Understanding unconventional superconductivity through cuprate ladders*

Despite more than thirty years of research, even the minimal model required to understand the high critical temperature cuprate superconductors is still under debate. One model system that is well understood and believed by many to be relevant to real cuprates is the single band two-leg ladder. Particles doped into a ladder break rung singlet pairs, leading to an effective attraction and dominant superconducting pairing correlations in the long-range limit. This result appears to explain the superconductivity found in the one known cuprate with a coupled ladder structure, Sr_14-xCa_xCu₂₄O₄₁ (SCCO), where superconductivity is found under simultaneous doping and application of pressure.  Increases in computer power now allow accurate solutions of cuprate ladders within a three-band model including both copper and oxygen atoms. We present Density Matrix Renormalization Group results for single and coupled cuprate ladders. Our results show that unlike the single-band model, dominant superconducting correlations are not present in the hole doped cuprate ladder. Our coupled ladder calculations show that while the three-band model can explain the quasi-one-dimensional conductivity found in SCCO under ambient pressure, neither increased inter-ladder hopping nor carrier density can explain the dimensional crossover found under pressure prior to superconductivity. We propose that superconductivity in SCCO and other cuprates results can be explained within a valence transition model, following which there is a large increase in carriers on the oxygen sites.