石墨烯虫洞：弯曲空间中狄拉克费米子的condensed matter图解
Graphene wormholes: A condensed matter illustration of Dirac fermions in curved space
摘要：
我们研究了石墨烯虫洞的性质，其中短纳米管作为两个石墨烯片之间的桥梁，其中蜂窝状碳晶格因存在12个七边形缺陷而弯曲。通过采取非常小的长度相比，半径的纳米管桥，我们开发了一个有效的狄拉克费米子理论来解释的低能量的电子特性的虫洞在连续极限，其中的挫折感生的七边形缺陷是模仿的虚拟规范通量线连接到他们每个人。我们特别发现，当拓扑缺陷的有效规范通量达到最大时，狄拉克方程的零能模可以被排列成两个三重态，这可以被认为是在大球形富勒烯的连续极限的对偶实例中出现的两个零模三重态的对应物。我们进一步研究了石墨烯虫洞光谱进行数值对角化的紧束缚哈密顿非常大的晶格实现虫洞几何。在数值方法中观察到的局域电子态的数量与在连续极限中预测的有效规范通量之间的对应关系表明，石墨烯虫洞可以一致地由虫洞的弯曲几何形状中的两个狄拉克费米子场的有效理论来描述，打开了使用碳材料的真实样品作为实验场地的可能性，曲率和狄拉克场
英文摘要：
We study the properties of graphene wormholes in which a short nanotube acts as a bridge between two graphene sheets, where the honeycomb carbon lattice is curved from the presence of 12 heptagonal defects. By taking the nanotube bridge with very small length compared to the radius, we develop an effective theory of Dirac fermions to account for the low-energy electronic properties of the wormholes in the continuum limit, where the frustration induced by the heptagonal defects is mimicked by a line of fictitious gauge flux attached to each of them. We find in particular that, when the effective gauge flux from the topological defects becomes maximal, the zero-energy modes of the Dirac equation can be arranged into two triplets, that can be thought as the counterpart of the two triplets of zero modes that arise in the dual instance of the continuum limit of large spherical fullerenes. We further investigate the graphene wormhole spectra by performing a numerical diagonalization of tight-binding hamiltonians for very large lattices realizing the wormhole geometry. The correspondence between the number of localized electronic states observed in the numerical approach and the effective gauge flux predicted in the continuum limit shows that graphene wormholes can be consistently described by an effective theory of two Dirac fermion fields in the curved geometry of the wormhole, opening the possibility of using real samples of the carbon material as a playground to experiment with the interaction between the background curvature and the Dirac fields.
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