Valley-contrasting physics in a two-dimensional px,y -orbital honeycomb lattice

In valley physics, large spin-orbit coupling (SOC) is the key, which is however rather weak for many materials with two-dimensional (2D) hexagonal honeycomb lattice. In contrast to conventional materials such as graphene with active ${p}_z$ orbitals, we proposed that large SOC splitting could be realized in ${p}_x,y$-orbitals active honeycomb lattice, i.e., the $XYH$ lattice. In particular, our model analysis confirmed that dynamically and magnetically induced valley polarizations are experimentally accessible. In accordance to the first-principles calculation and many-body perturbation theory, quaternary-layer ${\mathrm{BiSbC}}₃$ proves our proposed physics, with extremely large SOC splitting of 567.9 meV, excitonic energy difference of 496 meV for characteristic $A$ and $B$ excitons, and valley polarization of 168.7 meV by V doping.