低维纳米结构的态密度及输运特性的数值计算研究

发布时间：2018-01-15 20:42

本文关键词：低维纳米结构的态密度及输运特性的数值计算研究　出处：《东华大学》2015年硕士论文　论文类型：学位论文

【摘要】：低维材料的态密度与输运特性研究是表征固态材料和器件的重要手段。本论文首先利用时间演化方法研究了一维原子链和石墨烯纳米带的态密度，比较了不同时间演化算法的计算效率，为后续大尺寸材料的态密度研究奠定了基础；我们还利用散射矩阵方法研究了含马约拉纳束缚态的T型结构的输运特性，以用于表征马约拉纳束缚态。本文的主要的研究结果如下：计算能态密度的传统方法依赖于静态哈密顿量的性质。但是，对于自由度较大的固态材料，这一方法的计算量非常巨大，在实际应用中有很大的局限性。本论文采用时间演化方法，通过计算波函数的时间演化性质，研究了低维材料的态密度性质。相比静态哈密顿方法而言，这一方法的计算量大大降低，其计算复杂度随着系统尺度线性增加。我们将这一方法应用在一维原子链结构，研究其态密度的性质，并比较了两种时间演化算法：切比雪夫方法和Crank-Nicolson方法。结果表明，切比雪夫方法的计算效率更高。这为后续大尺度材料的能态密度分析提供了参考依据，并为低维结构的光电导等物理性质的计算奠定了基础。其后，我们将这一方法用于石墨烯纳米带结构，讨论了石墨烯纳米带的态密度，分析带宽、带长和安德森无序等因素对态密度的影响。最近的研究中，马约拉纳束缚态受到了物理学界的广泛关注。在纳米结构中寻找马约拉纳束缚态是近期凝聚态研究的热点。马约拉纳束缚态是一类特殊的粒子，其反粒子就是它自身。在凝聚态材料中，马约拉纳束缚态能够以准粒子的形式存在。理论预言马约拉纳束缚态可以在一维半导体纳米线中存在。相关实验结果也定性的与理论预言一致。但是，零偏压电导峰的定量大小与理论预言依然存在较大的差异，所以，这一实验证据的物理起源仍然存在大量争论。因此，，探索马约拉纳束缚态的特征输运性质是当前理论研究的重要课题。针对此课题，我们研究了含马约拉纳束缚态的T型结构的输运特性，采用散射矩阵方法推导出了微分电导的峰值与零温时散粒噪声Fano因子的关系式。研究表明，微分电导的峰值和零偏压时的散粒噪声Fano因子具备线性关系，这一普适结果与马约拉纳束缚态和左右两端电极的耦合强度的相对大小无关。这一特点在不需要考虑耦合细节的条件下为探测马约拉纳束缚态提供了思路。
[Abstract]:The study of the density of states and transport characteristics of low-dimensional materials is an important means to characterize solid materials and devices. Firstly, the density of states of one-dimensional atomic chains and graphene nanobelts is studied by time evolution method. The computational efficiency of different time evolution algorithms is compared, which lays a foundation for the further study on the density of states of large scale materials. We also use the scattering matrix method to study the transport characteristics of the T-type structure containing the Mayorana bound state, which can be used to characterize the Mayorana bound state. The main results of this paper are as follows: The traditional method for calculating the density of energy states depends on the properties of the static Hamiltonian. However, for solid materials with large degrees of freedom, the computational complexity of this method is very large. In this paper, the time-evolution method is used to study the properties of the density of states in low-dimensional materials by calculating the temporal evolution properties of wave functions, compared with the static Hamiltonian method. The computational complexity of this method is greatly reduced and the computational complexity increases linearly with the scale of the system. We apply this method to the one-dimensional atomic chain structure to study the properties of the density of states. Two time evolution algorithms, the Chebyshev method and the Crank-Nicolson method, are compared. The Chebyshev method is more efficient, which provides a reference for the energy density analysis of large-scale materials, and lays a foundation for the calculation of physical properties such as photoconductivity of low-dimensional structures. This method is applied to the structure of graphene nanobelts. The effects of the density of states, bandwidth, band length and Anderson disorder on the density of states of graphene nanoribbons are discussed. In recent research. The Majoorana bound state has attracted wide attention in the field of physics. Finding the Mayorana bound state in nanostructures is a hot topic in recent studies of condensed matter. The Mayorana bound state is a special kind of particles. Its antiparticles are itself. In condensed matter. The Majoorana binding state can exist in the form of quasiparticle. The theoretical prediction that the Mayorana binding state can exist in one-dimensional semiconductor nanowires is also qualitatively consistent with the theoretical prediction. The quantitative magnitude of the zero bias conductance peak is still different from the theoretical prediction. Therefore, the physical origin of this experimental evidence is still controversial. Exploring the characteristic transport properties of the Mayorana bound state is an important subject in the current theoretical research. In view of this problem, we study the transport characteristics of the T-type structure with the Mayorana bound state. The relationship between the peak value of differential conductance and the Fano factor of particle noise at zero temperature is derived by using the scattering matrix method. There is a linear relationship between the peak value of differential conductance and the Fano factor of particle noise at zero bias voltage. This universal result is independent of the relative magnitude of the Majoorana binding state and the coupling strength between the left and right electrodes. This feature provides a way to detect the Mayorana binding state without considering the coupling details.
【学位授予单位】：东华大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB383.1

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