Topological node line semimetal state in two-dimensional tetragonal allotrope of Ge and Sn

Realizing semimetal states in two-dimensional (2D) materials are of great importance for their future application in novel quantum devices at the nanoscale. Using first-principles calculations based on density functional theory, we propose a new 2D tetragonal allotrope of Ge and Sn, 2D T-Ge and T-Sn, which consists of repeated square and octagon rings. The calculated cohesive energy, ab initio molecular dynamic simulations and phonon dispersions indicate that 2D T-Ge and T-Sn are stable at room temperature and possibly synthesized in the experiments under appropriate growth conditions. In the absence of spin–orbital coupling (SOC), 2D T-Ge and T-Sn are node line semimetals and the nodal loop in 2D T-Ge and T-Sn are protected by the combination of the spatial inversion P and time-reversal T symmetries. Remarkably, when SOC is included, 2D T-Ge and T-Sn are still node line semimetals although small gap is opened along the nodal loop, which are identified by nontrivial Z 2 invariant and topological edge states at the sample boundaries. Furthermore, our calculations show that node line semimetal states in 2D T-Ge and T-Sn are robust with the biaxial strains in the range of −3% to 3%. Our results provide a new 2D material platform for realization of 2D topological node line semimetals and innovative applications of topological node line semimetals.