Theoretical study for the Kondo effect in the quantum transport

(1)研究了有限偏置电压下量子点的非平衡近藤效应。具体地说，我们重新表述了描述非平衡稳态的密度矩阵，并通过积分出两个传导通道中的一个得到了简化的密度矩阵。该公式使我们能够用单通道模型处理电流流动状态，并可用于构建新的非平衡状态的非摄动方法。(2)我们研究了超导体连接量子点的近藤效应。在近藤体系中，点有一个定义明确的局部矩，一个简单的标度论证预测基态是变成单线态还是磁重态是由近藤温度和超导间隙的值决定的。我们已经指出，在量子点中，偏离标度行为是重要的，因为库仑相互作用和超导间隙可以是同一阶的。我们已经证明了在超导原子极限中可以看到偏差的一些重要特征，这是在大间隙中实现的。(3)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。我们的结果阐明了超导隙内出现的安德烈夫束缚态的精确特征，以及隙附近的态密度。(4)我们还研究了的输运性质。超点法连接点。结果表明，由于与普通引线的耦合，低洼能态可以用局部费米-液体理论的广义版本来描述。利用数值重正化群计算了准粒子的重正化参数，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.