论文标题
对称的Helmholtz Fermi-Surface谐波，用于在费米表面的各向异性数量的最佳表示：应用于电子问题
Symmetric Helmholtz Fermi-surface harmonics for an optimal representation of anisotropic quantities on the Fermi surface: Application to the electron-phonon problem
论文作者
论文摘要
我们概述了一个数值程序，将晶体对称性结合在Helmholtz Fermi-Surface谐波基集中，这是在费米表面定义的Helmholtz方程的解决方案。这种改进允许根据集合几乎没有对称元素在费米表面定义的各向异性数量的最佳表示。我们通过确定具有不同晶体结构的几个代表性系统的完全对称的Helmholtz Fermi-Surface Harmonics子集来证明我们的方法的一般有效性，即，FCC-CU，Hex-MGB $ _2 $和BCC-yh $ _6 $。此外，我们说明了应用于电子音波问题的方法的潜力，表明各向异性电子质量质量增强参数$λ_{\ bf k} $可以通过几种系数来表示高精度。这是一种有效的过滤器，为减少超导性，杂质问题或任何其他费米表面依赖性的金属的依赖性的数量级铺平了道路。
We outline a numerical procedure to incorporate the crystal symmetries in the Helmholtz Fermi-surface harmonics basis set, which are the solutions of the Helmholtz equation defined on the Fermi surface. This improvement allows for an optimal representation of anisotropic quantities defined on the Fermi surface in terms of few symmetric elements of the set. We demonstrate the general validity of our approach by identifying the fully symmetric Helmholtz Fermi-surface harmonics subset for several representative systems with different crystal structures, namely, FCC-Cu, HEX-MgB$_2$, and BCC-YH$_6$. Furthermore, we illustrate the potential of the method applied to the electron-phonon problem, showing that the anisotropic electron-phonon mass-enhancement parameter $λ_{\bf k}$ can be represented to high accuracy by a handful of coefficients. This works as an effective filter, paving the way for a reduction of several orders of magnitude in the computation of superconductivity, impurity problems, or any other Fermi surface dependent property of metals from first principles.
