Theoretical study for the Kondo effect in the quantum transport

(1)研究了有限偏压下量子点中的非平衡近藤效应。具体地说，我们已经重新制定的密度矩阵，它描述了非平衡稳态，并已获得约化的密度矩阵，通过整合出的两个传导通道之一。该公式使我们能够用单通道模型处理电流流动状态，并可用于构造新的非平衡态的非微扰方法。(2)我们研究了与超导体相连的量子点中的近藤效应。在Kondo区，量子点具有一个定义明确的局域矩，一个简单的标度方程预言基态是单线态还是磁二重态取决于Kondo温度和超导能隙的大小.我们已经指出，偏离标度行为是重要的量子点，因为库仑相互作用和超导带隙可以是相同的数量级。我们已经表明，在超导原子极限，这是实现在大的差距，看到一些重要的功能的偏差。(3)本文用数值重整化群方法计算了超导体上量子点的单粒子绿色函数。我们的结果澄清了Andreev束缚态的精确特征，它出现在超导带隙内，以及差距附近的态密度。(4)我们还研究了的输运性质。超点正常连接结果表明，由于与正常铅的耦合，可以用局域费米液体理论的广义版本来描述的低的能量状态。利用数值重整化群，我们还计算了准粒子的重整化参数，阐明了近藤效应与Andreev反射竞争的特征。

(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.