Orbital-selective nature of the $3d$ electronic structure of the ThFeAsN superconductor

Based on local-density approximation plus dynamical mean-field theory ($\mathrm{LDA}+\mathrm{DMFT}$) calculations, we perform a comprehensive analysis of electronic structure reconstruction of the ThFeAsN superconductor, showing how the normal and $s$ wave superconducting spectra are reshaped by many-particle electron-electron interactions. Here, the ThFeAsN parent compound is described as an orbital-selective marginal Fermi liquid metal, with coexisting Fermi liquid quasiparticles and pseudogapped electronic states. Upon electron doping, an additional Kondo insulating state is predicted to exist in this system. Furthermore, we show how dynamical correlations strongly renormalize the bare Bogoliubov quasiparticles in the $s$ wave superconducting state into totally correlated lineshapes. These findings contribute to the microscopic understanding of the role played by dynamical multiorbital electronic correlations in the low energy spectrum relevant to unconventional Fe-based superconductors.

Figure 1

Crystal structure of tetragonal ThFeAsN superconductor (Fe red, As blue, Th light-blue, N green). The tetragonal coordination of Fe by As is represented as a red tetrahedron. Within a single layer, the square planar arrangement of Fe atoms is shown (orange connections). The tetragonal unit cell is drawn in gray.

Figure 2

LDA and $\mathrm{LDA}+\mathrm{DMFT}$ orbital resolved density-of-states (DOS) of a tetragonal ThFeAsN superconductor, showing spectral weight redistribution over large energy scales with increasing onsite Coulomb interaction $U$. While all orbitals are metallic at $U=2.5\mathrm{eV}$, orbital-selective localization within the $xy$ orbital sets in for $U=3.0\mathrm{eV}$. Particular interesting features to be seen are the peak-dip-hump within the $3z^2-r^2,xy,yz,x^2-y^2$ orbitals and the local moment (lower Hubbard band) formation in the $3z^2-r^2$ orbital at $U=3.5\mathrm{eV}$.

Figure 3

Orbital-resolved self-energies imaginary (main panels) and real (insets) parts of ThFeAsN parent compound, showing their evolution with increasing $U$ for fixed $J_H=0.7\mathrm{eV}$. Particular features seen are the particle-hole asymmetry and the almost perfect Fermi liquid $\left({\omega }^2\right)$ behavior of $Im{\mathrm{\Sigma }}_a\left(\omega \right)(a=3z^2-r^2,xz,yz{x}^2-y^2)$, suggesting the coexistence of itinerant electrons and nearly Mott localized electronic states with $xy$ orbital character in the unconventional electronic fluid of ThFeAsN. Also interesting is the frequency dependence of the self-energy real parts, showing orbital dependent electron correlation effects.

Figure 4

Low energy view of orbital resolved spectral functions of pure and electron-doped ThFeAsN. Notice the robustness of the $xy$ pseudogapped electronic state and the emergence of a Kondo insulating state with $3z^2-r^2$ orbital character upon increasing the total electron band filling of the Fe-$3d$ shell.

Figure 5

$T$ dependence of electrical resistivity (normalized at 300 K) for pure and electron-doped ThFeAsN, showing visible doping dependence below 100 K. Inset: theory-experiment comparison of resistivity versus temperature normalized to the experimental value at $T_c=30\mathrm{K}$ [11, 12]. Notice the good agreement between theory, experiment, and the fitting curve from 215 K down to $T_c$.

Figure 6

$xz,yz$ and total spectral functions in the single gap $s$-wave superconducting state [13] of a bulk ThFeAsN crystal, showing their evolution with changing the pair-field $\mathrm{\Delta }$ and fixed $n=6.4$ (main and right inset panels), and by enhancing the electron band filling with fixed $\mathrm{\Delta }=0.1\mathrm{eV}$ (left inset panel). Notice the particle-hole asymmetry and the nearly similar correlated spectral functions at low energies. Also noteworthy are the Bogoliubov quasiparticles obtained in the $U=0.0\mathrm{eV}$ limit, which are strongly reshaped due to dynamical spectral weight transfer induced by multiorbital electron interactions at energies above the $s$-wave superconducting gap.