Dynamics of Vacancy and Vacancy Lines Formation in Graphene for Qubit Arrays

Nitrogen-Vacancy (NV) in graphene can be used for making qubits. The generation of ordered vacancies (V) during sustained tensile strain of graphene can be done in a controlled fashion if the V generation dynamics is clarified. We report on the dynamics of formation of single V and V arrays in pristine graphene sheet under tensile load. To that end, we performed Molecular Dynamics for uniaxial loads using LAMMPS and AIREBO potential. First, we investigated AIREBO potential capability to accurately capture the interactions of carbon atoms in graphene. Various computing environments were tested, including Solo supercomputer at Sandia National Labs, Intel compilers and multi-cores x86 servers using GNU compilers. In order to obtain accurate graphene properties, we used atomic systems of about one million atoms. The carbon-based interactions in AIREBO are parameterized with cut-off function that truncates the potential energy between certain inner and outer cut-off interatomic distances. These values appeared to have major effects on calculated mechanical properties. For instance, improper cut-off values resulted in under or over coordination between atoms, which led to non-physical interactions and properties. Runs on Solo supercomputer with AIREBO “as is”, produced stress-strain curves of graphene similar to brittle materials, and mechanical properties very close to experimental data. These accurate results were obtained without modifying the inner C-C cut-off value of the AIREBO potential, unlike most published work [1]. Tensile tests run on Solo, on large samples with the right compilers gave accurate results, whereas runs on X86 servers led to the spurious high bond forces and non-linear reversible behavior, which is unphysical. The “as defined” AIREBO potential can properly describe the elastic and plastic regimes of graphene, which refutes the approach used in other work, where the cutoff function in AIREBO is adjusted. A distinct advantage in using the Intel compiler implemented on Solo appeared due to the much improved vectorization through SSE and AVX instructions. These enable high degrees of vectorization hence, better performances and maximum accuracy through the size of its registers for floating point number representation that considerably minimizes the propagation of round-off errors.<br/>For the first time, we could observe during the plastic regime, the complete dynamics of single V, V array and crack formation in pristine graphene. Note that published work on defect propagation in graphene started with defected graphene sheets [2]. MD simulation performed on Solo, allowed us to consistently observe the formation of single V then V array parallel to the pulling direction. Under the tensile load V cluster in vacancy lines (VL) defect. Each VL is bordered on one side with a single-atom Klein edge defect and on the opposite side with a zigzag edge. The first V appears at 4.2% strain as a result of stress of 35GPa in the pulling direction (// to the zigzag). The V line appears at 5.4% strain, at a stress of 44GPa with an average interval of 7 C-cycles (equal to 16A spacing). During subsequent loading a mirror defect image parallel to the original VL emerges and the graphene patch between two VLs keeps sliding through successive “zipping” and “unzipping” of the VLs. Subsequent load increase generates several vacancy line pairs.<br/>Ordered VL(s) in graphene are useful since doped with N, they form an array of coupled quantum dots. DFT showed that NV is a stable complex in N doped graphene. We also found that NV complex behaves as binary system and we have obtained the electron energy spectrum. The complex exhibited localized and delocalized states.<br/>[1] M. Dewapriya et al., Atomistic modeling of out-of-plane deformation of a propagating Griffith crack in graphene, Acta Mech. 228, 3063 (2017).<br/>[2] X. Sun et al., Effects of vacancy defect on the tensile behavior of graphene, Theo. & Appl. Mech. Let. 4, 051002 (2014).