Low-symmetrical Topological Graphene Metasurfaces with Quantum Valley and Spin Hall Effects

As topological phases in the physics of condensed matter have evolved over the last few years, topological photonics began to emerge and therefore attracted wide attention. Photonic crystals provide an excellent platform for the study of topological phenomena, combining the flexibly tuned symmetries of photonic crystals with the macroscopic properties of classical photonic systems. Graphene's special physical properties make it an excellent candidate for the realization of topological photonic systems at terahertz (THz) and mid-infrared (MIR) frequencies. Topological valley transport based on graphene plasmons was studied, as well as bilayer systems for valley and layer pseudospin studies. However, high point group symmetry topological systems have been the focus of most of the relevant studies to date. In this paper, it is shown for the first time that graphene plasmonic crystals with $C_{1v}$ symmetry are able to open the Dirac cone, leading to topological band gap. Subsequently, a domain-wall interface will be constructed and quantum valley Hall plasmons will be demonstrated in a monolayer graphene metasurface. In a graphene metasurface consisting of two layers, we also demonstrate quantum pseudospin Hall plasmons. Further exploration of the Dirac points protected by low-symmetry and their promising practical applications will be facilitated by the initial study and demonstration of the low-symmetric $C_{2v}$ and $C_{1v}$ point groups. Furthermore, this new low point group symmetry design principle is extendable to other classical waves.