Three-dimensional network model for strong topological insulator transitions

We construct a three-dimensional (3D), time-reversal symmetric generalization of the Chalker-Coddington network model for the integer quantum Hall transition. In addition to a weak topological insulator phase already accommodated by the network model framework in the preexisting literature, our network model hosts strong topological insulator phases. We unambiguously demonstrate that strong topological insulator phases emerge as intermediate phases between a trivial insulator phase and a weak topological phase. Additionally, we found a duality that relates a trivial insulator phase and a weak topological phase in our network model. Remarkably, strong topological phases are mapped to themselves under this duality. We show that upon adding sufficiently strong disorder, the strong topological insulator phases undergo phase transitions into a metallic phase. We numerically determine the critical exponent of the insulator-metal transition. Our network model explicitly shows how a semiclassical percolation picture of topological phase transitions in two dimensions can be generalized to 3D and opens up a venue for studying 3D topological phase transitions.