A family of titanium oxypnictide materials $\mathrm{Ba}{\mathrm{Ti}}_2{Pn}_2\mathrm{O}$ ($Pn=\mathrm{pnictogen}$) 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 $T_{\mathrm{c}}$. 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 $T_{\mathrm{c}}$ via the density of states at the Fermi level and the McMillan formula systematically fails to yield the observed $T_{\mathrm{c}}$ variation. On the other hand, spin-fluctuation theory pairing calculations allow us to consistently explain the $T_{\mathrm{c}}$ increase with doping. All alkali-doped materials ${\mathrm{Ba}}_{1-x}{A}_x{\mathrm{Ti}}_2{\mathrm{Sb}}_2\mathrm{O}$ ($A=\mathrm{Na},\mathrm{K},\mathrm{and}\mathrm{Rb}$) 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.

• Received 24 August 2021
• Revised 14 October 2021
• Accepted 19 November 2021

DOI:https://doi.org/10.1103/PhysRevB.104.184519