  A family of titanium oxypnictide materials BaTi2Pn2O (Pn = pnictogen) becomes
superconducting when a charge and/or spin density wave is suppressed. With hole
doping, isovalent doping and pressure, a whole range of tuning parameters is
available. We investigate how charge doping controls the superconducting
transition temperature Tc. To this end, we use experimental crystal structure
data to determine the electronic structure and Fermi surface evolution along
the doping path. We show that a naive approach to calculating Tc via the
density of states at the Fermi level and the McMillan formula systematically
fails to yield the observed Tc variation. On the other hand, spin fluctuation
theory pairing calculations allow us to consistently explain the Tc increase
with doping. All alkali doped materials Ba1-xAxTi2Sb2O (A = Na, K, Rb) are
described by a sign-changing s-wave order parameter. Susceptibilities also
reveal that the physics of the materials is controlled by a single Ti 3d
orbital.
