Asymmetrically optimized structure in a high-T _c single unit-cell FeSe superconductor

We report asymmetric Se heights in a single unit-cell (UC) FeSe on SrTiO₃(0 0 1) substrate with the highest superconducting transition temperature (T _c) among the Fe-based superconductors revealed by total-reflection high-energy positron diffraction measurements. Among various iron-based superconductors, this single UC FeSe on the SrTiO₃(0 0 1) has been the best material to achieve the highest-T _c above 50 K. We found the asymmetric Se heights of 1.44  ±  0.03 and 1.33  ±  0.03 Å from the single Fe layer by the intensity analysis based on dynamical diffraction theory. The average Se height results in 1.39  ±  0.04 Å, corresponding to the optimum value for Fe-based superconductors. In addition, the average of bond angles of Se-Fe-Se, 107.2  ±  1.1 and 111.5  ±  1.2° becomes 109.3  ±  1.6°, which is close to the optimum value of 109.5° for a regular tetrahedron. Thus, this single UC FeSe is found to have asymmetrically optimized structure. Based on our first-principles calculations, the asymmetry does not change the bandwidth whereas it splits the electron bands at the M point only at the bottom. These calculations suggest that at low electron doping, the structural asymmetry is expected to lead to exotic properties of non-centrosymmetric superconductivity, whereas after a certain amount of electron doping, average anion height plays an important role for high-T _c.