We present a unifying framework that allows us to study the mixed crystalline-electromagnetic responses of topological semimetals in spatial dimensions up to D=3 through dimensional augmentation and reduction procedures. We show how this framework illuminates relations between the previously known topological semimetals and use it to identify a new class of quadrupolar nodal line semimetals for which we construct a lattice tight-binding Hamiltonian. We further utilize this framework to quantify a variety of mixed crystalline-electromagnetic responses, including several that have not previously been explored in existing literature, and show that the corresponding coefficients are universally proportional to weighted momentum-energy multipole moments of the nodal points (or lines) of the semimetal. We introduce lattice gauge fields that couple to the crystal momentum and describe how tools including the gradient expansion procedure, dimensional reduction, compactification, and the Kubo formula can be used to systematically derive these responses and their coefficients. We further substantiate these findings through analytical physical arguments, microscopic calculations, and explicit numerical simulations employing tight-binding models. Published by the American Physical Society 2024

中文翻译：

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半金属中的异常晶体电磁响应


我们提出了一个统一的框架，使我们能够通过维度增强和缩减程序研究拓扑半金属在高达 D=3 的空间维度上的混合晶电磁响应。我们展示了这个框架如何阐明先前已知的拓扑半金属之间的关系，并使用它来识别一类新的四极节点线半金属，我们为此构建了一个晶格紧束缚哈密顿量。我们进一步利用这个框架来量化各种混合晶电磁响应，包括一些以前在现有文献中未探讨过的响应，并表明相应的系数与半金属节点（或线）的加权动量-能量多极矩成正比。我们介绍了耦合于晶体动量的晶格规范场，并描述了如何使用包括梯度扩展程序、降维、压缩和 Kubo 公式在内的工具来系统地推导这些响应及其系数。我们通过分析物理论证、微观计算和采用紧密绑定模型的显式数值模拟进一步证实了这些发现。 美国物理学会 2024 年出版