Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA.
Phys Rev Lett. 2011 Mar 18;106(11):116803. doi: 10.1103/PhysRevLett.106.116803. Epub 2011 Mar 16.
A model of electrons hopping from atom to atom in graphene's honeycomb lattice gives low-energy electronic excitations that obey a relation formally identical to a 2+1 dimensional Dirac equation. Graphene's spin equivalent, "pseudospin," arises from the degeneracy introduced by the honeycomb lattice's two inequivalent atomic sites per unit cell. Previously it has been thought that the usual electron spin and the pseudospin indexing the graphene sublattice state are merely analogues. Here we show that the pseudospin is also a real angular momentum. This identification explains the suppression of electron backscattering in carbon nanotubes and the angular dependence of light absorption by graphene. Furthermore, it demonstrates that half-integer spin like that carried by the quarks and leptons can derive from hidden substructure, not of the particles themselves, but rather of the space in which these particles live.
在石墨烯的蜂窝晶格中，电子从一个原子跳跃到另一个原子的模型产生了低能电子激发，其遵循的关系在形式上与 2+1 维狄拉克方程完全相同。石墨烯的自旋等价物“赝自旋”源自单位胞内两个不等价的原子位置所引入的简并。此前人们认为通常的电子自旋和石墨烯子晶格状态的赝自旋索引只是类似物。在这里，我们表明赝自旋也是一种真实的角动量。这种识别解释了碳纳米管中电子背散射的抑制以及石墨烯对光吸收的角度依赖性。此外，它表明像夸克和轻子携带的半整数自旋可以源自隐藏的亚结构，而不是粒子本身，而是这些粒子所处的空间。
