Topological switch between second-order topological insulators and topological crystalline insulators

Understand

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.
• We take examples of square nanodisks on the square lattice and hexagonal nanodisks on the triangular lattice.
• When inplane magnetic field is introduced parallel to one of the helical edges, the system becomes a TCI.