Theoretical study for the Kondo effect in the quantum transport

量子输运中近藤效应的理论研究

基本信息

批准号：
18540322
负责人：
OGURI Akira
金额：
$ 1.18万
依托单位：
Osaka City University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2006
资助国家：
日本
起止时间：
2006 至 2007
项目状态：
已结题

项目摘要

(1) We studied the nonequilibrium Kondo effect in quantum dots under finite bias voltage. Specifically, we have reformulated the density matrix which describes the nonequilibrium steady state, and have obtained the reduced density matrix, by integrating out one of the two conduction channels. This formulation enables us to treat the current flowing state with a single-channel model, and may be applied to construct new nonperturbative approaches to the nonequilibrium state.(2) We have studied the Kondo effect in quantum dots connected to superconductors. In the Kondo regime where the dot has a well-defined local moment, a simple scaling argu-ment predicts that whether the ground state becomes a singlet or a magnetic doublet is determined by the value of the Kondo temperature and superconducting gap. We have pointed out that the deviation from the scaling behavior is important in quantum dots, because the Coulomb interaction and the superconducting gap can be the same order. We have shown that some important features of the deviation are seen in the superconducting atomic limit, which is realized at large gaps.(3) We have calculated the single-particle Green's function for the quantum dots connected to the superconductors, using the numerical renormalization group. Our results clarify the precise features of the Andreev bound state, which emerges inside the superconducting gap, and the density of states near the gap.(4) We have also studied the transport properties of. the super-dot-normal junctions. It is shown that the low-lying energy states can be described by a generalized version of the local Fermi-liquid theory, owing to the coupling with the normal lead. Using the numerical renormalization group, we have also calculated the renormalized parameters for the quasi-particles, and have clarified the features of the competition between the Kondo effect and the Andreev reflection.

(1)研究了有限偏压下量子点的非平衡近藤效应。具体来说，我们重新表述了描述非平衡稳态的密度矩阵，并通过积分两个传导通道之一获得了约简密度矩阵。这个公式使我们能够用单通道模型来处理电流流动状态，并且可以应用于构建新的非平衡态非微扰方法。(2)我们研究了连接到超导体的量子点中的近藤效应。在近藤体系中，点具有明确的局部矩，一个简单的标度论证预测基态是变成单重态还是磁双态取决于近藤温度和超导间隙的值。我们已经指出，缩放行为的偏差在量子点中很重要，因为库仑相互作用和超导间隙可以是相同的量级。我们已经证明，在超导原子极限中可以看到偏差的一些重要特征，这是在大间隙下实现的。（3）我们使用数值重正化计算了连接到超导体的量子点的单粒子格林函数团体。我们的结果阐明了超导能隙内部出现的安德烈夫束缚态的精确特征，以及能隙附近的态密度。(4) 我们还研究了的输运特性。超点法线结。结果表明，由于与普通铅的耦合，低能态可以用局域费米液体理论的广义版本来描述。利用数值重整化群，我们还计算了准粒子的重整化参数，并阐明了近藤效应和安德烈夫反射之间的竞争特征。