标题： 脱钠态Na$_{2}$Mn$_3$O$_7$中的Grotthuss型氧空位极化子输运 显示英文标题

标题： Grotthuss-type oxygen hole polaron transport in desodiated Na$_{2}$Mn$_3$O$_7$

摘要： 极化子是在极性材料中电子或空穴与离子振动耦合而产生的准粒子。通常，它们要么局域在一个单一的原子位点上，要么离域到多个位点上。然而，在Na$_{2}$Mn$_{3}$O$_{7}$脱钠后，我们识别出一种罕见的分裂空穴极化子，其中单个空穴共享在两个相邻的氧原子之间，而不是完全局域化或离域化。 我们呈现了关于这些氧空位极化子在NaMn$_{3}$O$_{7}$和 Na$_{1.5}$Mn$_{3}$O$_{7}$中迁移和输运性质的密度泛函理论（DFT）研究。 我们的计算表明，靠近钠空位处的分裂极化子构型是基态，而局域化的极化子则作为过渡态。 迁移通过沿$b$轴逐步电荷转移机制发生，在此过程中分裂空穴极化子通过局域化的空穴状态进行转变。 这种输运行为与描述质子在H$_{2}$O中迁移的Grotthuss机制非常相似。 我们计算了极化子的迁移率，得到 $μ$ = 1.37 $\times$ 10$^{-5}$ cm$^2$/(V$\cdot$s)，能量势垒为 242 meV。 利用Mulliken-Hush理论，我们确定电子耦合参数 $V_{AB}$ = 0.87 eV。 类似迁移机制在Na$_{1.5}$Mn$_{3}$O$_{7}$中被观察到，其中分裂极化子比局域态更加稳定。 本研究首次对分裂空穴极化子的迁移进行了理论探索，为包括电池正极、热电材料、光催化剂以及下一代光电设备在内的多种功能材料中的奇异极化子型载流子传输提供了新的见解。 显示英文摘要

摘要： 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 Na$_{2}$Mn$_{3}$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 (DFT) study on the migration and transport properties of these oxygen hole polarons in NaMn$_{3}$O$_{7}$ and Na$_{1.5}$Mn$_{3}$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 H$_{2}$O. We compute the polaron mobility as $μ$ = 1.37 $\times$ 10$^{-5}$ cm$^2$/(V$\cdot$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 Na$_{1.5}$Mn$_{3}$O$_{7}$, where the split polaron remains more stable than in the localized state. This study provides the first theoretical investigation of split-hole polaron migration, offering new 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.