An attractive critical point from weak antilocalization on 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 $g\sim L^{-\epsilon }$, for $0<\epsilon <{\beta }_{\max }\approx 0.15$, 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 $\epsilon$ expansion.

References in corpus (7)

• Anderson Transitions
• Transport and optical properties of an electron gas in a Sierpinski carpet
• Unconventional localisation transition in high dimensions
• Topology vs. Anderson localization: non-perturbative solutions in one dimension
• Effective field theory of the disordered Weyl semimetal
• Disorder-driven transition in a chain with power-law hopping
• Electronic shot noise in fractal conductors

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• Gapless Spin Liquid and Non-local Corner Excitation in the Spin-1/2 Heisenberg Antiferromagnet on Fractal
• Borel-Padé re-summation of the $\beta$-functions describing Anderson localisation in the Wigner-Dyson symmetry classes
• Linearized spectral decimation in fractals
• Resonant helical multi-edge transport in Sierpiński carpets