The manipulation of layer-coupled chiral edge states by interlayer interactions in Janus RuClX (X = F, Br) bilayers

The weak interlayer van der Waals (vdW) interactions in two-dimensional layered materials allow the layer degrees of freedom to be used as a quantum index and couple with the charge or spin of electrons, leading to quantum layertronics. In our work, we investigate the layer-coupled topological properties in RuClX (X = F, Br) bilayers through strain-engineering and interlayer interactions. Multiple stacking patterns could be achieved by interlayer sliding and stacking orders with different interfaces. By the first-principles calculations, two stacking patterns from RuClF and RuClBr bilayers could be confirmed to be stable by the interlayer antiferromagnetic order. Our results reveal that the interlayer interactions in RuClF bilayers are much stronger than that in RuClBr bilayers, which indicates RuClX bilayers could behave as a promising platform to engineering the edge states. In the RuClBr bilayer, the negligible hybridization between the states from top and bottom layer results in the strain-induced quantum layer-spin-Hall effect (QLSHE) with quantized spin Hall conductivity and two opposite propagating chiral edge states coupled with each layer. However, in the RuClF bilayer, the unnegligible interlayer hybridization will induce the quantum anomalous Hall effect with one chiral edge state. By the tensile strain effect, a hybrid QLSHE will be emerged as the band inversion appeared in the Janus RuClF bilayer. Our work demonstrates that magnetic vdW layered materials could exhibit rich physical properties, which promise future applications in quantum layertronics.