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

## TL;DR

This paper introduces a symplectic quantum network model for two-dimensional disordered spinful electrons, revealing a phase diagram with a normal-metal phase influenced by spin-mixing tunneling, and explores transitions between quantum phases.

## Contribution

The paper develops a novel SMT-QNM model that treats SMT and SPT as independent channels and links the phase diagram to disordered weak topological insulators.

## Key findings

- Normal-metal phase appears between QSH and NI phases with SMT.
- Phase diagram closely related to disordered 3D weak topological insulators.
- SMT-driven transition from QSH to NI when TRS is broken.

## Abstract

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