# Unusual Metal to Marginal-Metal Transition in Two-Dimensional Ferromagnetic Electron Gases

## TL;DR

This paper investigates the quantum criticality and phase transitions in two-dimensional ferromagnetic electron gases with disorder and spin-orbit interactions, revealing a novel marginal metal phase and unorthodox scaling laws.

## Contribution

It uncovers a new marginal metal phase with critical states and demonstrates unconventional scaling laws near quantum phase transitions in 2D ferromagnetic electron gases.

## Key findings

- Identification of a marginal metal phase with critical states
- Unusual exponential divergence of correlation lengths near transitions
- Universal fractal dimension of critical states D=1.90±0.02

## Abstract

Two-dimensional ferromagnetic electron gases subject to random scalar potentials and Rashba spin-orbit interactions exhibit a striking quantum criticality. As disorder strength $W$ increases, the systems undergo a transition from a normal diffusive metal consisting of extended states to a marginal metal consisting of critical states at a critical disorder $W_{c,1}$. Further increase of $W$, another transition from the marginal metal to an insulator occurs at $W_{c,2}$. Through highly accurate numerical procedures based on the recursive Green's function method and the exact diagonalization, we elucidate the nature of the quantum criticality and the properties of the pertinent states. The intrinsic conductances follow an unorthodox single-parameter scaling law: They collapse onto two branches of curves corresponding to diffusive metal phase and insulating phase with correlation lengths diverging exponentially as $\xi\propto\exp[\alpha/\sqrt{|W-W_c|}]$ near transition points. Finite-size analysis of inverse participation ratios reveals that the states within the critical regime $[W_{c,1},W_{c,2}]$ are fractals of a universal fractal dimension $D=1.90\pm0.02$ while those in metallic (insulating) regime spread over the whole system (localize) with $D=2$ ($D=0$). A phase diagram in the parameter space illuminates the occurrence and evolution of diffusive metals, marginal metals, and the Anderson insulators.