We formulate a Majorana mean-field theory for the extended JKΓ Kitaev model in a magnetic Zeeman field of arbitrary direction, and apply it for studying spatially inhomogeneous states harboring vortices. This mean-field theory is exact in the pure Kitaev limit and captures the essential physics throughout the Kitaev spin liquid phase. We determine the charge profile around vortices and the corresponding quadrupole tensor. The quadrupole-quadrupole interaction between distant vortices is shown to be either repulsive or attractive, depending on parameters. We predict that electrically biased scanning probe tips enable the creation of vortices at preselected positions. Our results paves the way for the electric manipulation of Ising anyons in Kitaev spin liquids.

我们为任意方向的塞曼磁场中的扩展J K Γ Kitaev 模型制定了马约拉纳平均场理论，并将其应用于研究包含涡旋的空间非均匀状态。这种平均场理论在纯基塔耶夫极限下是精确的，并捕获了整个基塔耶夫自旋液相的基本物理原理。我们确定涡旋周围的电荷分布和相应的四极张量。远距离涡旋之间的四极-四极相互作用被证明是排斥的或吸引的，具体取决于参数。我们预测电偏压扫描探针尖端能够在预选位置产生涡流。我们的结果为基塔耶夫自旋液体中伊辛任意子的电操纵铺平了道路。