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

Abstract

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 timereversal 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.

Electronic Structures of Group III–V Element Haeckelite Compounds: A Novel Family of Semiconductors, Dirac Semimetals, and Topological Insulators

“…Being the 2D limit of haeckelite compounds with P4 2 /mnm space group, they exhibit a range of phases. For example, T-structures of single layers of pure Si and C behave as Dirac semimetal, [30,31] Ge and Sn as topological nodal line semimetals, [32,33] and P, As, Sb, and Bi as trivial band insulators. [34][35][36] On the other hand, T-structures of single or bilayers of III-V (AlN, GaN) [37,38] or VA-VA (SbBi, AsBi, PBi, AsSb, PAs) [39] element compounds are mostly semiconducting.…”

Impressive Thermoelectric Figure of Merit in Two-Dimensional Tetragonal Pnictogens: a Combined First-Principles and Machine-Learning Approach

“…19 Not only carbon, Si and Ge also form buckled tetragonal allotropes named tetragonal silicene and germanene. 20,21 These tetragonal forms also exhibit node-line semimetal with double Dirac cones. 22 On the other hand, research related to group-V elements got boosted after the synthesis of phosphorus thin films.…”

Tetragonal Silicene and Germanene Quantum Dots: Candidates for Enhanced Nonlinear Optical and Photocatalytic Activity

“…In 2012, Wang et al established the stability and electronic characteristics of the armchair and zigzag T-graphene nanoribbons . Besides, extensive research has revealed applications of T-graphene in various intriguing fields, such as in gas sensors, , hydrogen storage, , current rectification devices, and optoelectronic devices. − Similar to graphene, the hexagonal forms of Si and Ge are the next two stable candidates from the same group. − One of the major advantages of working with silicene and germanene is that considering the spin–orbit coupling effects, the zero-band-gap feature can be avoided. , Recently, the tetragonal counterparts of Si and Ge, i.e., T-Si and T-Ge, have been predicted to be stable on satisfying various stability criteria. − Contrary to planar T-graphene, T-Si and T-Ge possess semimetallic band structures with double Dirac cones. , To generate and tune the band gap in these tetragonal systems, several approaches have been taken. , Hence, relative to T-graphene, T-Si and T-Ge are expected to be better candidates for nanodevice applications.…”