Electron-Phonon Scattering in the Presence of Soft Modes and Electron Mobility in ${\mathrm{SrTiO}}_3$ Perovskite from First Principles

Structural phase transitions and soft phonon modes pose a long-standing challenge to computing electron-phonon ($e$-ph) interactions in strongly anharmonic crystals. Here we develop a first-principles approach to compute $e$-ph scattering and charge transport in materials with anharmonic lattice dynamics. Our approach employs renormalized phonons to compute the temperature-dependent $e$-ph coupling for all phonon modes, including the soft modes associated with ferroelectricity and phase transitions. We show that the electron mobility in cubic ${\mathrm{SrTiO}}_3$ is controlled by scattering with longitudinal optical phonons at room temperature and with ferroelectric soft phonons below 200 K. Our calculations can accurately predict the temperature dependence of the electron mobility in ${\mathrm{SrTiO}}_3$ between 150–300 K, and reveal the microscopic origin of its roughly $T^{-3}$ trend. Our approach enables first-principles calculations of $e$-ph interactions and charge transport in broad classes of crystals with phase transitions and strongly anharmonic phonons.

Figure 1

Phonon dispersions of cubic ${\mathrm{SrTiO}}_3$, computed with TDEP at 200 K (teal lines) and 300 K (red lines), and for comparison with DFPT (gray dashed line). Experimental results at room temperature (from Refs. [41, 42]) are shown with open circles.

Figure 2

(a) Absolute value of the $e$-ph matrix elements computed with anharmonic phonons from TDEP at 200 K (teal dots) and harmonic phonons from DFPT (red dots). (b) Phonon dispersions overlaid with a log-scale color map of $|g_{\nu }(\mathit{q})|$.

Figure 3

(a) Computed electron mobility as a function of temperature (blue circles), compared with experimental values (black squares) taken from Ref. [10]. (b) Mode-resolved $e$-ph scattering rates, as a function of conduction band energy, at temperatures of 300, 200, and 150 K (one per panel from left to right). The scattering rates are given for the two LO modes, the ferroelectric soft mode, and the LA mode labeled in Fig. 2. For better visualization, only the scattering rates of electronic states with $\mathit{k}$ along $\mathrm{\Gamma }-X$ and $\mathrm{\Gamma }-M$ are shown, which correspond to the lower and upper bounds of the $\mathit{k}$-dependent scattering rates. The integrand in Eq. (2), which shows how much electronic states at a given energy contribute to transport, is also plotted at each temperature. The zero of the energy axis is the CBM.