Two-dimensional anisotropic Dirac materials PtN4C2 and Pt2N8C6 with quantum spin and valley Hall effects

Abstract

We propose two different two-dimensional topological Dirac materials, planar ${\mathrm{PtN}}_{4}{\mathrm{C}}_{2}$ and ${\mathrm{Pt}}_{2}{\mathrm{N}}_{8}{\mathrm{C}}_{6}$, which exhibit graphenelike electronic structures with linearly dispersive Dirac-cone states exactly at the Fermi level. Moreover, the Dirac cone is anisotropic, resulting in anisotropic Fermi velocities and making it possible to realize orientation-dependent quantum devices. Using first-principles electronic structure calculations, we have systemically studied the structural, electronic, and topological properties. We find that spin-orbit coupling opens a sizable topological band gap so that the materials can be classified as quantum spin Hall insulators as well as quantum valley Hall insulators. Helical edge states that reside in the insulating band gap connecting the bulk conduction and valence bands are observed. Our work not only expands the Dirac-cone material family, but also provides another avenue to search for more two-dimensional topological quantum spin and valley Hall insulators.