论文标题
无限结合的状态和由平坦带诱导的氢原子样能谱
Infinite bound states and hydrogen atom-like energy spectrum induced by a flat band
论文作者
论文摘要
在这项工作中，我们用平坦的频带研究了一维旋转1狄拉克·哈密顿尔顿尔顿尔顿尔顿的界限问题。发现平面对结合状态具有重大影响。例如，对于Dirac Delta潜在$Gδ（X）$，存在一个界面状态，即正面和负势强度$ G $。此外，当潜力较弱时，结合状态能量与潜在强度$ g $成正比。对于平方井的潜力，平坦带导致存在无限结合状态的任意弱潜力。此外，当结合状态的能量非常靠近平坦带时，能量将显示氢原子样光谱，即，界面的能量与自然数$ n $的平方成反比（例如，$ e_n \ propto 1/n^2，n^2，n = 1,2,3,3，... $）。上述大多数非平凡行为可以归因于扁平频段的一定密度及其随之而来的$ 1/z $的绿色功能。短势势和平坦带的组合为获得无限数量的结合状态和氢原子样能量谱提供了新的可能性。此外，我们的发现将为理解平面带的多体物理学提供一些有用的见解。
In this work, we investigate the bound state problem in one dimensional spin-1 Dirac Hamiltonian with a flat band. It is found that, the flat band has significant effects on the bound states. For example, for Dirac delta potential $gδ(x)$, there exists one bound state for both positive and negative potential strength $g$. Furthermore, when the potential is weak, the bound state energy is proportional to the potential strength $g$. For square well potential, the flat band results in the existence of infinite bound states for arbitrarily weak potential. In addition, when the bound state energy is very near the flat band, the energy displays hydrogen atom-like spectrum, i.e., the bound state energies are inversely proportional to the square of natural number $n$ (e.g., $E_n\propto 1/n^2, n=1,2,3,...$). Most of the above nontrivial behaviors can be attributed to the infinitely large density of states of flat band and its ensuing $1/z$ singularity of Green function. The combination of a short-ranged potential and flat band provides a new possibility to get infinite number of bound states and hydrogen atom-like energy spectrum. In addition, our findings would provide some useful insights in the understanding of many-body physics of flat band.
