发表机构
Universidad Técnica Federico Santa María（费德里科·圣玛丽亚技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究有限程跳跃对最大陈数的限制，通过代数方法确定第十一至第十三个近邻跳跃的最大陈数值，并提出几何设计原则，为高陈数能带和莫尔系统提供指导。
AI 中文摘要
有限程跳跃同时限制了狄拉克点的数量以及使它们产生能隙的质量。我们确定了正方晶格上Qi-Wu-Zhang模型的各向同性有限程扩展在直到第十三个近邻跳跃时的最大绝对陈数。代数零点计数和质量加权求和规则给出了全局界限，我们构造了达到这些界限的显式哈密顿量。我们发现第十一、十二和十三个近邻跳跃的最大陈数分别为|C|max=36,40,51。相等数量的狄拉克点可以产生不同的最大值，因为有限程质量谐波以不同方式区分相反涡旋电荷。两倍的跳跃半径平方限制了直到第十二个近邻跳跃的每个最大值，并在第十一和第十二个近邻跳跃时达到饱和，但第十三个近邻跳跃的最大值超过了该界限。因此，有限程跳跃通过两种互补方式限制最大陈数：通过它能产生的狄拉克涡旋数量以及通过它能分配给这些涡旋的质量符号模式。这种几何观点为高陈数能带提供了设计原则，并为莫尔超晶格及其他晶格系统中的类似界限提供了途径。
英文摘要
Finite-range hopping constrains both the number of Dirac points and the masses that gap them. We determine the maximal absolute Chern numbers of an isotropic finite-range extension of the Qi--Wu--Zhang model on a square lattice through thirteenth-neighbor hopping. Algebraic zero counting and mass-weighted sum rules yield global bounds, and we construct explicit Hamiltonians that saturate them. We find $|C|_{\max}=36,40,51$ for eleventh-, twelfth-, and thirteenth-neighbor hopping. Equal numbers of Dirac points can produce different maxima because finite-range mass harmonics distinguish opposite vortex charges differently. Twice the squared hopping radius bounds every maximum through twelfth-neighbor hopping and is saturated at the eleventh and twelfth, but the thirteenth-neighbor maximum exceeds it. Thus finite-range hopping constrains the maximal Chern number in two complementary ways: through the number of Dirac vortices it can generate and through the mass-sign patterns it can assign to them. This geometric viewpoint provides a design principle for high-Chern bands and a route to analogous bounds in moiré and other lattice systems.
Comments8 pages, 2 figures, SM as ancillary file
