Polaron spectral properties in doped ZnO and ${\mathrm{SrTiO}}_3$ from first principles

We reveal polaron signatures in the spectral function of $n$-doped ${\mathrm{SrTiO}}_3$ and ZnO through first-principles interacting Green's function calculations. In ${\mathrm{SrTiO}}_3$ we observe a clear replica band at 94 meV below the conduction band, which shows that the observed replica in recent angle-resolved photoemission spectroscopy experiment is an intrinsic feature from electron-phonon coupling in ${\mathrm{SrTiO}}_3$. In contrast, we observe an elongated tail in the spectral function for ZnO but no well-separated replicas. By increasing the electron doping level, we identify kinks in the spectral function at phonon frequencies and a decreasing intensity of the tail structure. We find that the curvature of the conduction band bottom vanishes due to additional electron-phonon scattering channels enabled by increased occupied states at high-enough doping levels, beyond which the spectral function becomes a stronger quasiparticle one with a single peak structure. We further compare the spectral function computed from the Migdal-Dyson approach and the cumulant method, and show that the cumulant method can correctly reproduce the polaronic features observed in experiments.

Figure 1

Spectral function of doped ${\mathrm{SrTiO}}_3$ along the $\mathrm{\Gamma }\text{−}M$ direction computed with the Migdal-Dyson theory (left) and the cumulant expansion method (right). The doping density is $n=1.6\times {10}^{19}\mathrm{electrons}/{\mathrm{cm}}^3$. The color scale is the normalized spectral function in units of states/unit cell/meV.

Figure 2

Comparison of the calculated spectral function with ARPES measurements of the conduction band of ${\mathrm{SrTiO}}_3$ at $\mathrm{\Gamma }$. Blue line: The spectral function from cumulant expansion method, open circle: Experiment data from Ref. [2]. The peak position of the calculated spectral function is shifted to align with the experiment data. The background intensity is subtracted from the experimental data. The doping level is $n=1.6\times {10}^{19}{\mathrm{cm}}^{-3}$.

Figure 3

Evolution of the spectral function of ZnO as a function of doping. The doping concentration is given by the indicated Fermi-level energy relative to the conduction band minimum shown in each panel.

Figure 4

Mass enhancement parameter $\lambda$ of ZnO as a function of doping measured as the Fermi level relative to the conduction band minimum.

Figure 5

Computed phonon band structure of STO (top) and ZnO (bottom).

Figure 6

Convergence of the self-energy with respect to the number of $q$-points ($N_q$) for the conduction band minimum of undoped STO (left) and undoped ZnO (right).