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，我们重新表述了描述非平衡定态的密度矩阵，并通过积分两个传导通道中的一个得到了约化密度矩阵。这个公式使我们能够用单通道模型来处理当前的流态，并且可以用来构造非平衡态的新的非微扰方法。(2)我们研究了与超导体相连的量子点中的近藤效应。在点具有明确局域矩的Kondo区，一个简单的标度方程预测基态是单态还是双磁态由Kondo温度和超导带隙的值决定。我们已经指出，在量子点中，偏离标度行为是很重要的，因为库仑相互作用和超导能隙可以是同一级的。我们发现在超导原子极限中出现了一些重要的偏离特征，这种偏离是在大能隙中实现的。(3)我们利用数值重整化群计算了与超导体相连的量子点的单粒子格林函数。我们的结果阐明了出现在超导禁带内的Andreev束缚态的精确特征，以及禁带附近的态密度。(4)我们还研究了超导禁带的输运性质。超点正常的结合点。结果表明，由于与正常铅的耦合，低能态可以用广义的局域费米液体理论来描述。利用数值重整化群，我们还计算了准粒子的重整化参数，阐明了近藤效应和安德列夫反射之间的竞争特征。

(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.