Correlation-driven metal-insulator transition in proximity to an iron-based superconductor

We report the direct spectroscopic observation of a metal to correlated-insulator transition in the family of iron-based superconducting materials. By means of optical spectroscopy we demonstrate that the excitation spectrum of ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$ develops a large gap with increasing copper substitution. Dynamical mean-field theory calculations show a good agreement with the experimental data and suggest that the formation of the charge gap requires an intimate interplay of strong on-site electronic correlations and spin-exchange coupling, revealing the correlated Slater-insulator nature of the antiferromagnetic ground state. Our calculations further predict the high-temperature paramagnetic state of the same compound to be a highly incoherent correlated metal. We verify this prediction experimentally by showing that the doping-induced weakening of antiferromagnetic correlations enables a thermal crossover from an insulating to an incoherent metallic state. Redistribution of the optical spectral weight in this crossover uncovers the characteristic energy of Hund's-coupling and Mott-Hubbard electronic correlations essential for the electronic localization. Our results demonstrate that ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$ continuously transitions from the typical itinerant phases of iron pnictides to a highly incoherent metal and ultimately a correlated insulator. Such an electronic state is expected to favor high-temperature superconductivity.

Figure 1

Phase diagram of ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$. Below $x=0.05$ ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$ shows the ubiquitous phases of iron-based compounds (left axis): superconductivity (red symbols, line, and shaded area), SDW order (orange symbols and line), and a tetragonal-to-orthorhombic structural transition $\sim 10\mathrm{K}$ above $T_{\mathrm{SDW}}$ (green symbols and line). Data after Ref. [21]. At high doping levels, ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$ exhibits real-space ordering of copper and iron ions [see Fig. 4] and an antiferromagnetic phase transition (blue symbols and line, right axis). Data after Ref. [22]. In this paper we find that upon increasing copper concentration, a metal-insulator transition (MIT) occurs, gapping the Fe-$3d$ states and eliminating itinerant SW (black symbols, middle axis).

Figure 2

(a) Energy dependence of ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$ reflectance for $x=0.02$ (black), 0.05 (purple), $x=0.18$ (blue), 0.30 (cyan), 0.44 (green), and 0.48 (red solid line) at $T=300\mathrm{K}$. Dashed lines indicate the low-energy single-band Drude fit. (b) Temperature dependence of ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$ reflectance for $x=0.48$. Gradual suppression of the reflectance at lowest energies with decreasing temperature indicates the thermally activated character of the low-energy response. (c) Temperature dependence of the directly measured dc conductivity (open symbols, from Ref. [22]) and the corresponding quantity (black filled symbols) extracted from a Drude-Lorentz analysis of the infrared reflectance in panel (b) (for details see Ref. [38]). The quasiparticle scattering rate obtained in the same analysis (blue filled symbols). Dashed vertical line indicates the Néel transition temperature determined by means of neutron diffraction on the same compound in Ref. [22]. (d) Real part of the optical conductivity at $T=300\mathrm{K}$ as a function of photon energy for the same doping levels as in panel (a). Vertical dashed line shows the characteristic energy scale of the SW transfer from low to high energies with increasing copper substitution. This SW is composed of two main contributions: itinerant intraband (Drude term, left hatched area) and $\mathrm{Fe}\text{−}d–\mathrm{Fe}\text{−}d$ interband (Lorentz oscillator, right hatched area) optical transitions.

Figure 3

(a) Energy dependence of ${\left({\varepsilon }_2{\omega }^2\right)}^2$ in ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$ for $x=0.48$ and $x=0.44$ (offset vertically by $500{\mathrm{meV}}^4$ for clarity) at $T=300\mathrm{K}$. Linear segments (dashed lines) in this quantity are characteristic of direct allowed interband transitions [39]. The corresponding absorption edges are given by the intercepts of the linear dependence with the horizontal axis and are indicated by arrows. (b) Low-energy part of the optical conductivity shown in Fig. 2 below the lowest direct absorption edge identified in panel (a) for $x=0.44$ at $T=300\mathrm{K}$ (green line) and $x=0.48$ at $T=300\mathrm{K}$ (red line) and, additionally, at $T=10\mathrm{K}$ (gray line). The energy dependence at $x=0.44$ can be approximated by a power law with an exponent of 1.5 over an extended spectral range (dashed line) and at $x=0.48$ over a somewhat narrower range.

Figure 4

(a),(b) The arrangement of the magnetic moments in the antiferromagnetic ground state of ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$ in the itinerant parent $x=0$ (a) and localized $x=0.5$ (b) compound (after Refs. [22, 41]). Nonmagnetic arsenic ions are excluded for clarity. (c),(d) Evolution of the pDOS near $E_{\mathrm{F}}$ in the band structure of ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$ calculated using DFT+DMFT in the paramagnetic state upon increasing copper substitution from $x=0$ (c) to $x=0.5$ (d). (e) Same for the antiferromagnetic ground state at $x=0.5$. Arrows in (c) and (e) indicate dominant interband optical transitions. (f),(g) Simulated distribution of ARPES intensity in an energy-momentum cut along several high-symmetry directions in the Brillouin zone for the paramagnetic (f) and antiferromagnetic (g) state at $x=0.5$. (h) The corresponding enlarged pDOS from panel (e) obtained in the same calculation (h). The presence of a soft gap of order $0.8\mathrm{eV}$ is evident in the pDOS (h). (i),(j) Comparison of the experimental (solid lines) and theoretical (dashed lines) optical conductivity spectra of ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$ at $x=0$ (i) and $x=0.5$ (j). Shaded areas indicate the itinerant (intraband) and localized (interband) contributions to the optical conductivity extracted by means of a Drude-Lorentz analysis (see Ref. [38]). Vertical arrows and dashed lines show the center location of the lowest-lying clearly identifiable interband optical transition in both experimental and theoretical optical conductivity. Theoretical in-plane optical conductivity spectra for the $x=0.5$ compound in the direction of the $a$ and $b$ crystal axis were averaged to take into account domain twinning [22].

Figure 5

(a) Energy dependence of ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$ reflectance for $x=0.3$ at various temperatures. Vertical dashed line indicates the energy scale beyond which the temperature-induced changes in infrared reflectance largely vanish. (b) Temperature dependence of reflectance at $10\mathrm{meV}$ photon energy. Gray shaded area indicates the temperature window for the Néel transition temperature in this compound (according to the phase diagram in Fig. 1). (c) Energy dependence of the real part of the optical conductivity at various temperatures. Dashed vertical line as in panel (a). Hatched area indicates the missing infrared spectral weight between $300\mathrm{K}$ and $10\mathrm{K}$. (d) Energy dependence of the difference partial spectral weight between room temperature and $200\mathrm{K}$ (red line) as well as $10\mathrm{K}$ (black line).