Hund's coupling assisted orbital-selective superconductivity in Ba1-xKxFe2As2

TL;DR

This study investigates how Hund's coupling shapes orbital-selective superconductivity in $Ba_{1-x}K_xFe_2As_2$ by combining high-resolution ARPES and DFT calculations. It reveals a strongly orbital-dependent superconducting gap, with the $d_{xy}$ gap vanishing around $x \approx 0.53$ prior to a Lifshitz transition, while $d_{xz}$/$d_{yz}$ gaps persist, suggesting that pairing is governed more by orbital-selective correlations than by Fermi surface topology. Normal-state data show increasing $d_{xy}$ band renormalization and incoherence with hole-doping, consistent with Hund's coupling driving orbital-selective localization. Collectively, the results support orbital-selective pairing as a central mechanism in this multiorbital superconductor and have broader implications for other correlated, multiorbital superconductors.

Abstract

While the superconducting transition temperature of hole-doped Ba_{1-x}K_{x}Fe_{2}As_{2} decreases past optimal doping, superconductivity does not completely disappear even for the fully doped KFe_{2}As_{2} compound. In fact, superconductivity is robust through a Lifshitz transition where electron bands become hole-like around the zone corner at around x=0.7, thus challenging the conventional understanding of superconductivity in iron-based systems. High-resolution angle-resolved photoemission spectroscopy is used to investigate the superconducting gap structure, as well as the normal state electronic structure, around optimal doping and across the Lifshitz transition. Our findings reveal a largely orbital-dependent superconducting gap structure, where the more strongly correlated d_{xy} band has a vanishing superconducting gap at higher doping, aligning with the Hund's metal behavior observed in the normal state. Notably, the superconducting gap on the d_{xy} band disappears before the Lifshitz transition, suggesting that the Fermi surface topology may play a secondary role. We discuss how these results point to orbital-selective superconducting pairing and how strong correlations via Hund's coupling may shape superconducting gap structures in iron-based and other multiorbital superconductors.

Figures (5)

