Zhang Yi-Cai
School of Physics and Materials Science, Guangzhou University, Guangzhou, 510006, People's Republic of China.
Sci Rep. 2022 Jul 8;12(1):11670. doi: 10.1038/s41598-022-15860-w.
In this work, we investigate the bound states in the continuum (BIC) of a one-dimensional spin-1 flat band system. It is found that, when the potential is sufficiently strong, there exists an effective attractive potential well surrounded by infinitely high self-sustained barriers. Consequently, there exist some BIC in the effective potential well. These bound states are protected by the infinitely high potential barriers, which could not decay into the continuum. Taking a long-ranged Coulomb potential and a short-ranged exponential potential as two examples, the bound state energies are obtained. For a Coulomb potential, there exists a series of critical potential strengths, near which the bound state energy can go to infinity. For a sufficiently strong exponential potential, there exist two different bound states with a same number of wave function nodes. The existence of BIC protected by the self-sustained potential barriers is quite a universal phenomenon in the flat band system under a strong potential. A necessary condition for the existence of BIC is that the maximum of potential is larger than two times band gap.
在这项工作中，我们研究了一维自旋-1平带系统中的连续域束缚态（BIC）。结果发现，当势足够强时，存在一个有效的吸引势阱，其周围环绕着无限高的自持势垒。因此，在有效势阱中存在一些BIC。这些束缚态受到无限高势垒的保护，不会衰减到连续域中。以长程库仑势和短程指数势为例，得到了束缚态能量。对于库仑势，存在一系列临界势强度，在其附近束缚态能量可以趋于无穷大。对于足够强的指数势，存在两个具有相同波函数节点数的不同束缚态。由自持势垒保护的BIC的存在在强势下的平带系统中是一种相当普遍的现象。BIC存在的一个必要条件是势的最大值大于两倍的带隙。
