Theoretical study on quantum transport through strongly correlated electrons in quantum dots and nano materials

我们研究了电子间相互作用对量子点和纳米材料输运的影响。我们提出了一个新的大N展开式，其中N是轨道简并。这种方法不同于传统的方法，使我们能够在RPA之外进行系统的计算。我们还得到了高偏压下安德森杂质失稳的精确相互作用格林函数。此外，我们还给出了低能费米液区中包含铁磁Hund规则耦合的量子点的非平衡电流涨落的精确表达式。我们的结果表明，在粒子-空穴对称的情况下，散粒噪声可以用相对于平衡基态定义的准粒子的重整化参数来表示。我们还研究了由正常导线和超导导线组成的三端耦合量子点的近藤效应和Andreev-Josephson效应之间的相互作用。

We have studied effects of inter-electron interaction on transport through quantum dots and nanoscale materials. We have proposed a novel large N expansion, where N is an orbital degeneracy. This method is different from the conventional ones and enables us a systematic calculation beyond the RPA. We have also obtained exact interacting Green's function for the Anderson impurity out of equilibrium at high bias voltages. Furthermore, we have provided an exact expression for nonequilibrium current fluctuations through a quantum dot, which includes a ferromagnetic Hund's rule coupling, in the low-energy Fermi liquid regime. Our result shows that the shot noise can be expressed in terms of renormalized parameters of quasiparticles defined with respect to equilibrium ground state in the particle-hole symmetric case. We have also studied interplay between Kondo and Andreev-Josephson effects of a quantum dot coupled to three terminals, consisting of normal and superconducting leads.