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 the parameters. We predict that electrically biased scanning probe tips enable the creation of vortices at preselected positions. Our results open new perspectives for the electric manipulation of Ising anyons in Kitaev spin liquids.

We provide all the data used for "Electric polarization near vortices in the extended Kitaev model" and a notebook used to produce the figures in the main text as well as in the supplementary material. Extract the "Files.zip" file in the same directory as the notebook. Total size 5.47 GB. Rename the folder to 'Files'.