Theoretical study for electron correlations in quantum transport phenomena

[1]我们在久保理论的基础上重新研究了与非相互作用导线相连的小相互作用系统输运的微观公式，并相当普遍地表明，用Landauer型形式表示直流电导的多体传输系数Τ(ε)，其中f(ε)是费米函数，可以与实时定义的三点延迟函数有关。[2]我们将线性响应公式应用于量子点超晶格，它由连接到两个不相互作用的引线的二维Hubbard簇模拟。利用二阶自能对库仑相互作用U的微扰展开得到的结果说明了共振峰的结构如何受库仑相互作用的影响。特别是共振的宽度和位置对相关效应非常敏感。[3]我们还研究了基于Anderson模型的量子点中近藤效应在有限偏压V下的非平衡特性。结果表明，对于小而有限的V，激发谱的低能行为和电流的非线性响应可以用局域费米液体理论来描述。此外，我们还推导了格林函数在大偏压V极限下的精确渐近行为。[4]我们还用数值重整化群方法对输运性质进行了非微扰计算。用这种方法研究了约瑟夫森结中量子点的近藤效应，阐明了非磁性单态和磁性双态基态之间量子相变的精确特征。我们现在正在将这种方法应用于纳米级的莫特-哈伯德绝缘体。

[1]We have re-examined the microscopic formulation of the transport through small interacting systems connected to noninteracting leads based on the Kubo formalism, and have shown quite generally that the many body transmission coefficient Τ(ε), by which the dc conductance is expressed in a Landauer type form g=(2e^2/h) ∫ dε (-∂f/∂ε) Τ(ε) where f(ε) is the Fermi function, can be related to a three-point retarded function defined in the real time.[2]We have applied the linear-response formulation to the quantum-dot superlattice, which is modeled by a two-dimensional Hubbard cluster connected to two noninteracting leads. The results, which are obtained by using the second-order self-energy in the perturbation expansion with respect to the Coulomb interaction U, demonstrate how the structure of resonance peaks is affected by the interaction. Especially, the width and the position of the resonance are sensitive to the correlation effects.[3]We have also studied nonequilibrium properties of the Kondo effects in quantum dots based on the Anderson model under a finite bias voltage V. We have shown that for small but finite V the low-energy behaviors of the excitation spectrum and nonlinear response of the current can be described by the local Fermi-liquid theory. Furthermore, we have deduced the exact asymptotic behavior of the Green's function in the limit of the large bias voltage V.[4]We have also launched nonperturbative calculations of the transport properties using the numerical renormalization group method. With this approach, we have studied the Kondo effect of a quantum dot in a Josephson junction, and have clarified precise features of the quantum phase transition between the non-magnetic singlet and magnetic doublet ground states. We are now applying the method to a Mott-Hubbard insulator of a nanometer scale.