Theoretical study for electron correlations in quantum transport phenomena

我们基于Kubo的形式重新检验了通过连接到非相互作用引线的小相互作用系统的输运的微观公式，并相当普遍地表明，多体传输系数Τ（ε）可以与实时定义的三点延迟函数相关，通过该系数，直流电导可以用朗道尔型形式g=(2e^2/h)∫d（-∂f/∂ε） Τ（ε）表示，其中f（ε）是费米函数。我们已经将线性响应公式应用于量子点超晶格，它是由连接到两个非相互作用引线的二维哈伯德簇来建模的。利用库仑相互作用U的扰动展开中的二阶自能得到的结果，证明了相互作用对共振峰结构的影响。特别是共振的宽度和位置对相关效应非常敏感。我们还研究了有限偏压V下基于Anderson模型的量子点Kondo效应的非平衡性质。我们已经证明，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部费米-液体理论来描述。此外，我们还推导了在大偏置电压V.[4]极限下格林函数的确切渐近行为。我们还利用数值重整化群方法对输运性质进行了非微扰计算。利用这种方法，我们研究了约瑟夫森结中量子点的近藤效应，并明确了非磁性单重态和磁性双重态基态之间的量子相变的精确特征。我们现在正把这种方法应用到纳米尺度的莫特-哈伯德绝缘体上。

[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.