Two-dimensional (2D) materials with planar hypercoordinate motifs are extremely rare due to the difficulty in stabilizing the planar hypercoordinate configurations in extended systems. Furthermore, such exotic motifs are often unstable. We predict a novel Cu2Si 2D monolayer featuring planar hexacoordinate copper and planar hexacoordinate silicon. This is a global minimum in 2D space which displays reduced dimensionality and rule-breaking chemical bonding. This system has been studied with density functional theory, including molecular dynamics simulations and electronic structure calculations. Bond order analysis and partitioning reveals 4c-2e σ bonds that stabilize the two-dimensional structure. We find that the system is quite stable during short annealing simulations up to 900 K, and predict that it is a nonmagnetic metal. This work opens up a new branch of hypercoordinate two-dimensional materials for study.

We discover unusual chemical bonding in a novel planar hyper-coordinate Ni2Ge free-standing 2D monolayer, and also in a nearly planar slightly buckled Ni2Si monolayer. This unusual bonding is revealed by Solid State Adaptive Natural Density Partitioning analysis. This analysis shows that a new type of 2c-2e Ni-Si σ and 3c-2e Ni-Ge-Ni σ bonds stabilize these 2D crystals. This is completely different from any previously known 2D crystals. Both of these free-standing monolayers are global minima in two-dimensional space. Although their exotic structure has unprecedented chemical bonding, they show extraordinary stability as single layers. The stabilities of these frameworks are confirmed by phonon dispersion calculations and ab initio molecular dynamics calculations. For Ni2Si, the framework was maintained during short 10 ps molecular dynamics annealing up to 1500 K, while Ni2Ge survived 10 ps runs up to 900 K. Both systems are predicted to be non-magnetic and metallic. As these new 2D crystals contain hypercoordinated Group 14 atoms, they are examples of a new class of 2D crystals with unconventional chemical bonding and potentially exciting new properties. Interestingly, we find that the stabilities of Ni2Si and Ni2Ge are much higher than that of silicene and germanene. Thus, this work provides a novel way to stabilize 2D sheets of Group 14 elements.

We theoretically demonstrate features of Anderson localization in the Tonks-Girardeau gas confined in one-dimensional (1D) potentials with controlled disorder. That is, we investigate the evolution of the single particle density and correlations of a Tonks-Girardeau wave packet in such disordered potentials. The wave packet is initially trapped, the trap is suddenly turned off, and after some time the system evolves into a localized steady state due to Anderson localization. The density tails of the steady state decay exponentially, while the coherence in these tails increases. The latter phenomenon corresponds to the same effect found in incoherent optical solitons.

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