发表机构
Louisiana State University（路易斯安那州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
通过完整鞍点计算（含瞬子与涨落），解决了外尔半金属中零能态密度是否为零的争议，证明其在任意无序强度下有限，并与精确数值在四个数量级上吻合。
AI 中文摘要
文献中对于三维外尔半金属的节点是否能经受弱短程无序存在分歧：包含涨落的瞬子计算声称零能量态密度 $\rho(0)$ 消失，而精确数值计算则发现一个系统性的有限值。我们通过一个完整的鞍点计算（包括瞬子和涨落）解决了这一分歧。在无序的超对称形式中，瞬子满足非线性外尔方程，其解是一个精确的 $j=1/2$ 的刺猬构型，我们数值计算了其完整的泛函形式。然后我们计算了该鞍点周围的涨落，仔细识别了所有零模，并将约化超行列式计算为收敛的Fredholm行列式。除了一个Kramers双重态外，不存在其他费米零模，并且在有限无序 $w$ 下，涨落变为有限的一圈前置因子，$\rho(0)=\mathcal{A} w^{-4} \exp(-s^*/w^2)(1+O(w^2))$，在归一化单位下，对于高斯关联无序，$s^* = 6.4163(2)$ 和 $\mathcal{A} = 27.47(8)$。该表达式在四个数量级范围内与单个外尔锥上的精确数值计算吻合，且无任何拟合参数（振幅为单圈值的 $\times 0.76$），从而确立了态密度对于任何无序强度都是有限的。
英文摘要
There is disagreement in the literature concerning whether the nodal point of a three-dimensional Weyl semimetal survives weak short-range disorder: instanton calculations including fluctuations claim that the zero-energy density of states $ρ(0)$ vanishes, while exact numerics find a systematically finite number. We settle this disagreement with a full saddle-point calculation, including both instanton and fluctuations. Within the supersymmetric formulation for disorder, the instanton obeys a nonlinear Weyl equation whose solution is an exact $j=1/2$ hedgehog whose full functional form we numerically compute. We then compute the fluctuations about this saddle point, carefully identifying all zero modes, and computing the reduced superdeterminant as a convergent Fredholm determinant. No fermionic zero mode beyond a Kramers doublet exists, and at finite disorder $w$, the fluctuations become a finite one-loop prefactor, $ρ(0)=\mathcal{A} w^{-4} \exp(-s^*/w^2)(1+O(w^2))$, in normalized units with $s^* = 6.4163(2)$ and $\mathcal{A} = 27.47(8)$ for Gaussian-correlated disorder. This expression matches exact numerics on a single Weyl cone over four orders of magnitude with no fitted parameters (the amplitude is $\times 0.76$ the one-loop value), establishing that the density of states is finite for any disorder strength.
Comments21 pages, 5 figures, 2 tables
