Effective Doping and Suppression of Fermi Surface Reconstruction via Fe Vacancy Disorder in ${\mathbf{K}}_x{\mathrm{Fe}}_{2\mathbf{-}y}{\mathrm{Se}}_2$

We investigate the effect of disordered vacancies on the normal-state electronic structure of the newly discovered alkali-intercalated iron selenide superconductors. To this end, we use a recently developed Wannier function based method to calculate from first principles the configuration-averaged spectral function $⟨A(k,\omega )⟩$ of ${\mathrm{K}}_{0.8}{\mathrm{Fe}}_{1.6}{\mathrm{Se}}_2$ with disordered Fe and K vacancies. We find that the disorder can suppress the expected Fermi surface reconstruction without completely destroying the Fermi surface. More interestingly, the disorder effect raises the chemical potential significantly, giving enlarged electron pockets similar to highly doped ${\mathrm{KFe}}_2{\mathrm{Se}}_2$, without adding carriers to the system.

Figure 1

(a) An example of a large sized supercell used for the configurational average and (b) 1-Fe Brillouin zone. Band structure, density of states and Fermi surface of $\sqrt{5}\times \sqrt{5}$ ordered Fe and K vacancies (c), disordered ${\mathrm{K}}_{0.8}{\mathrm{Fe}}_{1.6}{\mathrm{Se}}_2$ (d) and ${\mathrm{KFe}}_2{\mathrm{Se}}_2$ (e). The dashed lines in the Fermi surface plots mark the 2-Fe Brillouin zone boundaries. The band structure and Fermi surface of the disordered ${\mathrm{K}}_{0.8}{\mathrm{Fe}}_{1.6}{\mathrm{Se}}_2$ are enhanced by a factor of 2 and 10 respectively for better visualization.

Figure 2

Spectral function obtained from disordered removal of Fe orbitals alone (without the impurity potentials) (a), and from the virtual crystal of the impurity potentials (without the removal of Fe orbitals). Both show negligible effective doping in comparison with the full disordered calculation. (c), (d) Illustration of microscopic mechanisms contributing to effective doping through broadening in frequency.

Figure 3

Disorder induced spectral weight distributions, represented in the 2-Fe Brillouin zone, (a) as a function of crystal momentum $k$ and orbital indices $n$, and at fixed crystal momenta $k_0$ and band index $j$ with (b) $k_0=0.8\mathrm{ZR}$ and $j=12$ belonging to the large electron pocket in the zone corner, (c) $k_0=0.5\mathrm{ZR}$ and $j=10$ belonging to the hole pocket leaking into the Fermi surface, (d) $k_0=0.5\mathrm{ZR}$ and $j=14$ displaying an incoherent satellite at the Fermi surface and (e) their integrations displaying $\sim 20\%$ loss of spectral weight due to the Fe vacancies.