Microscopic mechanisms for the Fermi-liquid behavior of Nb-doped strontium titanate

The relaxation rate in Nb-doped strontium titanate involving different scattering channels is investigated theoretically. It is demonstrated that the total relaxation rate in SrTi${}_{1-x}$Nb${}_x$O${}_3$ is provided mainly by two mechanisms. The Baber electron-electron scattering with participation of both Coulomb and phonon-mediated electron-electron interactions provides the $T^2$ dependence of the relaxation rate. The scattering on the potential landscape caused by impurities is responsible for the residual relaxation rate at low temperatures. A good agreement with experiment is achieved accounting for all phonon branches in strontium titanate, both the optical and acoustic phonons. It is shown that the effective electron-electron interaction can be attractive in strontium titanate, and provides superconductivity at low temperatures and Fermi-liquid response in a wide range of temperatures. Thus our microscopic model supports the notion that superconductivity and Fermi-liquid properties of $n$-type SrTiO${}_3$ have a common origin.

Figure 1

Relaxation rate provided by the Baber scattering in Nb-doped SrTiO${}_3$ as a function of the temperature for the actual electron densities corresponding to the experimental values of the doping from Ref. 1.

Figure 2

Residual relaxation rate provided by the scattering of the electrons on the impurities in Nb-doped SrTiO${}_3$ as a function of the temperature (a) using the Thomas-Fermi screening length and (b) using the model screening length, the same for all samples.

Figure 3

Contribution to the relaxation rate in Nb-doped SrTiO${}_3$ due to the direct electron–LO-phonon scattering as a function of the temperature for the electron densities from Ref. 1.

Figure 4

Relaxation rate due to the umklapp electron-electron scattering in SrTi${}_{1-x}$Nb${}_x$O${}_3$ multiplied by $\hslash /{\mathcal{G}}^2$ [where $\mathcal{G}$ is the interference factor for the umklapp processes (Ref. 14)] as a function of the electron density for $T=80$ K. The arrows indicate the electron density for the samples of the experiment (Ref. 1). There are different scales at the $x$ axis for the densities $n_0<4\times {10}^{20}{\mathrm{cm}}^{-3}$ and $n_0>4\times {10}^{20}{\mathrm{cm}}^{-3}$.

Figure 5

Relative contributions of different scattering mechanisms to the total relaxation rate as a function of temperature for the doping content $x=0.002$.

Figure 6

Curves: The calculated total relaxation rate in Nb-doped SrTiO${}_3$ as a function of the temperature for the actual electron densities corresponding to the experimental values of the doping (Ref. 1). Symbols: Experimentally determined relaxation rate in Nb-doped SrTiO${}_3$ from Fig. 2 of Ref. 1.