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

## TL;DR

This paper proposes that certain Ruddlesden-Popper compounds contain hidden ladder structures in their orbitals, which could lead to high-temperature superconductivity due to interband pair scattering between wide and narrow bands.

## Contribution

It introduces the concept of hidden ladders in bilayer Ruddlesden-Popper compounds and predicts potential high-$T_c$ superconductivity arising from these structures.

## Key findings

- Sr$_3$Mo$_2$O$_7$ and Sr$_3$Cr$_2$O$_7$ are candidate materials with suitable electronic structures.
- First-principles calculations support the presence of hidden ladder bands near the Fermi level.
- Analysis suggests interband pair scattering could induce high-temperature superconductivity.

## Abstract

We introduce a 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 along the leg direction $x$ ($y$) on top of the rung $z$ direction. We predict that Sr$_3$Mo$_2$O$_7$ and Sr$_3$Cr$_2$O$_7$ are candidates for the hidden-ladder material with a right position of $E_F$, from a first-principles band calculation. Based on the analysis of Eliashberg equation for these systems, we propose a possible occurrence of high temperature superconductivity in these materials arising from the interband pair scattering processes between the wide and "incipient" narrow bands on the ladder.