Coexistence of type-I and type-II nodal lines in monolayer TiBF

Abstract

Topological nodal line semimetals with protected 1-D Fermi lines have continuously attracted great interest. In this study, based on first-principles calculations, we demonstrate that type-I and type-II nodal lines can coexist in the dynamically stable monolayer TiBF. Both types of nodal lines are protected by mirror symmetry in the absence of spin-orbital coupling. Besides, we find that the closed nodal lines can be effectively tuned by applying biaxial tensile strain. Interestingly, with a moderate compressive biaxial strain, a novel metal-semimetal-semiconductor phase transition can be induced, during which a 2-D double Weyl fermion emerges. The 2-D double Weyl fermion features a single Fermi point, where the conduction and the valence bands contact quadratically. We construct an effective Hamiltonian to characterize the 2-D double Weyl fermion. Additionally, we show that TiBX (X = Cl, Br, I) monolayers possess similar properties. Our findings show that the monolayer TiBF is a fascinating platform to investigate unique topological phases and that it demonstrates a great potential for nanoscale device applications.