Speaker
Description
The piecewise linearity condition is a property satisfied by the exact density functional and has been found to yield band gaps in accord with experiment when imposed to hybrid functionals [1,2]. Here, we address the self-interaction in relation to polarons in density functional theory. The self-interaction can be corrected by focusing on its one-body form like it appears in Hartree-Fock theory or through the enforcement of the piecewise linearity condition, also referred to as the correction of the many-body self-interaction. We develop a unified theoretical framework encompassing one-body and many-body forms of self-interaction [3,4]. In this way, we establish a quantitative connection between the two forms of self-interaction, by which the many-body form is seen to account for the effect of electron screening [3,4]. Further support for the enforcement of piecewise linearity is provided by the fact that, under this condition, it is possible to unify charged and neutral polaron formulations in density functional theory [5]. In our investigation, we consider widely used functionals such as the global hybrid functional PBE0($\alpha$) [3-7], and the Hubbard-corrected functional DFT+$U$ [6,7,8], as well as a newly developed semilocal scheme, called $\gamma$-DFT, which involves the use of a weak localized potential [3,4,7]. The enforcement of the piecewise linearity condition is achieved by imposing the generalized Koopmans’ condition to the neutral and charged states of the polaron upon proper consideration of finite-size effects induced by the lattice polarization [9]. The polaron properties are found to be robust upon variation of the functional, including charge densities [3-8], structural distortions [3-8], formation energies [3-8], energy barriers [7,8], hyperfine and superhyperfine parameters [7], and charge hopping rates [7].
[1] G. Miceli, W. Chen, I. Reshetnyak, and A. Pasquarello, Nonempirical hybrid functionals for band gaps and polaronic distortions in solids, Phys. Rev. B 97, 121112(R) (2018).
[2] J. Yang, S. Falletta, and A. Pasquarello, One-shot approach for enforcing piecewise linearity on hybrid functionals: Application to band gap predictions, J. Phys. Chem. Lett. 13, 3066-3071 (2022).
[3] S. Falletta and A. Pasquarello, Many-body self-interaction and polarons, Phys. Rev. Lett. 129, 126401 (2022).
[4] S. Falletta and A. Pasquarello, Polarons free from many-body self-interaction in density functional theory, Phys. Rev. B 106, 125119 (2022).
[5] S. Falletta, J. Coulter, J. B. Varley, D. Aberg, B. Sadigh, B. Kozinsky, and A. Pasquarello, Equivalence of charged and neutral density functional formulations for correcting the many-body self-interaction of polarons, preprint 2025, https://doi.org/10.21203/rs.3.rs-8160837/v1.
[6] S. Falletta and A. Pasquarello, Hubbard $U$ through polaronic defect states, npj Comput. Mater. 8, 265 (2022).
[7] S. Falletta and A. Pasquarello, Polaron hopping through piecewise-linear functionals, Phys. Rev. B 107, 205125 (2023).
[8] G. Palermo, S. Falletta, and A. Pasquarello, Migration of hole polarons in anatase and rutile TiO$_2$ through piecewise lienar functionals, Phys. Rev. B 110, 235205 (2024).
[9] S. Falletta, J. Wiktor, and A. Pasquarello, Finite-size corrections of defect energy levels involving ionic polarization, Phys. Rev. B 102, 041115(R) (2020).