论文标题
完全各向异性超导性，很少
Fully anisotropic superconductivity with few Helmholtz Fermi-surface harmonics
论文作者
论文摘要
我们提出了超导性的各向异性EliAshberg方程的替代表示，其数值解会在动量空间中的常规表示方面产生多个数量级的效率增长。我们的方法是对长期追求的方法的实用实现，其本质是从常规$ {\ bf k} $空间到一组定义为Fermi表面上Helmholtz方程的解决方案的线性转换。这样，问题的所有各向异性都可以用少数具有内置对称性的系数来描述。我们对MGB $ _2 $的差距各向异性进行基准计算，并以明显降低的计算成本重现了先前的结果。此外，我们应用方法来有效地确定压缩的YH $ _6 $ hydride的过渡温度，并与最近的实验测量获得了非常好的一致性。我们方法引入的简化实现了对超导材料的高通量探索，而无需诉诸于各向同性近似，并为最先进的超导性理论计算第一原则开辟了可能性。
We present an alternative representation for the anisotropic Eliashberg equations of superconductivity, whose numerical solution yields an efficiency gain of several orders of magnitude with respect to the conventional representation in momentum space. Our method is a practical realization of a long-sought approach, whose essence is a linear transformation from regular ${\bf k}$ space to a set of orthonormal functions defined as the solutions of the Helmholtz equation on the Fermi surface. In this way, all the anisotropy of the problem can be described by a handful of coefficients with built-in symmetry. We perform benchmark calculations on the gap anisotropy of MgB$_2$, and reproduce previous results at a remarkably reduced computational cost. Furthermore, we apply our methodology to efficiently determine the transition temperature of the compressed YH$_6$ hydride, obtaining very good agreement with recent experimental measurements. The simplification introduced by our method enables the high-throughput exploration of superconducting materials without having to resort to the isotropic approximation, and opens up possibilities towards first principles calculations of more advanced theories of superconductivity.
