论文标题
无限绑定状态和$ 1/n $的能量频谱在平坦带系统中的类型III的潜力引起
Infinite bound states and $1/n$ energy spectrum induced by a Coulomb-like potential of type III in a flat band system
论文作者
论文摘要
在这项工作中，我们在具有类似库仑的型III潜力的一维自旋-1平面系统中调查了绑定的状态，该系统具有唯一的非变化矩阵元素，基于$ | 1 \ rangle $。发现，对于这种潜力，存在着无限的结合状态。接近连续光谱的阈值，结合状态能与带有Rydberg校正的普通氢原子能级公式一致。此外，扁平频带对结合状态具有重大影响。例如，有一些无限结合的状态是从平坦带中产生的。此外，当电势较弱时，结合状态的能量与类似库仑的潜在强度$α$成正比。当绑定状态能量非常接近平坦频段时，它们与自然数$ n $成反比（例如，$ e_n \ propto 1/n，n = 1,2,3，... $）。此外，我们发现能量谱可以通过准古典近似（WKB方法）很好地描述。最后，我们给出了关键的潜在强度$α_c$，在该强度达到连续频谱的阈值，在该强度上。 \ textbf {越过阈值后，在这种平坦的频段系统中可能存在连续体（BIC）中的界状态。
In this work, we investigate the bound states in a one-dimensional spin-1 flat band system with a Coulomb-like potential of type III, which has a unique non-vanishing matrix element in basis $|1\rangle$. It is found that, for such a kind of potential, there exists infinite bound states. Near the threshold of continuous spectrum, the bound state energy is consistent with the ordinary hydrogen-like atom energy level formula with Rydberg correction. In addition, the flat band has significant effects on the bound states. For example, there are infinite bound states which are generated from the flat band. Furthermore, when the potential is weak, the bound state energy is proportional to the Coulomb-like potential strength $α$. When the bound state energies are very near the flat band, they are inversely proportional to the natural number $n$ (e.g., $E_n\propto 1/n, n=1,2,3,...$). Further we find that the energy spectrum can be well described by quasi-classical approximation (WKB method). Finally, we give a critical potential strength $α_c$ at which the bound state energy reaches the threshold of continuous spectrum. \textbf{After crossing the threshold, the bound states in the continuum (BIC) may exist in such a flat band system.
