We report characteristic vortex configurations in $s+id$ superconductors with time reversal symmetry breaking, exposed to magnetic field. A vortex in the $s+id$ state tends to have an opposite phase winding between $s-$ and $d-$wave condensates. We find that this peculiar feature together with the competition between $s-$ and $d-$wave symmetry results in three distinct classes of vortical configurations. When either $s-$ or $d-$ condensate absolutely dominates, vortices form a conventional lattice. However, when one condensate is relatively dominant, vortices organize in chains that exhibit skyrmionic character, separating the chiral components of the $s\pm id$ order parameter into domains within and outside the chain. Such skyrmionic chains are found stable even at high magnetic field. When $s-$ and $d-$ condensates have a comparable strength, vortices split cores in two chiral components to form full-fledged skyrmions, i.e. coreless topological structures with an integer topological charge, organized in a lattice. We provide characteristic magnetic field distributions of all states, enabling their identification in e.g. scanning Hall probe and scanning SQUID experiments. These unique vortex states are relevant for high-T${}_c$ cuprate and iron-based superconductors, where the relative strength of competing pairing symmetries is expected to be tuned by temperature and/or doping level, and can help distinguish $s+is$ and $s+id$ superconducting phases.

中文翻译：

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天体离子链和晶格ins + id超导体

我们在 $s+\mathrm{一世}d$具有时间反转对称性破坏的超导体，暴露于磁场中。漩涡$s+\mathrm{一世}d$ 状态趋向于在 $s-$ 和 $d-$波凝结。我们发现，这一独特功能与$s-$ 和 $d-$波对称性导致三种不同的涡旋构型。什么时候$s-$ 要么 $d-$冷凝水绝对占主导地位，涡流形成常规晶格。但是，当一种冷凝物相对占主导地位时，涡旋会组织成具有天体离子特征的链，从而将旋涡的手性成分分开。$s\pm \mathrm{一世}d$将参数排序到链内外的域中。发现即使在高磁场下，这种空中离子链也是稳定的。什么时候$s-$ 和 $d-$冷凝水具有可比的强度，涡旋将核分裂成两个手性组分，形成成熟的天空粒子，即无整数拓扑电荷的无核拓扑结构，以晶格组织。我们提供所有状态的特征性磁场分布，从而可以在扫描霍尔探头和扫描SQUID实验中识别它们。这些独特的涡旋状态与高T有关${}_C$ 铜酸盐和铁基超导体，其中竞争配对对称性的相对强度预计将通过温度和/或掺杂水平进行调整，并有助于区分 $s+\mathrm{一世}s$ 和 $s+\mathrm{一世}d$ 超导阶段。