我們在外爾半金屬(Weyl semimetal)中的研究雜質對掌性磁效應(chiral magnetic effect)的影響。在線性響應理論的框架之下，推廣了在乾淨的極限之下的二能 帶模型當中的關聯函數，加上了非交換圖以及交換圖的雜質修正對關聯函數的 影響，分別對應到費曼圖中費米子圈的頂角修正以及Cooperon修正。我們發現 除了和一般拓樸絕緣體當中電導係數的弱局域化(weal localization)與反弱局域 化(anti-weaklocalization)的現象的以外，雜質對於掌性磁效應存在Cooperon的 高階修正，使得局域化與反局域化的量子干涉行為更為顯著。我們的研究顯示，雖然在乾淨的極限之下，交流磁場引起的電流雖然存在，但是加入雜質後 掌性磁效應會被與自旋無關的雜質強烈地抑制。

We investigate the effect of disorders on the chiral magnetic effect (CME) in Weyl semimetals.
Based on a minimum two-band model of the Weyl semimetal, the disorder effect is examined
in the quantum diffusion limit by considering the correction to the CME coefficient due to
the Cooperon channel. It is shown that instead of making contribution through diffusive propagation, 1/(Q^2+1/\tau),
the contribution of Cooperon to the CME coefficient is governed by subdiffusive propagation, 1/(Q^4+1/\tau^2).
As a result, unlike the weak localization and weak antilocalization effects observed in surface states of topological insualtors, we find that
the CME coefficients manifest strong localization or strong anti-localization scalings depending on types of disorders.
Our results indicate that while the chiral magnetic current due to oscillating magnetic fields can
exist in clean systems, it will be strongly suppressed by scalar disorders.

1:Weyl semimetal p.7
1.1: Basic properties of Weyl semimetal p.7
1.2: Candidate materials and experimental realization p.9
1.3: Chiral anomaly p.9
2:Chiral magnetic effect of Weyl semimetal p.11
2.1: debate of existence of chiral magnetic effect p.11
2.2: two-band model and chiral magnetic effect p.13
2.3: result p.17
2.4: Diagramatic techniques on CME p.23
2.4.1:Calculation for vertex renormalization p.24
2.4.2:Calculation for Cooperon p.26
2.4.3:Calculation for Weight factor p.40

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