Topological materials with both insulating and semimetal phases can be protected by crystalline (e.g., mirror) symmetry. The insulating phase, called a topological crystalline insulator (TCI), has been investigated intensively and observed in three-dimensional materials. However, the predicted two-dimensional (2D) materials with TCI phase are explored much less than 3D TCIs and 2D topological insulators, while the 2D TCIs considered thus far possess almost exclusively a square-lattice structure with the mirror Chern number ${\mathcal{C}}_M=-2$. Here, we predict theoretically that a hexagonal monolayer of Dirac semimetal ${\mathrm{Na}}_3\mathrm{Bi}$ is a 2D TCI with a mirror Chern number ${\mathcal{C}}_M=-1$. The large nontrivial gap of 0.31 eV is tunable and can be made much larger via strain engineering, while the topological phases are robust against strain, indicating a high possibility for room-temperature observation of quantized conductance. In addition, a nonzero spin Chern number ${\mathcal{C}}_S=-1$ is obtained, indicating the coexistence of a 2D topological insulator and a 2D TCI, i.e., the dual topological character. Remarkably, a spin-valley polarization is revealed in the ${\mathrm{Na}}_3\mathrm{Bi}$ monolayer due to the breaking of crystal inversion symmetry. The dual topological character is further explicitly confirmed via the unusual behavior of the edge states under the corresponding symmetry breaking.

• Received 4 November 2016

DOI:https://doi.org/10.1103/PhysRevB.95.075404