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Spin-orbit related power-law dependence of the diffusive conductivity on the carrier density in disordered Rashba two-dimensional electron systems

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 two-dimensional electron system with Rashba spin-orbit coupling in the low-density region. 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).