势垒与势阱型静电相互作用下的Lieb晶格与赝自旋-1动力学
Lieb lattices and pseudospin-1 dynamics under barrier- and well-like electrostatic interactions
AI总结：
研究Lieb晶格在矩形静电势垒下的电子限域与散射，考虑各向异性跃迁与自旋轨道耦合，发现束缚态携带电流、存在超Klein隧穿及平带耦合导致的完美反射。
摘要：
本文研究了在矩形静电势垒影响下，Lieb晶格中电子的限域与散射现象。在该设定中，考虑了正交方向上最近邻之间的跃迁幅值不同，且次近邻相互作用描述了自旋轨道耦合。这使得限域电子并产生束缚态成为可能，对于平行于势垒的动量为零的情况，束缚态的精确数量被精确确定。在此情况下，证明了始终会产生一个偶宇称和一个奇宇称的束缚态，并且对于非零且逐渐增大的平行动量值，束缚态的数量随之增加。也就是说，束缚态能够携带电流。在散射区域中，确定了发生共振隧穿时的精确能量值。证明了无论能隙是否开启，以超Klein隧穿形式存在的完美隧穿能级始终存在。最后，表明当解与中间平带解耦合时，会出现完美反射。
英文摘要：
This work considers the confining and scattering phenomena of electrons in a Lieb lattice subjected to the influence of a rectangular electrostatic barrier. In this setup, hopping amplitudes between nearest neighbors in orthogonal directions are considered different, and the next-nearest neighbor interaction describes spin-orbit coupling. This makes it possible to confine electrons and generate bound states, the exact number of which is exactly determined for null parallel momentum to the barrier. In such a case, it is proved that one even and one odd bound state is always generated, and the number of bound states increases for non-null and increasing values of the parallel momentum. That is, bound states carry current. In the scattering regime, the exact values of energy are determined where the resonant tunneling occurs. The existence of perfect tunneling energy in the form of super-Klein tunneling is proved to exist regardless of the bang gap opening. Finally, it is shown that perfect reflection appears when solutions are coupled to the intermediate flat-band solution.
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