Possible High-$T_c$ Superconductivity in “Hidden Ladder” Materials

Abstract

In this chapter, we introduce a concept of “hidden ladder” for the bilayer Ruddlesden-Popper type compounds as a way to realize a ladder-like electronic structure: While the bilayer structure seems to have nothing to do with ladders, $d_{xz}$ ($d_{yz}$) 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 concept leads us to propose that Sr$_3$Mo$_2$O$_7$ and Sr$_3$Cr$_2$O$_7$ are candidates for the hidden-ladder material with the Fermi energy in the vicinity of the narrow band edge, which is suggested to work in favor of superconductivity by the previous study on the two-leg Hubbard ladder. Based on the first-principles band calculation and the analysis of the Eliashberg equation within the FLEX approximation, we propose a possible occurrence of high temperature superconductivity in these non-copper materials arising from the coexistence of a wide band and an “incipient” narrow band introduced in Chap. 2.