Hierarchical equations of motion approach to transport through an Anderson impurity coupled to interacting Luttinger liquid leads
Hierarchical equations of motion approach to transport through an Anderson impurity coupled to interacting Luttinger liquid leads
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DOI：
10.1103/physrevb.94.235411
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发表时间：
2016-08
影响因子：
3.7
通讯作者：
J. Okamoto;L. Mathey;R. Hartle
中科院分区：
文献类型：
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作者：
J. Okamoto;L. Mathey;R. Hartle
我们概括了运动方法的层次方程，以研究通过耦合到一维相互作用引线（可以被描述为卢廷格液体）的量子点或分子的电子传输。这种引线可以通过例如量子线或分数量子霍尔边缘态来实现。与非相互作用的金属引线相比，路廷格液体引线涉及多体相关性，并且单粒子隧道态密度在化学势处表现出幂律奇点。使用广义层次运动方程方法，我们评估了奇点和次前导多体相关性的重要性。为此，我们将数值收敛结果与我们方法固有的杂交扩展的二阶和一阶结果进行比较。作为一个测试案例，我们研究了通过单能级量子点或分子的传输，可以用安德森杂质模型来描述。如果实现点和引线之间的激子耦合，则对于引线中的吸引相互作用或排斥相互作用，共隧道效应最为明显。我们还发现，与一阶和/或速率方程结果相比，库仑封锁阈值附近相互作用引起的负微分电导受到轻微抑制。此外，我们发现双粒子（$n$-粒子）相关性作为二阶（$n$-阶）效应进入，因此在我们考虑的高温和参数下不是很明显。
We generalize the hierarchical equations of motion method to study electron transport through a quantum dot or molecule coupled to one-dimensional interacting leads that can be described as Luttinger liquids. Such leads can be realized, for example, by quantum wires or fractional quantum Hall edge states. In comparison to noninteracting metallic leads, Luttinger liquid leads involve many-body correlations and the single-particle tunneling density of states shows a power-law singularity at the chemical potential. Using the generalized hierarchical equations of motion method, we assess the importance of the singularity and the next-to-leading order many-body correlations. To this end, we compare numerically converged results with second and first-order results of the hybridization expansion that is inherent to our method. As a test case, we study transport through a single-level quantum dot or molecule that can be described by an Anderson impurity model. Cotunneling effects turn out to be most pronounced for attractive interactions in the leads or repulsive ones if an excitonic coupling between the dot and the leads is realized. We also find that an interaction-induced negative differential conductance near the Coulomb blockade thresholds is slightly suppressed as compared to a first-order and/or rate equation result. Moreover, we find that the two-particle ($n$-particle) correlations enter as a second-order ($n$-order) effect and are, thus, not very pronounced at the high temperatures and parameters that we consider.