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Recent ab initio calculations for charge transport in KTaO$_3$ and SrTiO$_3$,
using the Boltzmann transport equation, showed an overestimated mobility by
$300\%$ compared to experimental data [1]. Ab initio polaron calculations for
these materials in Ref. [2] showed that localized solutions are possible for an
excess electron, hinting towards a polaron transport regime. However, for the
supercell sizes used, the localization was confirmed in one spatial dimension only
and a full localization was conjectured for larger supercell sizes.
This work further investigates polaron formation in KTaO$_3$ and SrTiO$_3$
based on the ab initio theory of polarons presented in Ref. [3] and implemented
in the EPW code [4, 5]. As a result, the conjecture of a large electron polaron
localized with respect to all spatial directions was confirmed for both materials.
Furthermore, the influence of anharmonic phonons, calculated with the SSCHA
code [6], on the formation of an electron polaron was investigated and found to
be negligible. Hole polaron calculations yielded consistent results compared to
Ref. [2]. Additionally polaron hopping was investigated for a hole polaron in
KTaO$_3$.
[1] L. Ranalli, C. Verdi, M. Zacharias, J. Even, F. Giustino, and C. Franchini,
Electron mobilities in SrTiO$_3$ and KTaO$_3$: Role of phonon anharmonicity,
mass renormalization, and disorder, Phys. Rev. Materials 8, 104603 (2024).
[2] L. Ranalli, Machine-learned anharmonic phonons and their impact on
electron–phonon coupling, Ph.D. thesis, University of Vienna, 2025.
[3] W. H. Sio, C. Verdi, S. Ponc´e, and F. Giustino, Ab initio theory of polarons:
Formalism and applications, Phys. Rev. B 99, 235139 (2019).
[4] S. Ponc´e, E. R. Margine, C. Verdi, and F. Giustino, EPW: Electron–phonon
coupling, transport and superconducting properties using maximally localized
Wannier functions, Comput. Phys. Commun. 209, 116 (2016).
[5] H. Lee, S. Ponc´e, K. Bushick, S. Hajinazar, J. Lafuente-Bartolome, J. Lev-
eillee, C. Lian, J. M. Lihm, F. Macheda, H. Mori, H. Paudyal, W. H. Sio,
S. Tiwari, M. Zacharias, X. Zhang, N. Bonini, E. Kioupakis, E. R. Margine,
and F. Giustino, Electron–phonon physics from first principles using the
EPW code, npj Comput. Mater. 9, 156 (2023).
[6] L. Monacelli, R. Bianco, M. Cherubini, M. Calandra, I. Errea, and F. Mauri,
The stochastic self-consistent harmonic approximation: Calculating vibra-
tional properties of materials with full quantum and anharmonic effects, J.
Phys.: Condens. Matter 33, 363001 (2021).