Band Structure and Fermi Surface of an Extremely Overdoped Iron-Based Superconductor ${\mathrm{KFe}}_2{\mathrm{As}}_2$

We have performed high-resolution angle-resolved photoemission spectroscopy on heavily overdoped ${\mathrm{KFe}}_2{\mathrm{As}}_2$ (transition temperature $T_c=3\mathrm{K}$). We observed several renormalized bands near the Fermi level with a renormalization factor of 2–4. While the Fermi surface around the Brillouin-zone center is qualitatively similar to that of optimally doped ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ ($x=0.4$; $T_c=37\mathrm{K}$), the Fermi surface topology around the zone corner ($M$ point) is markedly different: the two electron Fermi surface pockets are completely absent due to an excess of hole doping. This result indicates that the electronic states around the $M$ point play an important role in the high-$T_c$ superconductivity of ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ and suggests that the interband scattering via the antiferromagnetic wave vector essentially controls the $T_c$ value in the overdoped region.

Figure 1

ARPES spectra near $E_F$ of ${\mathrm{KFe}}_2{\mathrm{As}}_2$ ($T_c=3\mathrm{K}$) measured at 15 K with the He $I\alpha$ line along two high-symmetry lines (a) $\Gamma X$ and (b) $\Gamma M$. (c) and (d) ARPES-intensity plots as a function of wave vector and binding energy along the $\Gamma X$ and $\Gamma M$ lines, respectively, together with the band dispersion from the LDA calculations for $k_z=0$ and $\pi$ (blue and red curves, respectively). Calculated bands for ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ [20] are shifted upward by 200 meV and then renormalized by a factor of 2.

Figure 2

(a) ARPES-intensity plot at $E_F$ of ${\mathrm{KFe}}_2{\mathrm{As}}_2$ as a function of the two-dimensional wave vector measured at 15 K. The intensity at $E_F$ is obtained by integrating the spectra within $\pm 10\mathrm{meV}$ with respect to $E_F$. (b) Representative ARPES-intensity plots in the vicinity of $E_F$ as a function of binding energy and wave vector measured along cuts 1–6 indicated by green lines in (a). Blue dashed lines are guides for the eyes to trace the band dispersion. The black dashed line indicates the momentum on the $\Gamma M$ line.

Figure 3

(a) Comparison of experimentally determined $k_F$ points between overdoped ${\mathrm{KFe}}_2{\mathrm{As}}_2$ ($T_c=3\mathrm{K}$) and optimally doped ${\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}{\mathrm{Fe}}_2{\mathrm{As}}_2$ ($T_c=37\mathrm{K}$) [6] (blue and red circles, respectively). The $k_F$ points are symmetrized by assuming a fourfold symmetry with respect to the $\Gamma$ and $M$ points. (b) Experimental band dispersion in the vicinity of $E_F$ for two high-symmetry lines determined by tracing the peak position of the ARPES spectra. The chemical potential of the K1.0 sample is shifted downward with respect to that of the K0.4 sample.

Figure 4

Schematic view of the interband scattering by the AF wave vector $Q_{\mathrm{AF}}$ between the hole and electron bands (the $\alpha$ and $\gamma$ bands) centered at $\Gamma$ and $M$ points, respectively. The interband scattering is markedly suppressed in the overdoped region due to the absence of the electron FSs at $M$.