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arXiv 1908.06119cond-mat.mes-hall
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基于主方程的Pb/Si(111)薄膜量子限制态电子的弛豫

Relaxation of electrons in quantum-confined states in Pb/Si(111) thin films from master equation with first-principles-derived rates

Peter Kratzer, Maedeh Zahedifar

摘要:

Si(111)上的Pb原子薄膜提供了一种实验可调系统,其包括高度结构化的电子态密度。在这些状态下的激发电子的寿命受到电子-电子(e-e)和电子-声子(e-ph)散射的限制。我们采用主方程描述的电子占据数来分析这两种散射机制的相对重要性。电子和声子的能带结构,以及变形势理论中的电子-声子耦合的矩阵元素,从密度泛函计算,从而考虑到量子限制效应。对于弛豫动力学,碰撞电离过程对寿命的贡献是根据GW近似计算的电子自能的虚部来估计的。通过数值求解速率方程的职业铅衍生的电子态耦合到声子热浴,我们能够遵循的电子激发能的分布,以各种模式的铅晶格振动。虽然e-e散射是主要的弛豫机制,我们表明,e-ph散射是高度声子模式特定的,与表面声子的贡献很大。在费米面以上约0.3 eV的电子能量处,观察到具有良好分离的电子态的纳米结构中的弛豫的"声子瓶颈"特性。从模拟中提取的时间尺度进行比较,使用时间分辨双光子光电发射的泵浦-探测实验的数据。

英文摘要:

Atomically thin films of Pb on Si(111) provide an experimentally tunable system comprising a highly structured electronic density of states. The lifetime of excited electrons in these states is limited by both electron-electron (e-e) and electron-phonon (e-ph) scattering. We employ the description by a master equation for the electronic occupation numbers to analyze the relative importance of both scattering mechanisms. The electronic and phononic band structures, as well as the matrix elements for electron-phonon coupling within deformation potential theory were obtained from density functional calculations, thus taking into account quantum confinement effects. For the relaxation dynamics, the contribution of impact ionization processes to the lifetime is estimated from the imaginary part of the electronic self-energy calculated in the GW approximation. By numerically solving rate equations for the occupations of the Pb-derived electronic states coupled to a phononic heat bath, we are able to follow the distribution of the electronic excitation energy to the various modes of Pb lattice vibrations. While e-e scattering is the dominant relaxation mechanism, we demonstrate that the e-ph scattering is highly phonon-mode-specific, with a large contribution from surface phonons. At electron energies of about 0.3 eV above the Fermi surface, a 'phonon bottleneck' characteristic of relaxation in nanostructures with well-separated electronic states is observed. The time scales extracted from the simulations are compared to data from pump-probe experiments using time-resolved two-photon photoemission.

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