Possible high-$T_c$ superconductivity due to incipient narrow bands originating from hidden ladders in Ruddlesden-Popper compounds

We introduce the concept of “hidden ladders” for the bilayer Ruddlesden-Popper-type compounds: While the crystal structure is bilayer, $d_{xz}$ ($d_{yz}$) orbitals in the relevant $t_{2g}$ sector of the transition metal form a two-leg ladder along $x$ ($y$) since the $d_{xz}$ ($d_{yz}$) electrons primarily hop in the leg ($x,y$) direction along with the rung ($z$) direction. This leads us to propose that ${\mathrm{Sr}}_3{\mathrm{Mo}}_2{\mathrm{O}}_7$ and ${\mathrm{Sr}}_3{\mathrm{Cr}}_2{\mathrm{O}}_7$ are candidates for the hidden-ladder material, with the correct position of $E_F$ from a first-principles band calculation. Based on the analysis of Eliashberg equation, we predict the possible occurrence of high-temperature superconductivity in these noncopper materials arising from the interband pair-scattering processes between a wide band and an “incipient” narrow band on the ladder.

Figure 1

Schematics of hidden ladders composed of the $d_{xz}$ (left panel) and $d_{yz}$ (right) orbitals in the bilayer Ruddlesden-Popper compounds ${\mathrm{Sr}}_3{TM}_2{\mathrm{O}}_7$ ($\mathit{TM}$ indicates a transition metal). The middle panel depicts the crystal structure.

Figure 2

Band structures of (a) and (b) ${\mathrm{Sr}}_3{\mathrm{Mo}}_2{\mathrm{O}}_7$ and (c) and (d) ${\mathrm{Sr}}_3{\mathrm{Cr}}_2{\mathrm{O}}_7$ obtained from the first-principles calculation. The Brillouin zone is shown in the inset. The thickness of the lines in the left (right) panel depicts the weight of the $d_{xy} \left(d_{xz,yz}\right)$ orbital character. (e) and (f) For comparison, the band structure of a ladder cuprate ${\mathrm{SrCu}}_2{\mathrm{O}}_3$ is displayed along two paths in the conventional Brillouin zone, where the thickness of the lines represents the $d_{x^2-y^2}$ orbital character. The point $(\pi ,\pi ,0)$ in (e) and (f) corresponds to the $\mathrm{\Gamma }$ point in (a)–(d) because the sign of the hopping is reversed. Note that (e) and (f) superimposed form a band structure quite similar to those in (b) and (d), respectively, except for the position of the Fermi level.

Figure 3

Band structure (red lines) of the six-orbital tight-binding model for ${\mathrm{Sr}}_3{\mathrm{Mo}}_2{\mathrm{O}}_7$ constructed from the maximally localized Wannier orbitals. Gray lines represent the first-principles calculation.

Figure 4

FLEX result for the band-filling dependence of the eigenvalue $\lambda$ of the linearized Eliashberg equation for ${\mathrm{Sr}}_3{\mathrm{Mo}}_2{\mathrm{O}}_7$ for $U=3.0$ eV (red dots) and $U=2.5$ eV (purple diamonds). The vertical dashed line represents the stoichiometric point ($n=4$). Also displayed are the results for the 326 compound ${\mathrm{Sr}}_3{\mathrm{Mo}}_2{\mathrm{O}}_6$ (blue square) and F-doped ${\mathrm{Sr}}_3{\mathrm{Mo}}_2{\mathrm{O}}_6\mathrm{F}$ (green triangle) at $n=4$.

Figure 5

Band structures of fluorine-intercalated compounds (a) ${\mathrm{La}}_2{\mathrm{SrCr}}_2{\mathrm{O}}_7{\mathrm{F}}_2$ and (b) ${\mathrm{La}}_2{\mathrm{SrMo}}_2{\mathrm{O}}_7{\mathrm{F}}_2$.

Figure 6

A schematic hidden ladder in the triple-layer Ruddlesden-Popper materials, here displayed for $d_{yz}$ orbitals.

Figure 7

Band structures of triple-layer compounds (a) and (b) ${\mathrm{Sr}}_4{\mathrm{Cr}}_3{\mathrm{O}}_{10}$ and (c) and (d) ${\mathrm{La}}_4{\mathrm{Cr}}_3{\mathrm{O}}_{10}$. The thickness of the lines in the left (right) panels depicts the weight of the $d_{xy} \left(d_{xz,yz}\right)$ orbital character. (e) and (f) For comparison, the band structure of a three-leg ladder cuprate ${\mathrm{Sr}}_2{\mathrm{Cu}}_3{\mathrm{O}}_5$ is shown along two paths in the conventional Brillouin zone, where the thickness of the lines represents the $d_{x^2-y^2}$ character. Note that the sign of the energy is reversed to facilitate comparison between the $t_{2g}$ (present) and $e_g$ (cuprate) systems. As in the two-layer case, (e-1) and (e-2) [(f-1) and (f-2)] superimposed form a band structure quite similar to those in (a-2) and (c-2) [(b-2) and (d-2)]. Red dashed lines indicate the edge of the narrow bands.