Department of Chemistry, Northwestern University, Evanston, Illinois 60608, USA.
J Chem Phys. 2018 Apr 14;148(14):144707. doi: 10.1063/1.5009815.
The Landauer expression for computing current-voltage characteristics in nanoscale devices is efficient but not suited to transient phenomena and a time-dependent current because it is applicable only when the charge carriers transition into a steady flux after an external perturbation. In this article, we construct a very general expression for time-dependent current in an electrode-molecule-electrode arrangement. Utilizing a model Hamiltonian (consisting of the subsystem energy levels and their electronic coupling terms), we propagate the Schrödinger wave function equation to numerically compute the time-dependent population in the individual subsystems. The current in each electrode (defined in terms of the rate of change of the corresponding population) has two components, one due to the charges originating from the same electrode and the other due to the charges initially residing at the other electrode. We derive an analytical expression for the first component and illustrate that it agrees reasonably with its numerical counterpart at early times. Exploiting the unitary evolution of a wavefunction, we construct a more general Landauer style formula and illustrate the emergence of Landauer transport from our simulations without the assumption of time-independent charge flow. Our generalized Landauer formula is valid at all times for models beyond the wide-band limit, non-uniform electrode density of states and for time and energy-dependent electronic coupling between the subsystems. Subsequently, we investigate the ingredients in our model that regulate the onset time scale of this steady state. We compare the performance of our general current expression with the Landauer current for time-dependent electronic coupling. Finally, we comment on the applicability of the Landauer formula to compute hot-electron current arising upon plasmon decoherence.
Landauer 表达式可用于计算纳米器件中的电流-电压特性，效率很高，但不适合瞬态现象和时变电流，因为它仅适用于在外扰后电荷载流子进入稳定通量的情况。在本文中，我们构建了一个非常通用的电极-分子-电极排列的时变电流表达式。利用模型哈密顿量（由子系统能级及其电子耦合项组成），我们传播薛定谔波函数方程，以数值计算各个子系统的时变布居。每个电极中的电流（根据相应布居的变化率定义）有两个分量，一个来自同一电极的电荷，另一个来自初始位于另一电极的电荷。我们推导出第一个分量的解析表达式，并说明它在早期与数值结果相当吻合。利用波函数的幺正演化，我们构建了一个更通用的 Landauer 风格公式，并从模拟中展示了 Landauer 输运的出现，而无需假设电荷流动的时间独立性。我们的广义 Landauer 公式在所有时间都适用于超出宽带限制、非均匀电极态密度以及子系统之间时变和能变电子耦合的模型。随后，我们研究了调节这个稳态起始时间尺度的模型中的成分。我们将我们的通用电流表达式的性能与随时间变化的电子耦合的 Landauer 电流进行了比较。最后，我们对 Landauer 公式在计算等离子体退相干引起的热电子电流方面的适用性进行了评论。
