Fractal Confinement and Magnetic Self-sabotage of Current Flow: Electrons Near the Metal-insulator Crossover in a 2D $δ$-layer

Abstract

We study low-$T$ transport and itinerant magnetism in 2D $δ$-doped semiconductors. Large-scale Hartree-Fock calculations with random hoppings and repulsion $U_0$ reveal two transport regimes near a critical density. The conductivity $σ(T)$ initially increases as $T$ drops below $U_0 / 10$. However, at $T \sim U_0/100$, a tiny density of magnetic moments forms, driving an insulating downturn. Fractal wavefunctions locally amplify magnetic interactions, initially concentrating currents into branched filaments, but ultimately choking them off via dynamic SU(2) symmetry breaking.