Unconventional Rashba spin splitting and persistent spin helices based on SU(2) symmetry in PtSe$_2$ nanoribbons

Abstract

2D materials can host interesting physics and have important applications in various fields. Recent experiment shows that monolayer PtSe$_2$ nanoflakes with neutral zigzag edges are stable. Here, we study semiconducting stoichiometric PtSe$_2$ nanoribbons with the stable neutral zigzag edges (with $N$ describing different nanoribbon width) through combining detailed first-principles investigation with low-energy model analysis. Our careful analysis of first-principles conduction and valence bands (with the spin-orbits coupling taken into account) indicates that the low-energy bands assume relativistic energy dispersion in an energy window of [-0.2 eV, 0.2eV] (at least) and have large unconventional Rashba spin splitting (for even $N$). Furthermore, it is demonstrated that the low-energy bands can be well described by an effective one-dimensional electron model and the semiconductor gap will remain finite even for large $N$. Most importantly, it is shown that there exists SU(2) spin symmetry in both of the conduction and valence bands for each edge, which implies persistent spin helices (in the spin xy plane) and spin-conserving carrier transport. When the inter-edge interaction becomes weak ($N$ is large enough), a nearly-perfect Dirac fermion system can be achieved through combining the valence and conduction bands. Thus we realize unconventional Rashba splitting, double SU(2) spin symmetry, persistent spin helices/textures, and pure Dirac fermion systems in stable monolayer PtSe$_2$ nanoribbons.