Electron correlation and nonequilibrium current distribution in quantum transport through small systems

我们基于Kubo形式研究了连接非相互作用引线的小相互作用系统的电导，并阐明了电导在相互作用系统中也可以用Landauer型形式表示：g = (2e^2/h)∫d （-δf/δε）Τ（ε），其中f（ε）是费米函数，Τ（ε）是用顶点函数定义的传输概率。我们将此公式应用于一系列量子点，并表明Τ（ε）具有关于激发谱的许多信息。我们还利用Keldysh Green函数的Ward恒等式研究了有限偏置电压V下基于Anderson模型的量子点中近道效应的非平衡性质。结果表明，对于小而有限的V，激发谱的低能行为和电流的非线性响应可以用局部费米-液体理论来描述。我们还对有限偏置电压下的非平衡电流进行了数值计算。利用Keldysh形式中的递归格林函数技术，研究了磁场存在时局部电流的空间分布，该磁场由Peierls相描述。我们已经考虑了当前在各种系统中的分布。在一系列两点接触中，我们发现在V的线性响应区，点接触之间产生了一个大涡，而在非线性响应区，点接触之间存在一些小涡。在一个模拟被两个隧道结打断的金属环的系统中，观察到一个局部流，它对应于连接不同侧面边缘状态的共振隧道。我们还将递归方法应用于铁磁和超导材料中的隧道现象。

We have studied the conductance through small interacting systems connected to noninteracting leads based on the Kubo formalism, and have clarified that the conductance can be expressed in a Landauer type form also in the interacting systems: g = (2e^2/h)∫dε (-δf/δε)Τ(ε), where f(ε) is the Fermi function and Τ(ε) is the transmission probability which is defined in terms of the vertex function. We have applied this formulation to a series of quantum dots, and have shown that Τ(ε) has much information about the excitation spectrum. We have also studied nonequilibrium properties of the Kondo effects in quantum dots based the Anderson model under a finite bias voltage V using the Ward identities for the Keldysh Green function. It has been shown that for small but finite V the low-energy behaviors of the excitation spectrum and nonlinear response of the current can be described by the local Fermi-liquid theory.We have also carried out the numerical calculations of the nonequilibrium current under a finite bias voltage. Using the recursive Green function technique in the Keldysh formalism, we have studied the spatial distribution of local currents in the presence of the magnetic field which is described by the Peierls phase. We have considered the current distribution in various systems. In a series of two point contacts, we have found that a large vortex is created in between the point contacts in the linear response regime of V, while there exists several small vortcies in the nonlinear regime. In a system which simulates a metal ring interrupted by two tunnel junctions, a local flow which corresponds to resonant tunneling connecting the edge states of the different sides has been observed. We have also applied the recursion method to tunneling phenomena in ferromagnetic and superconducting materials.