A minimum single-band model for low-energy excitations in superconducting K${}_x$Fe${}_2$Se${}_2$

We propose a minimum single-band model for the newly discovered iron-based superconducting K${}_x$Fe${}_2$Se${}_2$. Our model is found to be numerically consistent with the five-orbital model at low energies. Based on our model and the random phase approximation, we study the spin fluctuation and the pairing symmetry of superconducting gap function. The $(\pi \mathrm{/}2,\pi \mathrm{/}2)$ spin excitation and the $d_{x^2-y^2}$ pairing symmetry are revealed. All of the results can well be understood in terms of the interplay between the Fermi surface topology and the local spin interaction, providing a sound picture to explain why the superconducting transition temperature is as high as to be comparable to those in pnictides and some cuprates. A common origin of superconductivity is elucidated for this compound and other high-T${}_c$ materials.