The Lieb nano-ribons with the spin-orbit coupling, the lattice modulation and the magnetic field are exactly studied. They are constructed from the Lieb lattice with open boundaries in a direction. The interplay between the spin-orbit coupling, the lattice modulation and the magnetic field emerges various exotic ground states. With certain conditions of the spin-orbit coupling, the lattice modulation, the magnetic field and filling the ground state becomes half metallic or half topological. | Exotic states emerged by spin-orbit coupling, lattice modulation and magnetic field in lieb nano-ribbons
