非局域电子-声子相互作用限制的电荷输运。II. 慢声子区域中的数值精确量子动力学
Charge transport limited by nonlocal electron-phonon interaction. II. Numerically exact quantum dynamics in the slow-phonon regime
AI总结：
本文利用HEOM方法研究一维Peierls模型中载流子输运，发现超扩散到亚扩散的交叉是瞬态的，并揭示了瞬态局域化图像在中等温度和相互作用下的局限性。
摘要：
机械软半导体中电荷载流子的输运主要受其与慢分子间声子相互作用的限制。载流子运动表现出从超扩散到亚扩散的交叉，在动态迁移率谱中产生一个独特的低频峰。这些特征可以在依赖载流子与声子动力学之间时间尺度分离的方法中理解，例如瞬态局域化图像（TLS）。然而，从完全量子动力学中恢复这些特征一直难以实现。利用伴随论文（arXiv:2501.05054）中阐述的基于层级运动方程（HEOM）的方法，我们研究了近绝热极限下一维Peierls模型中的载流子输运。我们发现，在较高温度和较强相互作用下，TLS非常好地近似HEOM动力学。此时，输运主要由声子辅助，并在一个声子周期之前就从亚扩散侧转变为扩散。相比之下，在中等温度和相互作用下，能带电流占主导地位，这与实际材料中的输运相关。我们随后得出结论：超扩散到亚扩散的交叉是瞬态的，因此扩散运动在与声子周期相当的时间尺度上从超扩散侧开始建立。此时，低频动态迁移率还额外在约一个声子频率处表现出一个凹陷，以及零频率峰。我们在这一中等区域的研究结果表明了TLS的局限性，并支持最先进的量子-经典模拟的结果。我们预期，对于更实际的声子态密度，HEOM与TLS动力学之间的定性差异将会减小。
英文摘要：
Transport of charge carriers in mechanically soft semiconductors is mainly limited by their interaction with slow intermolecular phonons. Carrier motion exhibits a crossover from superdiffusive to subdiffusive, producing a distinct low-frequency peak in the dynamical-mobility profile. These features can be understood within approaches relying on the timescale separation between carrier and phonon dynamics, such as the transient localization scenario (TLS). However, recovering them from fully quantum dynamics has proved elusive. Using the hierarchical equations of motion (HEOM)-based approach exposed in a companion paper (arXiv:2501.05054), we study carrier transport in the one-dimensional Peierls model near the adiabatic limit. We find that the TLS approximates HEOM dynamics very well at higher temperatures and for stronger interactions. Then, the transport is predominantly phonon-assisted, and turns diffusive from the subdiffusive side well before one phonon period. In contrast, the band current dominates at moderate temperatures and interactions, relevant for transport in realistic materials. We then conclude that the super-to-subdiffusive crossover is transient, so that the diffusive motion sets in from the superdiffusive side on timescales comparable to the phonon period. The low-frequency dynamical mobility then additionally exhibits a dip at approximately one phonon frequency, and the zero-frequency peak. Our findings in this moderate regime show limitations of the TLS, and support the results of the most advanced quantum--classical simulations. We expect that the qualitative differences between HEOM and TLS dynamics would diminish for a more realistic phonon density of states.
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