Microscopic mean field theory of competing orders and inter-layer tunnelling inhigh-Tc superconductors

Abstract

By using a microscopic mean field theory we investigate the effects of competing order(against the superconducting one) and inter-layer tunnelling on the transition temperatureTc of cuprate superconductors. We obtain the theoretical phase diagramsof mono- and bi-layer systems. For multi-layer systems we investigateTc as a function ofthe layer number N (within a unit cell). It turns out that near optimal dopingTc(N) is non-monotonicand peaks at N = 3, in qualitative agreement with existing experimental data. This arises from the cooperative effectsof competing order, charge redistribution and inter-layer tunnelling. However, the dropping ofTc withincreasing N inthis case is not as significant as in experiments. We also predict that in the very under- and over-doped regimesTc becomes a monotonicfunction of N and saturates for . This is because the competing order is either robust against thermal effects nearTc (in the very under-doped regime) or entirely absent (in the very over-doped regime), so thatTc as afunction of N is solely enhanced by inter-layer tunnelling.