Absence of Luther-Emery Phase in the three-band model for cuprate ladders

Ladders are one system where predictions of strongly-correlated models of superconductivity (SC) can be checked rigorously. Under weak doping the spin-gapped state in the undoped two-leg single band Hubbard model evolves into a Luther-Emery liquid with gapless charge and gapped spin modes. Density Matrix Renormalization Group (DMRG) calculations show quasi-long range order of superconducting pair-pair correlations with distance decay slower than 1/r. The presence of SC near a spin gapped state has strongly influenced many theories of correlated SC in two dimensions which claim a proximity of SC and spin gap. However, the single band ladder theory does not seem applicable to real cuprate ladder superconductors, which undergo a one-to-two dimensional crossover. The ladder picture of SC has not been tested within the more realistic three-band model for the cuprates. We argue that due to the presence of the oxygen orbitals, the effective mass of pairs is expected to be far larger within the three-band ladder, suppressing pairing correlations [1]. DMRG calculations on a three-band cuprate ladder confirm these ideas, finding a decay with distance of pair-pair correlations indistinguishable from that of free fermions.

[1] arxiv.org/abs/2010.10609