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We consider Anderson transitions in two-dimensional spinful electron gasessubject to random scalar potentials with time-reversal-symmetric spin-mixingtunneling (SMT) and spin-preserving tunneling (SPT) at potential saddle points(PSPs). A symplectic quantum network model, named as SMT-QNM, is constructed inwhich SMT and SPT have the same status and contribute independent tunnelingchannels rather than sharing a total-probability-fixed one. Two-dimensionalcontinuous Dirac Hamiltonian is then extracted out from this discrete networkmodel as the generator of certain unitary transformation. With the help ofhigh-accuracy numerics based on transfer matrix technique, finite-size analysison two-terminal conductance and normalized localization length provides a phasediagram drawn in the SMT-SPT plane. As a manifestation of symplectic ensembles,a normal-metal (NM) phase emerges between the quantum spin Hall (QSH) andnormal-insulator (NI) phases when SMT appears. We systematically analyze thequantum phases on the boundary and in the interior of the phase space.Particularly, the phase diagram is closely related to that of disorderedthree-dimensional weak topological insulators by appropriate parameter mapping.At last, if time-reversal symmetry in electron trajectories between PSPs isdestroyed, the system falls into unitary class with no more NM phase. A directSMT-driven transition from QSH to NI phases exists and can be explained byspin-flip backscattering between the degenerate doublets at the same sampleedge.

Spin-mixing-tunneling network model for Anderson transitions in two-dimensional disordered spinful electrons