Topological materials have attracted significant interest in condensed matter physics for their unique topological properties leading to potential technological applications. Topological nodal line semimetals, a subclass of topological materials, exhibit symmetry-protected nodal lines, where band crossings occur along closed curves in the three-dimensional Brillouin zone. When the nodal lines are gapped out due to perturbation in the Hamiltonian, a large Berry curvature (BC) arises in the surrounding area of the gapped nodal line, leading to exotic anomalous transport responses. In this paper, we studied the ${\mathrm{Co}}_2\mathrm{Cr}X$ ($X$=Ga, Ge) Heusler compounds that exhibit mirror symmetry-protected nodal line states below the Fermi level. The BC calculation yields anomalous Hall conductivity (AHC) of about 292 and 217 S/cm for ${\mathrm{Co}}_2\mathrm{Cr}X$ ($X$=Ga, Ge), respectively, at the Fermi level, which increases by up to 400% at the nodal line energy level. We theoretically analyzed that 20% and 60% zinc (Zn) alloying in ${\mathrm{Co}}_2\mathrm{Cr}X$ ($X$=Ga, Ge) effectively lowers the Fermi level by 50 meV and 330 meV, respectively, aligning with the protected crossings. Consequently, we identified ${\mathrm{Co}}_2{\mathrm{CrGe}}_{0.4}{\mathrm{Zn}}_{0.6}$ and ${\mathrm{Co}}_2{\mathrm{CrGa}}_{0.8}{\mathrm{Zn}}_{0.2}$ as compositions to achieve the significant AHC of 800 and 1300 S/cm, respectively. The explicit AHC calculation for these alloyed compositions is in good agreement with our predictions. Our findings highlight that chemical alloying is an efficient way to enhance AHC in nodal line hosting materials.

中文翻译：

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通过 Co2CrX(X=Ga, Ge) Heusler 化合物中的化学合金化调节节点线状态，以实现大的反常霍尔效应

拓扑材料因其独特的拓扑特性而引起了凝聚态物理学的极大兴趣，从而带来了潜在的技术应用。拓扑节点线半金属是拓扑材料的一个子类，表现出对称保护的节点线，其中能带交叉沿着三维布里渊区的闭合曲线发生。当节点线由于哈密顿量的扰动而出现间隙时，间隙节点线的周围区域会出现大的贝里曲率（BC），从而导致奇异的异常输运响应。在本文中，我们研究了${钴}_2\mathrm{铬}X$（$X$=Ga, Ge) Heusler 化合物，在费米能级以下表现出镜面对称保护的节线态。 BC 计算得出反常霍尔电导率 (AHC) 约为 292 和 217 S/cm${钴}_2\mathrm{铬}X$（$X$=Ga, Ge)，分别在费米能级，其在节线能级增加高达 400%。我们从理论上分析了 20% 和 60% 的锌 (Zn) 合金化${钴}_2\mathrm{铬}X$（$X$=Ga、Ge) 有效地将费米能级分别降低 50 meV 和 330 meV，与受保护的交叉点对齐。因此，我们确定了${钴}_2{\mathrm{铬锗}}_{0.4}{锌}_{0.6}$和${钴}_2{\mathrm{铬镓}}_{0.8}{锌}_{0.2}$作为分别实现800和1300 S/cm的显着AHC的组合物。这些合金成分的显式 AHC 计算与我们的预测非常一致。我们的研究结果强调，化学合金化是增强节点线承载材料中 AHC 的有效方法。