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Ruderman-Kittel-Kasuya-Yosida interaction in Weyl semimetals

机译：Weyl半金属中的Ruderman-Kittel-Kasuya-Yosida相互作用

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摘要

We theoretically demonstrate the Ruderman-Kittel-Kasuya-Yosida interaction between magnetic impurities that is mediated by the Weyl fermions embedded inside a three-dimensional Weyl semimetal (WSM). The WSM is characterized by a pair of Weyl points separated in the momentum space. Using the Green's function method and a two-band model, we show that four terms contribute to the magnetic impurity interaction in the WSM phase: the Heisenberg, Dzyaloshinsky-Moriya, spin-frustrated, and Ising terms. Except for the last term which is vanishingly small in the plane perpendicular to the line connecting two Weyl points, all the other interaction terms are finite. Furthermore, the magnetic spins of the Dzyaloshinsky-Moriya and spin-frustrated terms lie in the plane perpendicular to the line connecting two Weyl points, but in this plane, the magnetic spins of the Ising term have no components. For each contribution, an analytical expression is obtained, falling off with a spatial dependence as R~(-5) at Weyl points and showing beating behavior that depends on the direction between two magnetic impurities.
机译：我们从理论上证明了磁性杂质之间的Ruderman-Kittel-Kasuya-Yosida相互作用是由嵌入三维Weyl半金属（WSM）中的Weyl费米子介导的。 WSM的特点是在动量空间中有一对Weyl点。使用格林函数方法和两频带模型，我们证明了WSM相中的四个项对磁杂质相互作用有贡献：海森堡，Dzyaloshinsky-Moriya，自旋受阻和伊辛项。除了在垂直于连接两个Weyl点的线的平面中逐渐消失的最后一项之外，所有其他相互作用项都是有限的。此外，Dzyaloshinsky-Moriya的磁自旋和受挫的项位于与连接两个Weyl点的线垂直的平面中，但是在该平面中，Ising项的磁自旋没有分量。对于每个贡献，获得一个解析表达式，在We​​yl点处以R〜（-5）随空间变化而下降，并显示出取决于两种磁性杂质之间方向的跳动行为。

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