Fig. 3: Resistance anomaly as evidence of existence of polar metal.
a Resistivity values of our Sr0.985Ca0.015Ti1−xNbxO3 single crystals with x = 0.0005, 0.001, 0.002, 0.005, and 0.015 plotted versus T. b Curie temperature \(T_{{{\mathrm{C}}}}^{{{{\mathrm{FE}}}}}\) ~ 25 K of the ferroelectric transition for undoped Sr0.985Ca0.015TiO3 (open red circle) and temperatures TK at which the resistivity reaches a minimum for the doped samples (closed red triangles) plotted versus the carrier density n at TK (or at 5 K for TK = 0). The values of n at TK were obtained via interpolation (see the main text). The solid line represents the least-squares fit of TK. This line is quite close to \(T_{{{\mathrm{C}}}}^{{{{\mathrm{FE}}}}}\) at n = 0. The inset shows the temperature dependence of the relative permittivity ε, where the peak corresponds to a \(T_{{{\mathrm{C}}}}^{{{{\mathrm{FE}}}}}\) of ~25 K. This value is almost equal to that calculated using \(T_{{{\mathrm{C}}}}^{{{{\mathrm{FE}}}}} = A\sqrt{y - 0.0018}\) (where A = 298 K and y = 0.015) (ref. 32). c Resistivity of our Sr0.95Ba0.05Ti1−xNbxO3 single crystals with x = 0.00025, 0.0003, 0.0005, 0.002, 0.0035, 0.005, 0.007, 0.015 and 0.02. d \(T_{{{\mathrm{C}}}}^{{{{\mathrm{FE}}}}}\) ~ 50 K for undoped Sr0.95Ba0.05TiO3 (open blue circle), which corresponds to the peak of ε (see the inset), and TK values for the doped samples (closed blue triangles) plotted versus n at TK. The definition of the error bars is provided in the main text. The solid line represents the least-squares fit for TK.