• Figure 1: Ba$_{1-x}$K$_x$Fe$_2$As$_2$ Fermiology. (a) Schematic of the Lishitz transition that takes place above optimal doping around the M point. Solid lines are fitted FS’, dotted line shows incipient FS. In the $\Gamma-X$ direction the orbital character is not well defined and thus is shown as a mix of red and green. Only two of the FSs around M are shown for simplicity, although the FS displays $C_4$ symmetry. (b) Spectrum of $x=0.41$ (left) and $x=0.78$ (right) in the $\Gamma-M$ direction, with renormalized DFT bands overlayed. (c) Experimental FS for dopings of $x=0.41$, $x=0.53$, $x=0.78$, $x=1.0$. The solid black line shows the Brillouin Zone.
• Figure 2: Superconductivity around$\boldsymbol{\Gamma}$. (a) Superconducting spectrum of $x=0.41$ in the $\Gamma-M$ direction. Green/blue dotted line shows where the Energy Distribution Curve (EDC) is taken for (g)/(h). Inset shows the experimental geometry for the spectrum cut with respect to the FS.(b)-(c) Same as (a) but for doping levels of $x=0.53$, $x=0.78$. (d) Schematic of cut direction on the FS for (f)-(h) spectrum. (f) Superconducting spectrum of $x=0.41$ in the $\Gamma-X$ direction. Inset shows the experimental geometry for the spectrum cut. (e)-(f) Same as (f) but for doping levels of x$=0.53$, $x=0.78$. (g) (left) EDCs at the at momentum indicated by the green and blue lines shown in (a)-(c) representing the $d_{yz}$(green) and $d_{xy}$(blue) bands, respectively. Dotted green/blue lines indicate EDCs for $T<T_C$, and solid lines are the superconducting gap fit. (right) Dotted lines show EDCs taken at $T>T_C$ at the same $k_F$, the solid lines overlaid are the fitted gap. There is no detecatable gap indicating the gap closes above $T_C$. The legend shows colors corresponding to doping levels of $x=0.41$, $x=0.53$, $x=0.78$. From the EDCs it is seen that the superconducting gap on the $d_{xy}$ band closes for doping levels of $x=0.53$ and above, while the gap persists on the $d_{yz}$ band for all doping levels. (h) Variation of the superconducting gap for all three doping levels as the azimuthal angle from $\Gamma-M$ towards $\Gamma-X$ is changed.
• Figure 3: Superconductivity around $\boldsymbol{M}$.(a) Spectrum of $x=0.41$ below $T_c$. Blue dotted line shows where the EDC is taken for (i). Inset schematic shows where the spectrum cut is taken with respect to the FS in an experimental geometry to maximize the signal of the $d_{xy}$ orbital around $M$. (b) Same as (a) but for $x=0.53$. (c) Same as (a)/(b) but for $x=0.78$. Inset shows the cut geometry again but shows the FS has changed through the Lifshitz transition at this doping. (d) Spectrum of $x=0.41$ below $T_c$ for a different experimental geometry. Inset shows where the spectrum cut is taken to maximize the signal of the $d_{xz}$ orbital around $M$. Red dotted line shows where the EDC is taken for (i). Inset schematic shows where the spectrum cut is taken with respect to the FS in an experimental geometry to maximize the signal of the $d_{xy}$ orbital. (e)-(f) Spectrum of $x=0.53$, and $x=0.78$ below $T_C$ at the spectrum cut indicated by (d). Red dotted line shows where the EDC is taken for (j). Inset in (f) shows the cut geometry again with the FS to emphasize the Lifshitz transition has occurred at this doping level. (g) (left) EDCs at the at momentum indicated by the red and blue lines shown in (a)-(f) representing the $d_{xz}$ (red) and $d_{xy}$ (blue) bands, respectively. Dotted red/blue lines indicate EDCs for $T<T_C$, and solid lines are the superconducting gap fit to the experimental data. (right) Dotted lines show EDCs taken at $T>T_C$ at the same $k_F$, with solid lines the showing no gap is open above $T_C$. Legend shows colors corresponding to doping levels of x = 0.41, x = 0.53, x = 0.78. While the gap on the $d_{xz}$ band stays open for all doping levels, the $d_{xy}$ gap closes for doping including and above $x=0.53$, similar to the behavior of the superconducting gap around $\Gamma$. (h) Gap size for all orbitals around $\Gamma$ and $M$ in the $\Gamma-M$ direction as a function of doping, demonstrating the orbital selective behavior of the superconducting gap. The $d_{yz}$ band around $M$ does not cross $E_F$ before the Lifshitz transition, so there are no markers for $d_{yz}$$M$ prior to $x=0.78$ doping.
• Figure 4: Temperature dependent incoherence and spectral weight transfer.(a) Background subtracted spectra at 40 K (left) and 100 K (right) for dopings of $x=0.41$ (top), $x=0.53$, $x=0.78$, $x=1.0$ (bottom) in the $\Gamma-M$ direction. The black lines in the first spectrum show the representative energy range around $E_F$ where the MDC is taken. (b) MDCs around $E_F$ at 40 K (solid) and 100 K (dotted) for all doping levels depicting the disappearing $d_{xy}$ hump as a function of temperature, most visibly for doping levels of $x=0.78$, and $x=1.0$, as well as the transfer of intensity from the $d_{xy}$ peak to the $d_{yz}$ with increasing doping.
• Figure 5: Scattering properties and phase diagram of 122 family.(a) Experimental FS for $x=0.41$, with the experimentally determined orbital character overlayed. The solid black line shows the Brillouin Zone, and the dotted purple line shows $s_{\pm}$ nodal lines . (Top left) The magnetic excitation $Q$ vector taken from PhysRevLett.107.177003 is shown placed starting at the largest gaps on the left side of the hole $\Gamma$$\alpha, \beta$ bands. (Bottom left) Same as above, but placed on the right side of the $\alpha, \beta$ pockets. (Top/bottom right) Same as left but for the $\gamma$$d_{xy}$ pocket (left/right) hand side FS. The scattering vector connects the $\alpha, \beta$ pockets with both electron pockets around $M$ fairly well, but is poorly connects the $\gamma$$d_{xy}$ FS. (b) Same as (a) but for doping of $x=0.53$, demonstrating scattering does not necessarily favor the $d_{xz/yz}$ pockets. (c) (Top) Cartoon global phase diagram of BaFe$_{2}$As$_{2}$ with electron and hole doping. Note that relative temperatures are not exactly to scale. (Bottom) Zoomed in phase diagram for a region of hole-doped Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$. Black dots correspond to left axis depicting the superconducting transition temperature. Dark blue dots correspond to $d_{xy}$ band effective mass on the right side axis. The bottom includes inset depictions of the gap structure for doping levels of $x=0.41$, $x=0.53$, $x=0.78$.