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 ξ ∝ exp[α/ √ |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 ± 0.02 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.

By using the momentum-space Lanczos recursive method which considers rigorously all multiple-scattering events, we unveil that the non-perturbative disorder effect has dramatic impact on the charge transport of a twodimensional electron system with Rashba spin-orbit coupling in the low-density region. Surprisingly, our simulations find a power-law dependence of the dc longitudinal conductivity on the carrier density, with the exponent linearly dependent on the Rashba spin-orbit strength but independent of the disorder strength. Therefore, the classical charge transport influenced by complicated multiple-scattering processes also shows the characteristic feature of the spin-orbit coupling. This highly unconventional behavior is argued to be observable in systems with tunable carrier density and Rashba splitting, such as the LaAlO 3 /SrTiO 3 interface, the heterostructure of Rashba semiconductors bismuth tellurohalides and the surface alloy Bi x Pb y Sb 1−x−y /Ag(111).

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