Topological and Quantum Stability of Low-Dimensional Crystalline Lattices with Multiple Nonequivalent Sublattices

The terms of topological and quantum stabilities of low-dimensional crystalline carbon lattices with multiple non-equivalent sublattices are coined based on theoretical analysis and multilevel simulations. It is demonstrated that some planar lattices are prone to symmetry breakdown caused by non-compensated deformations generated by non-equivalent sublattices. To impose the limitations on the periodic boundary conditions, the Topology Conservation Theorem is formulated and proved. It is shown that the lack of perfect filling of planar 2D active crystalline space by structural units may cause the formation of i) Structure waves; ii) Nanotubes or rolls; iii) Saddle structures; iv) Aperiodic ensembles of atomic clusters; v) Stabilization of 2D lattices by aromatic resonance, correlation effects, or interactions with substrates. For infinite structural waves, the quasiparticle approach is used to study the effect of quantum instability and periodicity breakdown with lattice restructuring. In contrast with infinite structural waves, perfect finite-sized waves can exist and can be synthesized. It is shown that for complex low-dimensional lattices which prone to breakdown the translation invariance (TI), complete active space of structural coordinates cannot be reduced to a subspace of TI coordinates. As a result, constrained TI minimization may artificially return a regular point at the potential energy surface as a global/local minimum/maximum. It is proved that for such lattices, phonon dispersion cannot be used as solid and final proof of the lattice stability. A flowchart algorithm for structural analysis of low-dimensional crystals is proposed and proved to be a powerful tool for theoretical design of advanced complex nanomaterials.Comment: Main body of the manuscript: 69 pages, 17 figures, 4 tables. SI1 section: 4 tables, 15 figures. SI2 section: 2 figure