On the disorder-driven quantum transition in three-dimensional relativistic metals
On the disorder-driven quantum transition in three-dimensional relativistic metals
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三维相对论金属中无序驱动的量子跃迁
DOI：
10.1103/physrevb.94.220201
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发表时间：
2016
影响因子：
3.7
通讯作者：
A. A. Fedorenko
中科院分区：
文献类型：
--
作者：
Thibaud Louvet;D. Carpentier;A. A. Fedorenko
韦尔半金属在拓扑上受到保护，免受三维弱无序的间隙开口的影响。然而，强烈的无序性驱动这种相对论性半金属通过量子跃迁向扩散金属相转变，其特征在于带交叉处的状态密度有限。这种转变通常由 $U(N)$ Gross-Neveu 模型的 $d=2+\varepsilon$ 中的扰动重正化群在 $N \to 0$ 的限制下描述。不幸的是，这个模型在 $2+\varepsilon$ 维度上不能进行乘法重整化：需要无限数量的相关算子来描述关键行为。因此，它在对单环之外的转变的定量描述中的使用至少是值得怀疑的。我们提出了一条替代路线，建立在高能物理背景下开发的 Gross-Neveu 模型和 Gross-Neveu-Yukawa 模型之间的对应关系之上。它产生了一个具有随机非高斯虚势的 Weyl 费米子模型，该模型允许人们研究 $d=4-\varepsilon$ 展开中过渡的关键属性。我们还讨论了波函数的多重分形谱对跃迁的表征。
The Weyl semimetals are topologically protected from a gap opening against weak disorder in three dimensions. However, a strong disorder drives this relativistic semimetal through a quantum transition towards a diffusive metallic phase characterized by a finite density of states at the band crossing. This transition is usually described by a perturbative renormalization group in $d=2+\varepsilon$ of a $U(N)$ Gross-Neveu model in the limit $N \to 0$. Unfortunately, this model is not multiplicatively renormalizable in $2+\varepsilon$ dimensions: An infinite number of relevant operators are required to describe the critical behavior. Hence its use in a quantitative description of the transition beyond one-loop is at least questionable. We propose an alternative route, building on the correspondence between the Gross-Neveu and Gross-Neveu-Yukawa models developed in the context of high energy physics. It results in a model of Weyl fermions with a random non-Gaussian imaginary potential which allows one to study the critical properties of the transition within a $d=4-\varepsilon$ expansion. We also discuss the characterization of the transition by the multifractal spectrum of wave functions.