摘要
介观纳米体系的研究是目前凝聚态物理十分活跃的前沿研究领域之一。它不断揭示出一系列重要的物理内禀,同时也展现出广泛的应用前景。本论文运用格林函数方法研究了介观纳米体系的电子输运现象。其目的在于揭示这些结构中的新效应及其物理机制,并为设计和实现具有优良性能的量子器件提供物理模型和理论依据。
本论文共分八章。第一章介绍了介观纳米体系的结构和性质特征,特别是电子输运性质。
在第二章中,简单介绍了格林函数方法,并利用该方法计算了T型量子线在势调制下的电子输运性质。讨论了单个和耦合T型量子线垂直手臂中的势垒对输运的影响。对于单个T型量子线,在势调制下水平和拐角方向的电导上出现了一个谷峰对;势垒宽度的变化使得谷峰对变得更明显。这个谷峰对是由T型量子线中的束缚态引起的。对于两个耦合T型量子线,势调制与水平方向电导上的两个谷是紧密关联的。我们可以通过势调制来实现对电导谱的裁剪。
在第三章中,用模匹配方法计算了十字型、T型和L型量子线及量子点中束缚态在势调制下的能量和波函数,发现了束缚态能量与势调制之间的普适关系。用电子几率密度图显示了不同量子结构中束缚态之间的演化。同时我们的计算表明局域在量子点中的电子态在势调制下经历了一个从束缚态到准束缚态再到束缚态的演化过程。
在第四章中,研究了一个有限量子反点阵列中的束缚态及其引起的传输共振现象。我们计算了几种不同几何结构的电导,讨论了量子反点之间的距离对量子束缚态及电子输运的影响,也讨论了反点阵列的周期对高能束缚态的影响。发现了一些有趣的高能准束缚态,电子在这些态中主要是局域在结的交叉区域而不是在结中。
在第五章中,我们计算了两种典型的开放周期型结构的电导。对于包含n个限制区域的多波导管结构,在低能区域出现了(n-1)重的共振劈裂峰而在高能区域则是(n-2)重的共振劈裂峰。前者主要是由局域在突起中的束缚态引起的,而后着则对应于局域在限制区域的高能束缚态。对于高能束缚态,结构中突起的作用相当于一个势垒而不是一个势阱。当限制区域的长度增加时,更多的束缚态将存在于限制区域中。对于量子反点阵列结构,在电导第一起始能量处同样存在(n-2)重的共振劈裂。
在第五章的基础上,第六章研究了在磁调制下两种典型的周期结构中由束缚态引起的传输共振现象。对于包含n个垒的电超晶格结构,在第一电导台阶开始的地方出现了(n-1)重共振劈裂。这些共振峰是由磁场调制下的束缚态引起的,处于这些束缚态中的电子主要是局限在势垒而不是势阱中。对于包含n个限制区域的多波导管结构,高能区的(n-2)重共振劈裂在磁调制下变成了(n-1)重共振劈裂。
在第七章中,研究了四种L型石墨纳米带的电导和局域态密度。结果表明,这些结构在费米面附近的电导取决于扶手椅型边界石墨带的类型。当石墨纳米带的横向尺寸较小时,其电导及态密度对几何结构非常敏感。
第八章对本论文的工作进行了总结,并对以后的工作提出了一些设想。
Mesoscopic nano-systems are forefront in condensed matter physics. There existing in these systems a great deal of novel and marvelous physics properties and prospective potential applications. In this thesis, we study the electron transport properties of mesoscopic nano-system by using the Green’s function method. The aim is to explore the physical mechanisms of the found new effects in these systems, and to supply physical models and theoretical validity in designing novel quantum devices with better properties.
The thesis consists of eight chapters. In chapter one, we introduce typical structure of mesoscopic nano-systems and their characteristics, especially their transport properties.
In chapter two, the Green’s function method is simply introduced. By applying the method, we calculate the electron transport properties of T-shaped quantum wires under potential modulation. The influence of potential modulation in vertical quantum wire on electronic transport across one or two-coupled T-shaped quantum wire(s) is discussed. For a single T-shaped quantum wire, the potential induces a dip-peak couple structure in the conductance curves for parallel and bend transport. The change of the potential thickness induces the dip-peak couple more pronounced. For two coupled T-shaped quantum wires, two dips in the parallel conductance are associated with the potential modulation. Conductance profiles can be tailored by the modulation.
In chapter three, we calculate the bound state energies and wave functions of crossed, T-shaped, L-shaped quantum wire and quantum dot under potential modulation by using mode-match method. The relation of the bound state energy and the potential height for different structures is found. The contour plots of the probability density visualize the evolution of the bound state in different structures. The calculation to the lifetime of bound states in quantum dot indicates that there is an evolution of eigenstate in quantum dot from a bound state to a quasibound state and then to a bound state.
In chapter four, the resonant peaks via the quasibound states in the confined array of antidots are studied. We calculate the conductance of several structures, and discuss the influence of the distance between antidots on the bound states and electron transport. The influence of the period of antidot array on the higher-energy bound states is also discussed. Some interesting higher-energy bound states are found, electrons in the states are not localized at the junctions but at the intersections of the junctions.
In chapter five, we calculate the conductance of two typical open periodic structures. For the periodic multiwaveguide structure including n constrictions, (n-1)-fold splitting peaks appear at the low energies of conductance while (n-2)-fold splitting peaks appear at the high energies. The former resonant peaks are induced by the quasibound states mainly localized in the stubs, while the latter peaks are originated from the high quasibound states mainly localized in the constrictions. To the high quasibound states, the stubs act as potential barriers rather than wells. More quasibound states will exist in the constriction between two stubs, as the length of the constriction increases. For the periodic antidots arrays, (n-2)-fold splitting rule is also found around the first threshold energy.
Based on chapter five, transmission resonant via quantum bound states in two typical periodic structures under magnetic field is studied in chapter six. For the electric superlattice consisting of n barriers, (n-1)-fold resonant peaks are shown in the beginning of the first conductance step under magnetic modulation. The peaks are induced by the magnetically quasibound states which wavefunctions are confined in the potential barriers rather than in the wells. For the open periodic multi-waveguides consisting of n constrictions, under magnetic modulation, the (n-2)-fold resonant splitting at the higher-energy region will change into (n-1)-fold splitting.
In chapter seven, we study the conductance and local density of states of four kinds of L graphene nanoribbon. It is found that, the conductance around the Fermi-surface is determined by the type of graphene nanoribbon with armchair edge. As the nanoribbon is narrow, the conductance and density of states are very sensitive to the geometry of the structure.
The last chapter presents a conclusion of this thesis and some prospects for this investigation.
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