Low Temperature Specific Heat of Doped SrTiO$_3$: Doping Dependence of the Effective Mass and Kadowaki-Woods Scaling Violation

Abstract

We report wide-doping-range ($8 \times 10^{17}$ to $4 \times 10^{20}$ cm$^{-3}$ Hall electron density) low temperature specific heat measurements on single crystal SrTiO$_3$:Nb, correlated with electronic transport data and tight-binding modeling. Lattice dynamic contributions to specific heat are shown to be well understood, albeit with unusual sensitivity to doping, likely related to the behavior of soft modes. Electronic contributions to specific heat provide effective masses that increase substantially, from $1.8$ to $4.8 m_e$, across the two SrTiO$_3$ Lifshitz transitions. It is shown that this behavior can be quantitatively reconciled with quantum oscillation data and calculated band structure, establishing a remarkably doping-independent mass enhancement factor of $2.0$. Most importantly, with the doping-dependent $T^2$ resistivity prefactor and Sommerfeld coefficient known, Kadowaki-Woods scaling has been tested over the entire doping range probed. Despite classic Fermi liquid behavior in electronic specific heat, standard Kadowaki-Woods scaling is dramatically violated, highlighting the need for new theoretical descriptions of $T^2$ resistivity in SrTiO$_3$.