One-dimensional Mesoscopic Electronic Transport In Quantum Dot System Green's Function Method

The quantum dot of mesoscopic conductor systems has many similar characteristics with the real atoms and molecules. The study on the quantum dot system becomes an important field in condensed-matter physics. Especially, more and more researchers pay attention to the electronic transport properties in the quantum dot system. Theoretically, many approximative and iterative methods were used to investigate the quantum dot system. But the exact analytically algebraic structures of the transport properties in alternating quantum dot array is very difficult to be obtained.In this paper, based on the Green's function as an important method to study interactional multi-particle system, we calculate the electronic transport properties of alternating quantum dot array system. The algebraic structures of the DC current, the differential conductance, and the density of states for the alternating A/B quantum dot array are calculated analytically. These transport properties and formula may be used as a benchmark for numerical studies. The main research contains the following aspects:1. With the exact Green's function calculation, a new matrix D2 m ( xa ,xb )is obtained. Based on this matrix, the electronic transport properties in the alternating A/B quantum dot array is studied. The algebraic structures of the DC current, the differential conductance, and the density of states for the alternating A/B quantum dot array are calculated analytically. We find many interesting features in the alternating quantum dot system from the rigorous algebraic structures. The results show the DC current have the two-step-like structure, the differential conductance have the two-main-peak structure and the density of states have the dissymmetrical multi-peak structure. These properties have been sensitively modified by the quantity of the quantum dot array, the difference for A/B's one-electron level and the resornant widths between A/B and reserviors. Then the effect of the difference of A/B's one-electron level and the resornant widths on the electronic transport are analyzed and calculated. These exact solutions may be used for proofing the transport properties of various alternation quantum dot or other quantum dot system, though it's a simple quantum dot system.2. We indicate the difference of the electronic transport properties between the alternating A/B quantum dot array and an N-coupled quantum dot array by the calculation and comparison. As a result, the electronic transport properties of the two types of the quantum dot systems have many similar features, but for the alternating A/B quantum dot array, we find that the characteristics and structures of the electronic transport properties are more complex.