Photoemission and muon spin relaxation spectroscopy of the iron-based Rb${}_{0.77}$Fe${}_{1.61}$Se${}_2$ superconductor: Crucial role of the cigar-shaped Fermi surface

In this study, we investigate the electronic and magnetic properties of Rb${}_{0.77}$Fe${}_{1.61}$Se${}_2$ ($T_{\mathrm{c}}$ $=$ 32.6 K) in normal and superconducting states by means of photoemission and $\mu$SR spectroscopies as well as band-structure calculations. We demonstrate that the unusual behavior of these materials is the result of separation into metallic ($\sim$$12\%$) and insulating ($\sim$$88\%$) phases. Only the former becomes superconducting and has a usual electronic structure of electron-doped FeSe slabs. Our results thus imply that the antiferromagnetic insulating phase is just a by-product of Rb intercalation and its magnetic properties have no direct relation to the superconductivity. Instead, we find that also in this class of iron-based compounds, the key ingredient for superconductivity is a certain proximity of a Van Hove singularity to the Fermi level.

Figure 1

Metal: (a,b) Fermi-surface maps measured with horizontal and vertical polarizations of the incoming light with photon energy of 80 eV. Dashed lines are the FS contours with weaker intensity. (c,e) Photoemission intensity along the cuts with $k_{\mathrm{x}}=0$Å${}^{-1}\mathrm{and}{k}_{\mathrm{x}}=1.1$Å${}^{-1}$ which are close to the PTP high-symmetry direction in the BZ. (d) Band structure of the stoichiometric ${\mathrm{RbFe}}_2{\mathrm{Se}}_2$ along the PTP direction for comparison with ARPES data. (f) The PTN section of the calculated Fermi surface of ${\mathrm{RbFe}}_2{\mathrm{Se}}_2$, chosen as most representative for comparison with ARPES data. $T$ point is located halfway between $\Gamma$and $Z$ points of the BZ. (g) Schematic top view of $\mathrm{FeSe}$ slabs with disordered iron vacancies. Large patches of FeSe without Fe vacancies are shown as shaded areas.

Figure 2

Insulator: (a) Paramagnetic volume fraction as determined by weak transverse field (5 mT) $\mu$SR. Note the magnetic transition at $T_{\mathrm{N}}$ $=$ 535 K and the residual fraction of 12% staying paramagnetic down to the lowest temperatures. The lines are guides to the eye only. (b) Zero-field $\mu$SR spectra recorded at 2 and 40 K. The long-lived oscillation proves a well defined internal magnetic field at the muon site indicating a long-range-ordered magnetic structure within the magnetic volume of the sample. The lines are fits to the data yielding internal magnetic fields (magnetic order parameters) at the muon site of 2.929(7) T and 2.937(7) T at 2 and 40 K, respectively. (c) Band structure of the antiferromagnetic band insulator ${\mathrm{Rb}}_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$. (d) Schematic top view of FeSe slabs with ordered iron vacancies. The 2D unit cell of ${\mathrm{Rb}}_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$ is shown.

Figure 3

Superconductor: (a,b) Photoemission intensity in the superconducting state along the cuts running through the center and the corner of the BZ respectively. (c) $k_{\mathrm{F}}$ EDC with the peak at 8-meV binding energy corresponding to the superconducting gap. (d) EDC dispersion of the electronlike states from panel (b) showing typical BCS bending-back behavior.

Figure 4

Key features of the electronic structure: (a)–(e) Results of the band-structure calculations for five different iron-based superconductors along the cuts through the center of the BZ. Bands are shown for ten different $k_{\mathrm{z}}$ values to emphasize the importance of $k_{\mathrm{z}}$dispersion. Equal weight is ascribed to each band. The places where the bands overlap are thus brighter according to the color scale used in Figs. 1 and 3. Fermi levels in these calculations are shifted for a better agreement with the experiments. (f) Sketch of the relevant features close to the Fermi level. (g)–(k) Corresponding Fermi surfaces. The red from outside Fermi surfaces are electronlike, the green from outside are hole-like. Electron- and holelike Fermi surfaces for K${}_x$Ba${}_{1-x}$Fe${}_2$As${}_2$ are shown separately. The irrelevant $d_{xy}$ bands for RbFe${}_2$Se${}_2$ and LiFeAs seen in (a) and (c) were omitted to allow view of the relevant features.