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

我们研究了基于Kubo形式的小相互作用系统与非相互作用导线之间的电导，并阐明了在相互作用系统中电导也可以用Landauer型形式表示：g =（2e^2/h）<$dε（-δf/δε）T（ε），其中f（ε）是费米函数，T（ε）是用顶点函数定义的传输概率。我们已经将该公式应用于一系列量子点，并且已经表明T（ε）具有关于激发光谱的许多信息。我们还利用Keldysh绿色函数的Ward恒等式研究了有限偏压V下基于安德森模型的量子点中近藤效应的非平衡性质。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域费米液体理论来描述，并对有限偏压下的非平衡电流进行了数值计算。利用Keldysh形式中的递归绿色函数技术，我们研究了用Peierls相位描述的磁场存在时局域电流的空间分布。我们已经考虑了各种系统中的电流分布。在一系列的两点接触，我们已经发现，一个大的涡是在点接触之间的V的线性响应区，而存在几个小涡的非线性区域。在一个系统中，它模拟了一个金属环中断的两个隧道结，一个本地流，对应于共振隧穿连接的边缘状态的不同侧已被观察到。我们还将递归方法应用于铁磁和超导材料中的隧穿现象。

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.