Multi-band nature and anisotropy of heavily doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$

We have carried out a detailed study on single crystals of Ba$_{\mathrm{1-x}}$K$_{\mathrm{x}}$Fe$_{2}$As$_{2}$ with doping level x very close to 1, Ba$_{0.05}$K$_{0.95}$Fe$_{2}$As$_{2}$ with T$_{\mathrm{c}} = $ 6.6 K, which exceeds the Lifshitz transition around x $=$ 0.9. The heat capacity C(T) shows a relatively large nodeless energy gap of 1.93 k$_{\mathrm{B}}$T$_{\mathrm{c}}$ based on a three-band BCS model analysis, which suggests that the SC state with the biggest gap value shows a fully opened s-wave superconducting characteristic and a possible nodal gap that shows a rather small gap value. A full H-T phase diagram has been determined by measuring C(T) and resistivity under fields in ab plane and c direction. Angle-resolved resistivity measurements at low temperatures were used to probe the angular dependence of upper critical field, showing an anisotropy well explained by using the Ginzburg-Landau theory.