AI 中文总结
研究汤川正则化石墨烯位错，引入汤川型正则化取代奇异顶点，得到相关精确表达式，呈现尺度相关拓扑电荷等，还研究了无质量狄拉克准粒子动力学，为研究类石墨烯系统几何和拓扑效应提供框架。
AI 中文摘要
锥形几何提供了位错的标准描述，但它们将曲率集中在一个奇异顶点。我们引入了一种汤川型正则化，它通过平滑的曲率分布取代了这种奇异性，同时保留了缺陷的渐近拓扑。得到了共形因子、曲率和封闭拓扑电荷的精确表达式。所得几何呈现出与尺度相关的拓扑电荷和相应的与半径相关的和乐，在分布式曲率和几何相位之间建立了直接联系。我们进一步研究了无质量狄拉克准粒子在此背景下的动力学，表明正则化核心修改了自旋联络，同时保留了缺陷的渐近拓扑特征。这些结果提供了传统锥形描述的有限核心扩展，并为研究类石墨烯系统中的几何和拓扑效应提供了一个自然框架。
英文摘要
Conical geometries provide the standard description of disclinations, but they concentrate the curvature at a singular apex. We introduce a Yukawa-type regularization that replaces this singularity by a smooth curvature distribution while preserving the asymptotic topology of the defect. Exact expressions are obtained for the conformal factor, curvature, and enclosed topological charge. The resulting geometry exhibits a scale-dependent topological charge and a corresponding radius-dependent holonomy, establishing a direct connection between distributed curvature and geometric phases. We further investigate the dynamics of massless Dirac quasiparticles in this background and show that the regularized core modifies the spin connection while preserving the asymptotic topological signature of the defect. These results provide a finite-core extension of the conventional conical description and offer a natural framework for studying geometric and topological effects in graphene-like systems.
