Localized polarons and conductive charge carriers: Understanding CaCu3Ti4O12 over a broad temperature range

${\mathrm{CaCu}}_{3}{\mathrm{Ti}}_{4}{\mathrm{O}}_{12}$ (CCTO) has a large dielectric permittivity plateau near room temperature due to several dynamic processes. Here, we consider the combined effects of localized charge carriers (polarons) and conductive charge carriers using a recently proposed statistical model [Phys. Rev. B 96, 054115 (2017)] to fit and understand its permittivity measured at different frequencies over a broad temperature range. We found that, at the lowest temperature, the small permittivity is related to frozen polarons, and the increase at higher temperatures is associated with the thermal excitation of polarons that gives rise to the Maxwell-Wagner effect. The final rapid increase at the highest temperature is attributed to thermally activated conductivity. Such an analysis enables us to separate the contributions from localized polarons and conductive charge carriers and quantify their activation energies, which also explains the permittivity plateau near room temperature. In particular, we show that the subtle balance between the number of activated polarons and their polarizability causes CCTO to have a permittivity plateau with small dielectric loss.