Spin-valley polarized edge states in quasi-one-dimensional asymmetric kagome lattice

The spin-valley-related electronic properties of quasi-one-dimensional kagome lattices with intrinsic spin-orbit coupling are studied, based on the tight-binding formalism. Three types of kagome-lattice nanoribbons along the x-direction with various geometric boundaries are proposed, including two symmetric nanoribbons and one asymmetric one. It is found that two nonequivalent Dirac cones and helical edge states exist in all the three types of kagome-lattice nanoribbons at 1/3 filling. Among them in the asymmetric nanoribbon, the spin and valley are found to be locked to each other due to inversion symmetry breaking, resulting in spin-valley polarized edge states. Band structure and probability density of wave function show that the spin-up/-down edge states locate at the K/K′ valley, with opposite propagation direction at the upper and lower boundaries. Spin-resolved real-space local current confirms the spin-valley polarized helical edge state in the asymmetric nanoribbon. The device application of the asymmetric kagome-lattice nanoribbon is worth further investigation.