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The one-parameter scaling theory of localization predicts that all states ina disordered two-dimensional system with broken time reversal symmetry arelocalized even in the presence of strong spin-orbit coupling. While at constantstrong magnetic fields this paradigm fails (recall quantum Hall effect), it isbelieved to hold at weak magnetic fields. Here we explore the nature of quantumstates at weak magnetic field and strongly fluctuating spin-orbit coupling,employing highly accurate numerical procedure based on level spacingdistribution and transfer matrix technique combined with finite-sizeone-parameter scaling hypothesis. Remarkably, the metallic phase, (known toexist at zero magnetic field), persists also at finite (albeit weak) magneticfields, and eventually crosses over into a critical phase, which has alreadybeen confirmed at high magnetic fields. A schematic phase diagram drawn in theenergy-magnetic field plane elucidates the occurrence of localized, metallicand critical phases. In addition, it is shown that nearest-level statistics isdetermined solely by the symmetry parameter $\beta$ and follows the Wignersurmise irrespective of whether states are metallic or critical.

Absence of Localization in Disordered Two Dimensional Electron Gas at Weak Magnetic Field and Strong Spin-Orbit Coupling