Many-Body Self-Interaction and Polarons

We address the many-body self-interaction in relation to polarons in density functional theory. Our study provides (i) a unified theoretical framework encompassing many-body and one-body forms of self-interaction and (ii) an efficient semilocal scheme for charge localization. Our theoretical formulation establishes a quantitative connection between the many-body and one-body forms of self-interaction in terms of electron screening, thereby conferring superiority to the concept of many-body self-interaction. Our semilocal methodology involves the use of a weak localized potential and applies equally to electron and hole polarons. We find that polarons free from many-body self-interaction have formation energies that are robust with respect to the functional adopted.

Figure 1

(a) Formation energy as obtained with the hybrid functional $\mathrm{PBE}0(\alpha )$ for the hole polaron in MgO. Negative formation energies indicate polaron stability. The many-body and the one-body self-interaction are suppressed at $\alpha ={\alpha }_k$ and at $\alpha =1$, respectively. (b) Isodensity surface of the hole polaron at 5% of its maximum (Mg in pink, O in red). The hole polaron is centered on an O atom, leading to longer bonds with neighboring Mg atoms.

Figure 2

Many-body self-interaction corrected (a) total energy and (b) polaron level as a function of the charge $q$, in comparison with the PBE values, obtained for the geometry and wave functions of a localized hole polaron in MgO.

Figure 3

(a) Polaron density $n_p$ and (b) and (c) variation of the valence-electron densities $n_{\uparrow \mathrm{val}}$ and $n_{\downarrow \mathrm{val}}$ upon occupation $f$ of the hole polaron state in MgO. The densities are integrated over the $z$ direction and plotted in the $xy$ plane. For hole polarons in the spin channel $\downarrow ,n_{\uparrow }=n_{\uparrow \mathrm{val}}$ and $n_{\downarrow }=n_{\downarrow \mathrm{val}}-n_p$.

Figure 4

(a) The potential $V_{{\sigma }_p}^{{\gamma }_k}(Q)$ and the electrostatic potential $V_{\mathrm{elec}}$ generated by the polaron charge, averaged over $xy$ planes, for the hole polaron in MgO. (b) Polaron densities integrated over $xy$ planes obtained with schemes free from many-body self-interaction.