论文标题
基于新型路径交换对称性的2D晶格中的孤立平坦带
Isolated flat bands in 2D lattices based on a novel path-exchange symmetry
论文作者
论文摘要
使用材料,光子晶格或冷原子来设计二维(2D)系统的能力提高的能力已导致搜索具有有趣属性的2D结构。这样的属性之一就是平坦带的存在。通常,这些存在需要长时间的跳跃,对最近的邻居跳跃的微调或通过使用单位单元格中交错的通量分布来破坏时间反转对称性。我们提供基于从父系统进行预测以生成不同平坦频段系统的处方。我们确定保持平坦度的条件,并在这样的系统中确定路径交换对称性,从而导致平坦频带与其他分散性频段变性。打破这种对称性会导致提升退化,同时仍然保持乐队的平坦度。正如文献早期所建议的那样,该技术不需要更改拓扑或破坏时间反转对称性。该处方还消除了对任何微调的需求。此外,结果表明,随后的投影系统继承了文献中针对类似系统讨论的精确微调条件,以便拥有并隔离平坦的频段。作为示例,我们证明了使用处方来达到诸如Kagome,Lieb和Dice Lattices之类的流行系统的平坦频段条件。最后,我们还能够证明,只有在与量规场相关联时,扁平频带才存在于最近提出的kagome晶格的手性旋转状态,该状态与量规场相关联时,它会产生Chern-Simons类型的通量调制。
The increased ability to engineer two-dimensional (2D) systems, either using materials, photonic lattices, or cold atoms, has led to the search for 2D structures with interesting properties. One such property is the presence of flat bands. Typically, the presence of these requires long-ranged hoppings, fine-tuning of nearest neighbor hoppings, or breaking time-reversal symmetry by using a staggered flux distribution in the unit cell. We provide a prescription based on carrying out projections from a parent system to generate different flat band systems. We identify the conditions for maintaining the flatness and identify a path-exchange symmetry in such systems that cause the flat band to be degenerate with the other dispersive ones. Breaking this symmetry leads to lifting the degeneracy while still preserving the flatness of the band. This technique does not require changing the topology nor breaking time-reversal symmetry as was suggested earlier in the literature. The prescription also eliminates the need for any fine-tuning. Moreover, it is shown that the subsequent projected systems inherit the precise fine-tuning conditions that were discussed in the literature for similar systems, in order to have and isolate a flat band. As examples, we demonstrate the use of our prescription to arrive at the flat band conditions for popular systems like the Kagome, the Lieb, and the Dice lattices. Finally, we are also able to show that a flat band exists in a recently proposed chiral spin-liquid state of the Kagome lattice only if it is associated with a gauge field that produces a flux modulation of the Chern-Simons type.