Fig. 4: Superconductivity of the polar metals Nb:Sr_0.985Ca_0.015TiO₃ and Nb:Sr_0.95Ba_0.05TiO₃.

a Resistivity of the Sr_0.985Ca_0.015Ti_1−xNb_xO₃ single crystals (the same samples that were studied in Fig. 3a) below 1 K for 0.0005 ≤ x ≤ 0.015. b Resistivity of the Sr_0.95Ba_0.05Ti_1−xNb_xO₃ single crystals (the same samples that were studied in Fig. 3c) below 1 K for 0.00025 ≤ x ≤ 0.02. c The bottom panel depicts the superconducting domes of the polar metals Nb:Sr_0.985Ca_0.015TiO₃ (denoted by Nb:Ca) and Nb:Sr_0.95Ba_0.05TiO₃ (Nb:Ba), along with that of the nonpolar Nb:SrTiO₃ (Nb:) that was shown in Fig. 2b. The carrier density n of this plot was measured based on the Hall effect at 5 K. The dashed lines were obtained by performing a smoothing spline interpolation, with the lines becoming negative in some regions. However, this behaviour is an artefact of the smoothing process and is negligibly small. Therefore, it does not affect the discussion here. The top panel shows a replot of the T_K results shown in Fig. 3b and d versus the logarithmic values of n at T_K. The dashed lines correspond to the solid lines shown in Fig. 3b and d. The systems are polar within the hatched regions. The solid lines represent the differences between the T_c values of the polar metals and that of the nonpolar Nb:SrTiO₃. In both the top and bottom panels, the dash-dotted vertical lines correspond to n* for Nb:Sr_0.985Ca_0.015TiO₃ (light blue), and n* for Nb:Sr_0.95Ba_0.05TiO₃ (dark blue).