorder strength.

Critical disorder strength causes breakdown of superuniversality.

Global phase diagrams feature a multicritical point where phases meet.

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 $d > 2$.