Enhancement of the Superconducting Gap by Nesting in ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$: A New High Temperature Superconductor

We use high resolution angle resolved photoemission spectroscopy and density functional theory with measured crystal structure parameters to study the electronic properties of ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$. In contrast to the related ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ compounds, ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ has a high $T_c$ of 35 K at stochiometric composition. This presents a unique opportunity to study the properties of high temperature superconductivity in the iron arsenides in the absence of doping or substitution. The Fermi surface consists of several hole and electron pockets that have a range of diameters. We find that the values of the superconducting gap are nearly isotropic (within the explored portions of the Brillouin zone), but are significantly different for each of the Fermi surface (FS) sheets. Most importantly, we find that the momentum dependence of the gap magnitude plotted across the entire Brillouin zone displays a strong deviation from the simple $\cos (k_x)\cos (k_y)$ functional form of the gap function, proposed by the scenario of Cooper pairing driven by a short range antiferromagnetic exchange interaction. Instead, the maximum value of the gap is observed on FS sheets that are closest to the ideal nesting condition, in contrast to previous observations in other ferropnictides. These results provide strong support for the multiband character of superconductivity in ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$, in which Cooper pairing forms on the electron and the hole bands interacting via a dominant interband repulsive interaction, enhanced by band nesting.

Figure 1

Measured electronic structure of ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$. (a) Fermi surface (FS) intensity acquired using photon energy of 6.7 eV at $T=40\mathrm{K}$. (b) Sketch of the FS based on data in (a). (c) Measured ARPES intensity along a cut through the $\mathrm{\Gamma }$ point. Cut position is indicated in panel (b). (d) Sketch of the band structure based on data in (c). (e)–(h) Same as (a)–(d), but measured using a photon energy of 21.2 eV. Dashed lines in (b) and (d) mark the expected parts of the bands and FS that are not observed due to matrix elements and limited access to Brillouin zone at low photon energy.

Figure 2

(a) Calculated 3D Fermi surface of ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ (b) Band dispersion along the key symmetry directions with respective orbital contributions marked by color-coded outlines.

Figure 3

(a)–(d) Measured electronic structure at four selected temperatures along the cut indicated in (l). The data is divided by the Fermi-Dirac function. (e) Energy Distributed Curves (EDCs) at $k_F$ of $\beta$ FS pocket. (f) The data from panel (e) after symmetrization. (g)–(i) Symmetrized EDCs at $k_F$ of $\alpha$, $\gamma$, and $\delta$ FS pockets, respectively. ${\mathrm{k}}_F$ positions are marked in (l). (j) Symmetrized EDCs at $k_F$ for lowest measured temperature from (f)–(i). Red, vertical dashed lines mark the energy of largest gap ($\beta$ FS sheet). The black lines are the fits using phenomenological model [33]. (k) Temperature dependence of the superconducting gaps for all four pockets. Solid lines are BCS predictions for ${\mathrm{\Delta }}_0$ of 10.5 meV, 13 meV, 8 meV, and 12 meV. (l) Sketch of the FS with indication of the cut position and $k_F$ positions.

Figure 4

Momentum-dependent superconducting gap. (a)–(b) Symmetrized EDCs at different $k_F$ on the $\beta$ and $\delta$ FS pockets. (c) Extracted superconducting gap from EDCs in (a) and (b). The $\mathrm{\Gamma }\text{−}X$ direction is set to 0 degree. (d) $k_z$ dependence of superconducting gap on the $\beta$ FS pocket. Data were taken with a photon energy of 5.7 eV, 6.2 eV, and 6.7 eV. Data in (a)–(d) were taken at 22 K. (e) Plot of the extracted gap on four FS sheets in Fig. 3 versus momentum distance from $\mathrm{\Gamma }$. The black dashed line is a fit with the function $\mathrm{\Delta }|\cos k_x\cos k_y|$, $\mathrm{\Delta }=16\mathrm{meV}$. (f) Measured diameters of four Fermi pockets.