  We used angle resolved photoemission spectroscopy and thermoelectric power to
study the poorly explored, highly overdoped side of the phase diagram of
Ba(Fe1-xCox)2As2 high temperature superconductor. Our data demonstrate that
several Lifshitz transitions - topological changes of the Fermi surface - occur
for large x. Tc starts to decrease with doping when the cylindrical, central
hole pocket changes to ellipsoids centering at the Z point, and goes to zero
before these ellipsoids disappear around x = 0.2. Changes in thermoelectric
power occur at similar x-values. Beyond this doping level the central pocket
changes to electron-like and superconductivity does not exist. Our observations
reveal the crucial importance of the underlying Fermiology in this class of
materials. A necessary condition for superconductivity is the presence of the
central hole pockets rather than perfect nesting between central and corner
pockets.
