Polarons are quasiparticles that arise from the coupling of electrons or holes with ionic vibrations in polarizable materials. Typically, they are either localized at a single atomic site or delocalized over multiple sites. However, after the desodiation of ${\mathrm{Na}}_2{\mathrm{Mn}}_3{\mathrm{O}}_7$, we identify a rare split-hole polaron, where a single hole is shared between two adjacent oxygen atoms rather than fully localized or delocalized. We present a density functional theory study on the migration and transport properties of these oxygen hole polarons in ${\mathrm{NaMn}}_3{\mathrm{O}}_7$ and ${\mathrm{Na}}_{1.5}{\mathrm{Mn}}_3{\mathrm{O}}_7$. Our calculations reveal that the split polaron configuration near a sodium vacancy is the ground state, while the localized polaron acts as the transition state. Migration occurs via a stepwise charge transfer mechanism along the $b$ axis, where the split-hole polaron transitions through a localized hole state. This transport behavior closely resembles the Grotthuss mechanism, which describes proton transport in ${\mathrm{H}}_2\mathrm{O}$. We compute the polaron mobility as $\mu =1.37\times {10}^{-5}$ ${\mathrm{cm}}^2$/($\mathrm{V}\mathrm{s}$) with an energy barrier of 242 meV. Using the Mulliken-Hush theory, we determine the electronic coupling parameter $V_{AB}=0.87$ eV. A similar migration mechanism is observed in ${\mathrm{Na}}_{1.5}{\mathrm{Mn}}_3{\mathrm{O}}_7$, where the split polaron remains more stable than in the localized state. This study provides a theoretical investigation of split-hole polaron migration, offering insights into the charge transport of exotic polaronic species in materials with implications for a wide range of functional materials including battery cathodes, thermoelectrics, photocatalysts, and next-generation optoelectronic devices.

Close

PrevNext

View figure in article

• Polarons
• Transport phenomena
• Transition metal oxides
• Density functional calculations