Anisotropic vortex lattice structures in the FeSe superconductor

In the recent work by Song et al. [Science 332, 1410 (2011)], the scanning tunneling spectroscopy experiment in the stoichiometric FeSe reveals evidence for nodal superconductivity and strong anisotropy. The nodal structure can be explained with the extended s-wave pairing structure with the mixture of the $s_{x^2+y^2}$ and $s_{x^2{y}^2}$ pairing symmetries. We calculate the anisotropic vortex structure by using the self-consistent Bogoliubov-de Gennes mean-field theory. In considering the absence of magnetic ordering in the FeSe at the ambient pressure, orbital ordering is introduced, which breaks the $C_4$ lattice symmetry down to $C_2$, to explain the anisotropy in the vortex tunneling spectra.