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.
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