The major hindrances of implementing graphene in two-dimensional (2D) electronics are both mechanical (the tendency to crumble and form ripples) and electrical (the lack of a band gap). Moreover, the inevitable structural defects in graphene have a profound influence on its physical and chemical properties. Here, we propose a family of 2D egg-tray graphenes constructed by arranging pentagon and heptagon defects in the graphene lattice based on a careful analysis of the topological distribution of minima, maxima, and saddle points. First-principles calculations show that the egg-tray graphenes are dynamically stable, and their energies, which depend on the concentration of pentagons and heptagons, are the lowest among carbon allotropes. These 2D carbon allotropes exhibit a large variation in their electronic properties, ranging from semimetallic to semiconducting, including some allotropes that have Dirac cones in their band structures. Furthermore, some egg-tray graphenes are predicted to have negative Poisson’s ratios. The adsorption of Li atoms on the egg-tray graphenes is considerably stronger than the adsorption on perfect graphene, therefore they may absorb Li more effectively than graphene, which is important for improving the performance of rechargeable Li batteries.

在二维（2D）电子器件中实现石墨烯的主要障碍既是机械的（易碎并形成波纹的趋势）和电的（电气的）（缺乏带隙）。此外，石墨烯中不可避免的结构缺陷对其物理和化学性质具有深远的影响。在这里，我们通过仔细分析最小值，最大值和鞍点的拓扑分布，提出了通过在石墨烯晶格中排列五边形和七边形缺陷而构造的2D鸡蛋托盘石墨烯族。第一性原理计算表明，蛋盘中的石墨烯是动态稳定的，其能量（取决于五边形和七边形的浓度）是碳同素异形体中最低的。这些2D碳同素异形体在电子特性方面表现出很大的差异，范围从半金属到半导体，包括一些在其能带结构中具有狄拉克锥的同素异形体。此外，一些鸡蛋托盘石墨烯预计具有负的泊松比。蛋托盘石墨烯上的Li原子吸附比完全石墨烯上的Li吸附强得多，因此它们比Li石墨烯更有效地吸收Li，这对于提高可充电Li电池的性能很重要。