${\mathrm{NaFe}}_{0.56}{\mathrm{Cu}}_{0.44}\mathrm{As}$: A Pnictide Insulating Phase Induced by On-Site Coulomb Interaction

In the studies of iron pnictides, a key question is whether their bad-metal state from which the superconductivity emerges lies in close proximity with a magnetically ordered insulating phase. Recently, it was found that at low temperatures, the heavily Cu-doped ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$ ($x>0.3$) iron pnictide is an insulator with long-range antiferromagnetic order, similar to the parent compound of cuprates but distinct from all other iron pnictides. Using angle-resolved photoemission spectroscopy, we determined the momentum-resolved electronic structure of ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$ ($x=0.44$) and identified that its ground state is a narrow-gap insulator. Combining the experimental results with density functional theory (DFT) and $\mathrm{DFT}+U$ calculations, our analysis reveals that the on-site Coulombic (Hubbard) and Hund’s coupling energies play crucial roles in the formation of the band gap about the chemical potential. We propose that at finite temperatures, charge carriers are thermally excited from the Cu-As-like valence band into the conduction band, which is of Fe $3d$-like character. With increasing temperature, the number of electrons in the conduction band becomes larger and the hopping energy between Fe sites increases, and finally the long-range antiferromagnetic order is destroyed at $T>T_N$. Our study provides a basis for investigating the evolution of the electronic structure of a Mott insulator transforming into a bad metallic phase and eventually forming a superconducting state in iron pnictides.

Figure 1

Electronic structure of ${\mathrm{NaFe}}_{0.5}{\mathrm{Cu}}_{0.5}\mathrm{As}$ calculated by DFT and $\mathrm{DFT}+U$. (a) BZ with high symmetry points and lines indicated. The light green line indicates the projected BZ. Inset: Light green lines denote the projected BZ of ${\mathrm{NaFe}}_{0.56}{\mathrm{Cu}}_{0.44}\mathrm{As}$, black lines the BZ of the two-Fe unit cell of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ as defined in Refs. [17, 18]. (b) Temperature dependence of the in-plane resistivity for ${\mathrm{NaFe}}_{0.56}{\mathrm{Cu}}_{0.44}\mathrm{As}$. The arrow indicates $T_N$ as obtained from neutron diffraction [14]. (c) The crystal structure [19]. (d),(e) The band structure along high symmetry lines from DFT and $\mathrm{DFT}+U$ calculations, respectively. (f) Zoom-in of the red box in (e), showing the band gap about $E_F$.

Figure 2

ARPES spectra of ${\mathrm{NaFe}}_{0.56}{\mathrm{Cu}}_{0.44}\mathrm{As}$. (a1),(a2) ARPES spectrum along the $M\text{−}\mathrm{\Gamma }\text{−}M$ direction, taken at $T=15\mathrm{K}$ with $hv=52\mathrm{eV}$ and circularly polarized photons in (b1) and (b2), respectively. (c1),(c2) Curvature plot of the ARPES spectra in (a1) and (a2), respectively. The superimposed lines are the band dispersion from $\mathrm{DFT}+U$ and DFT calculations, as indicated. The calculated dispersion drawn in black is renormalized by a factor of 1.35. White lines represent nonrenormalized bands. (d1),(d2) The same as (b1) and (b2), but the ARPES spectrum is obtained at $T=260\mathrm{K}$. (e) Band dispersion as calculated by $\mathrm{DFT}+U$ for the AFM (green lines) and paramagnetic (PM) state (blue lines). (f) Curvature plot of the ARPES spectrum at $T=15\mathrm{K}$ along high symmetry lines as indicated in Fig. 1. The superimposed lines are the band dispersion from the $\mathrm{DFT}+U$ calculation.

Figure 3

(a),(b) ARPES intensity maps at energies $E\text{−}{E}_F=-25\mathrm{meV}$ and $E\text{−}{E}_F=-300\mathrm{meV}$, respectively. The spectra were acquired with $hv=52\mathrm{eV}$ and circularly polarized photons at $T=15\mathrm{K}$. The maps have been integrated over an energy window of $\pm 10\mathrm{meV}$. (c) ARPES intensity map at $E_F$, obtained at $T=260\mathrm{K}$. Because of the thermal broadening, finite intensity appears at the $E_F$. (d) ARPES intensity map at energies $E\text{−}{E}_F=-200\mathrm{meV}$ in the $k_{\parallel }-k_z$ plane, where $k_{\parallel }$ is along the $\mathrm{\Gamma }\text{−}M$ direction. (e) The dispersion along the $k_z$ direction at $k_{\parallel }=0$. (f) Sketch of the constant energy surface at $E\text{−}{E}_F=-200\mathrm{meV}$ in the 3D BZ, calculated by $\mathrm{DFT}+U$. (g) Schematic of the electronic structure of cuprate parent compounds and ${\mathrm{NaFe}}_{0.56}{\mathrm{Cu}}_{0.44}\mathrm{As}$ for the noninteracting case ($U=0$) and for the case of finite interactions. The quantity $\sim k_{B}T$ indicates the thermal excitations of electrons from the valence to conduction bands.