Cuprates, Pnictides and Sulfosalts: Lessons in Functional Materials

Abstract

Murunskite K$_2$Cu$_3$FeS$_4$ is a representative sulfosalt, isostructural to the pnictides, but with electronic properties more similar to the insulating parent compounds of the cuprates. We use it as a bridge to compare the chemical and physical roles of metal and ligand orbitals in cuprates and pnictides. In cuprates, ionicity, covalency, and metallicity are tightly interwoven to give rise to high-temperature superconductivity (SC). Their most remarkable property is the interaction of an ionically localized hole on the copper (Cu) with a Fermi liquid (FL) on the oxygens (O), which is critically important for understanding all key properties of these materials. The localization is due to strong correlations on the Cu $3d$ orbital. We describe a scenario in which the localized hole gives rise both to SC by Cooper scattering of O holes, and to Fermi arcs, as observed in cuprate spectroscopy, the latter by a purely kinematic projection of the static local disorder, without invoking any residual interactions between the mobile O FL carriers. In the pnictides, the orbitals responsible for binding and metallic conduction appear to be separate. The Fe $3d$ $e_{g}$ orbitals hybridized with the ligands set the lattice spacing. The $3d$ $t_{2g}$ orbitals overlap directly between the Fe atoms, resulting in several electronic bands appearing at the Fermi level. The ensuing Fermi liquid exhibits both charge and magnetic correlations. We argue that a similar SC scenario as in the cuprates is plausible in the pnictides, except that a light FL scatters on a slow nearly-antiferromagnetic (AF) one, rather than on localized holes as in the cuprates.

Figures (7)

• Figure 1: The $T=0$ K evolution of $n_{\mathrm{eff}}$ in various cuprates, extrapolated from resistivity: $n_{\rho}$ (full lines Barisic15Barisic19Pelc19), and from Hall coefcient: $n_H$ (circles Putzke21), clearly transitioning from $p$ to $1 + p$ from under- to overdoping, with $n_{\mathrm{eff}}\approx p$ up to optimal doping. The apparent discontinuity of the open green circles in Y123 Badoux16 disappears when chain anisotropy is taken into account (full green circles Putzke21Nicholls25) and a full agreement with evolution determined from resistivity is achieved. From Ref. Barisic22.
• Figure 2: (a) The four-band model of Eq. (\ref{['ham']}). The overlaps $t_{ps}$ are marked by gray patches. (b) The four $dp$ bands of the $2\times 2$ supercell model (\ref{['ham']}) in the scBZ, with the Fermi level corresponding to $15$% hole doping marked in yellow. (c) The same bands unfolded into the pcBZ by geometric translations. The ridge separating the red and green segments connects the van Hove points of the pcBZ. (d) The four $dp$ bands of the $2\times 2$ supercell model (\ref{['ham']}) in the scBZ, with a hole localized in one of the unit cells. The green band is above the Fermi level now. The double arrow marks the charge-transfer gap at half-filling. (e) The same bands unfolded into the pcBZ by geometric translations, as in (c). While the green band is gapped, the surviving Fermi surfaces of the blue and red segments are arc-like, stopping abruptly at the antidiagonal. (f) The correct projection onto the pcBZ of the schematic situation in (e). Points with less than $30$% weight are not shown. The energy $\varepsilon_{\mathrm{loc}}$ is the energy of the localized hole in the $d$ orbital, here higher than $\varepsilon_d$ because the figure is in the electron picture.
• Figure 3: Top row: Various Fermi-surface reconstructions proposed in the literature. (a) Electronic, AF Fang22. (b) Electronic, CDW Tabis21. (c) Structural, LTO Beck25. (d) Measured ARPES response from a five-layer cuprate with different doping levels in the layers Kunisada20. The optimally doped plane gives rise to an arc that does not touch the antidiagonal, while the underdoped planes give rise to asymmetric pockets enclosing it. (e) One-body DFT+U calculation with dopant disorder Lazic15. Red dots: Fermi surface crossings not reaching the antidiagonal (black line). Black dot: Gap onset. (f) Open Fermi surface: Same as in Fig. \ref{['fignonint']}f. Pocket: 5% doping with parameter evolution, such that the plaquette with $\varepsilon_d=\varepsilon_{\mathrm{loc}}/2\to \varepsilon_d=\varepsilon_{\mathrm{loc}}$.
• Figure 4: (a) Evolution of the carrier density with doping. On the underdoped side, there are many localized holes (green squares) but few free carriers (red dots). On the overdoped side, it is the opposite. The symbols are measurements in LSCO. The full curve is Eq. (\ref{['rhoS']}). The shaded areas are affected by percolative corrections. From Ref. Pelc19. (b) Evolution of T$_c$ with charge density on planar O sites $n_O$, called $2n_p$ in Ref. Rybicki16. From Ref. Rybicki16.
• Figure 5: (a) Recovery of SC ($T_{SC}$) under uniaxial strain which suppresses the LTT transition ($T_{LTT}$) in La$_{2-x}$Ba$_x$CuO$_4$ at doping $x=0.115$. All the other collective modes (charge density wave CDW, spin order SO and low-temperature less-orthorhombic order LTLO) are insensitive to SC. From Ref. Thomarat24. (b) Observation of continuous recovery of SC T$_c$ in La$_{2-x}$Ba$_x$CuO$_4$ at doping $x=0.125$ as the LTT tilt is suppressed. Note that there are two SC structural phases simultaneously present in the sample, of which only the LTT one is affected by the strain. From Ref. Gao25.