The absence of nesting between electron and hole pockets in LiFeAs with $T_{\mathrm{c}}=18$ K attracts great attention, as an important hint to understand the pairing mechanism of Fe-based superconductors. Here, we study the five-orbital model of LiFeAs based on the recently developed orbital-spin fluctuation theories. It is found that the experimentally observed gap structure of LiFeAs, which is a “fingerprint” of the pairing mechanism, is quantitatively reproduced in terms of the orbital-fluctuation-mediated $s_{++}$-wave state. Specifically, the largest gap observed on the two small hole pockets composed of ($d_{xz},d_{yz}$) orbitals can be explained, and this is a hallmark of the orbital-fluctuation-mediated superconductivity. The $s_{++}$-wave gap structure becomes more anisotropic in the presence of weak spin fluctuations. As the spin fluctuations increase, we obtain the “hole-$s_{\pm }$-wave state,” in which only the gap of the large hole pocket made of the $d_{xy}$ orbital is sign reversed, due to the cooperation of orbital and spin fluctuations. This gap structure with “sign reversal between hole pockets” is similar to that recently reported in $(\mathrm{Ba},\mathrm{K}){\mathrm{Fe}}_2{\mathrm{As}}_2$.

• Received 11 February 2014
• Revised 1 May 2014

DOI:https://doi.org/10.1103/PhysRevB.90.035104