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： 极化子是在极化材料中电子或空穴与离子振动耦合而产生的准粒子。通常，它们要么局限在单个原子位点上，要么分散在多个位点上。然而，在Na$_{2}$Mn$_{3}$O$_{7}$脱 sodiation 后，我们识别出了一种罕见的分裂空穴极化子，其中单个空穴分布在两个相邻的氧原子之间，而不是完全局限或分散。 我们提出了一个密度泛函理论（DFT）研究，探讨了这些氧空穴极化子在NaMn$_{3}$O$_{7}$和Na$_{1.5}$Mn$_{3}$O$_{7}$中的迁移和传输特性。我们的计算揭示，在钠空位附近，分裂极化子构型是基态，而局域化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空穴态进行转变。这种传输行为与Grotthuss机制非常相似，该机制描述了H$_{2}$O中的质子传输。 我们计算了极化子的迁移率，表示为 $\mu$ = 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。 在 Na$_{1.5}$Mn$_{3}$O$_{7}$中观察到类似的迁移机制，分裂极化子在这种情况下比局域态更加稳定。 本研究首次对分裂空穴极化子的迁移进行了理论探索，为具有广泛功能材料（包括电池正极、热电材料、光催化剂以及下一代光电设备）中的奇异极化子物种的电荷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 $\mu$ = 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.