# Network model for 2D and 3D Z_{2} topological insulators and its relation to quantum walks

## Hideaki Obuse

### (Department of Applied Physics, Hokkaido University, Japan)

Time: Tue Sep 3 14:00:00 2013

Location: Building 1, Room 114, Auditorium

In this seminar, I propose an efficient theoretical model, so-called network model, describing the time-reversal Z_{2} topological insulators in two and three dimensions. The network model is defined on a network built up from links and nodes and each node contains two input links of Kramers pairs and two output links and is described by scattering matrices. Since symmetry of the system is easily tuned through the scattering matrices and geometry of input and output links, the network model is useful to study topological insulators/superconductors which heavily depend on symmetry.

To begin with, I explain the network model for the two-dimensional time-reversal Z_{2} topological insulator (quantum spin Hall insulator), then extend the model to the three-dimensional weak Z_{2} topological insulator. By using these network models, we study the Anderson transition of the topological insulators with strong disorder. We find that the universality class of the Anderson transition for these topological insulators are identical to those of the ordinary symplectic class.

In the seminar, I also explain the relation between the network model and the discreet-time quantum walk which is an emergent experimental setup to investigate various topological phases.