An attractive critical point from weak antilocalization on fractals

TL;DR

This paper discovers a new attractive critical point in the Anderson localization flow on fractals, revealing a critical phase with scale-invariant conductance influenced by fractal geometry.

Contribution

It demonstrates the existence of an attractive critical point in symplectic models on fractals, extending the understanding of localization transitions to non-integer dimensional systems.

Findings

Identification of a new attractive critical point in fractal systems

Critical phase with scale-invariant conductance depending on fractal dimension

Verification of the $ ext{ε}$ expansion in disordered fractals

Abstract

We report a new attractive critical point occurring in the Anderson localization scaling flow of symplectic models on fractals. The scaling theory of Anderson localization predicts that in disordered symplectic two-dimensional systems weak antilocalization effects lead to a metal-insulator transition. This transition is characterized by a repulsive critical point above which the system becomes metallic. Fractals possess a non-integer scaling of conductance in the classical limit which can be continuously tuned by changing the fractal structure. We demonstrate that in disordered symplectic Hamiltonians defined on fractals with classical conductance scaling $g \sim L^{-\varepsilon}$, for $0 < \varepsilon < \beta_\mathrm{max} \approx 0.15$, the metallic phase is replaced by a critical phase with a scale invariant conductance dependent on the fractal dimensionality. Our results show that disordered fractals allow an explicit construction and verification of the $\varepsilon$ expansion.