标题： 平面涡旋对，彩色结构和低能狄拉克模态 显示英文标题

标题： Plane vortex pairs, colorful structures and low-lying Dirac modes

摘要： 我们研究了拓扑荷对单一单色平面涡旋对的不稳定零模和近零模的影响。 我们将单色平面涡旋与球面涡旋结合，并构建了由两个彩色涡旋组成的平面涡旋对。 分析了零模和近零模的稳定性，检查了费米子的各种边界条件。 此外，平面涡旋对可能显示出拓扑荷对改变费米子手性的角色。 结果清楚地表明了自发手性对称破缺的特征性质。 显示英文摘要

摘要： We investigate the influence of topological charges on non-stable zero and near-zero modes of the single uni-color plane vortex pairs. We combine the uni-color plane vortices with the spherical vortex and also construct the plane vortex pairs with two colorful vortices. The stability of zero and near-zero modes is analyzed where various boundary conditions for the fermions are checked. In addition, plane vortex pairs may show the role of the topological charges for changing the chirality of fermions. The results clearly indicate characteristic properties for spontaneous chiral symmetry breaking.