The Ba0.6K0.4Fe2As2 superconducting four-gap temperature evolution: A multi-band Chebyshev–BdG approach

•The Chebyshev–BdG method is generalized for multi-band superconductors.•The temperature dependence of the superconducting gaps of Ba0.6K0.4Fe2As2 are reproduced by a weak-coupling approach.•A small redistribution of the electron population among the bands causes higher coupling ratios 2Δ0/kBTc2Δ0/kBTc, as would be expected from a strong coupling approach.

We generalize the Chebyshev–Bogoliubov–deGennes method to treat multi-band systems to address the temperature dependence of the superconducting gaps of iron based superconductors. This approach is suitable to deal with large matrices required for multi-band systems and for the case when charge inhomogeneities are important. Four superconducting gaps associated with different electron and hole pockets of optimally doped Ba0.6K0.4Fe2As2 were clearly identified by angle resolved photo-emission spectroscopy. The few approaches that successfully reproduce this gap temperature dependence are based on strong-coupling theories. We show that a single weak-coupling approach with a redistribution of electron population between the hole and electron pockets ν   with evolving temperature reproduces the different coupling ratios 2Δν(0)/kBTc2Δν(0)/kBTc in these materials. We define the values that fit the four zero temperature gaps Δν(0)Δν(0) and after that all Δν(T)Δν(T) is obtained without any additional parameter.