Topological Switch between Second-Order Topological Insulators and Topological Crystalline Insulators

We investigate a topological switch between second-order topological insulators (SOTIs) and topological crystalline insulators (TCIs). Both the SOTI and the TCI are protected by the mirror and inversion symmetries, for which we define the bulk topological numbers of the same type. When an in-plane magnetic field is introduced parallel to one of the helical edges, the system becomes a TCI. The conductance along the edge is 1 in the unit of the conductance quantum e^2/h. When it becomes orthogonal to a diagonal line, two topological corner states emerge on its vertices, and the system becomes a SOTI. This may be used as a basis of a topological circuit-changing switch. Alternatively, the device may be used as a sensor to measure local magnetization on a sample surface with a resolution of 10 nm.