屈曲类石墨烯材料中的分形蝴蝶
Fractal butterflies in buckled graphene-like materials
摘要：
本文从理论上研究了在强垂直磁场和周期势场中，硅烯和锗烯等类石墨烯材料的屈曲性质。我们分析了自旋轨道相互作用和垂直电场对这些体系能谱的影响。当以磁通量量子测量的周期势的晶胞中的磁通量为有理数时，？= p/q，则在每个朗道能级中，能谱具有能带结构，其特征在于相应的带隙。我们研究了这些间隙的依赖性上的参数的屈曲类石墨烯材料。虽然有些间隙对自旋-轨道耦合和外部电场的大小有弱的依赖性，但也有一些间隙对这些参数表现出强烈的非单调依赖性。为什麽？= 1/2时，自旋-轨道相互作用也在朗道能级之一处打开了一个能隙。带隙的大小随自旋-轨道耦合而增大，随外加电场而减小。
英文摘要：
We study theoretically the properties of buckled graphene-like materials, such as silicene and germanene, in a strong perpendicular magnetic field and a periodic potential. We analyze how the spin-orbit interaction and the perpendicular electric field influences the energy spectra of these systems. When the magnetic flux through a unit cell of the periodic potential measured in magnetic flux quantum is a rational number, ? = p/q, then in each Landau level the energy spectra have a band structure, which is characterized by the corresponding gaps. We study the dependence of those gaps on the parameters of the buckled graphene-like materials. Although some gaps have weak dependence on the magnitude of the spin-orbit coupling and the external electric field, there are gaps that show strong nonomonotic dependence on these parameters. For ? = 1/2, the spin-orbit interaction also opens up a gap at one of the Landau levels. The magnitude of the gap increases with spin-orbit coupling and decreases with the applied electric field.
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