磁场中具有Rashba相互作用的周期结构
Periodic Structures with Rashba Interaction in Magnetic Field
摘要：
我们分析了存在磁场B的周期晶体上质点系的行为。这可以通过涉及周期势U（x）和耦合常数k_{so}的Rashba相互作用来完成。通过计算相应的谱，我们明确地确定了能带结构和Bloch旋量。这些使我们能够讨论系统的对称性方面的偏振，他们被证明是打破。动力学自旋将通过计算不同的量来研究。在极限：k_{so}和U（x）=0，我们再次分析系统，得出不同的结果。考虑到强$B$情形，我们得到了一个有趣的结果，即偏振守恒。通过对临界点λ_{k，σ}= \pm \sq{1\over 2}的分析，我们发现z方向上与谱相关的希尔伯特空间具有与石墨烯中无质量狄拉克费米子相似的零模能量.最后，我们给出了当B=0，U（x）为任意值时的能谱.
英文摘要：
We analyze the behaviour of a system of particles living on a periodic crystal in the presence of a magnetic field B. This can be done by involving a periodic potential U(x) and the Rashba interaction of coupling constant k_{so}. By resorting the corresponding spectrum, we explicitly determine the band structures and the Bloch spinors. These allow us to discuss the system symmetries in terms of the polarizations where they are shown to be broken. The dynamical spin will be studied by calculating different quantities. In the limits: k_{so} and U(x)=0, we analyze again the system by deriving different results. Considering the strong $B$ case, we obtain an interesting result that is the conservation of the polarizations. Analyzing the critical point λ_{k,σ}=\pm\sq{1\over 2}, we show that the Hilbert space associated to the spectrum in z-direction has a zero mode energy similar to that of massless Dirac fermions in graphene. Finally, we give the resulting energy spectrum when B=0 and U(x) is arbitrary.
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