本文關(guān)鍵詞：低維納米結(jié)構(gòu)的態(tài)密度及輸運特性的數(shù)值計算研究　出處：《東華大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 緊束縛模型 石墨烯納米帶 馬約拉納束縛態(tài) 態(tài)密度 輸運特性

【摘要】：低維材料的態(tài)密度與輸運特性研究是表征固態(tài)材料和器件的重要手段。本論文首先利用時間演化方法研究了一維原子鏈和石墨烯納米帶的態(tài)密度，比較了不同時間演化算法的計算效率，為后續(xù)大尺寸材料的態(tài)密度研究奠定了基礎(chǔ)；我們還利用散射矩陣方法研究了含馬約拉納束縛態(tài)的T型結(jié)構(gòu)的輸運特性，以用于表征馬約拉納束縛態(tài)。 本文的主要的研究結(jié)果如下： 計算能態(tài)密度的傳統(tǒng)方法依賴于靜態(tài)哈密頓量的性質(zhì)。但是，對于自由度較大的固態(tài)材料，這一方法的計算量非常巨大，在實際應(yīng)用中有很大的局限性。本論文采用時間演化方法，通過計算波函數(shù)的時間演化性質(zhì)，研究了低維材料的態(tài)密度性質(zhì)。相比靜態(tài)哈密頓方法而言，這一方法的計算量大大降低，其計算復(fù)雜度隨著系統(tǒng)尺度線性增加。我們將這一方法應(yīng)用在一維原子鏈結(jié)構(gòu)，研究其態(tài)密度的性質(zhì)，并比較了兩種時間演化算法：切比雪夫方法和Crank-Nicolson方法。結(jié)果表明，切比雪夫方法的計算效率更高。這為后續(xù)大尺度材料的能態(tài)密度分析提供了參考依據(jù)，并為低維結(jié)構(gòu)的光電導(dǎo)等物理性質(zhì)的計算奠定了基礎(chǔ)。其后，我們將這一方法用于石墨烯納米帶結(jié)構(gòu)，討論了石墨烯納米帶的態(tài)密度，分析帶寬、帶長和安德森無序等因素對態(tài)密度的影響。 最近的研究中，馬約拉納束縛態(tài)受到了物理學(xué)界的廣泛關(guān)注。在納米結(jié)構(gòu)中尋找馬約拉納束縛態(tài)是近期凝聚態(tài)研究的熱點。馬約拉納束縛態(tài)是一類特殊的粒子，其反粒子就是它自身。在凝聚態(tài)材料中，馬約拉納束縛態(tài)能夠以準(zhǔn)粒子的形式存在。理論預(yù)言馬約拉納束縛態(tài)可以在一維半導(dǎo)體納米線中存在。相關(guān)實驗結(jié)果也定性的與理論預(yù)言一致。但是，零偏壓電導(dǎo)峰的定量大小與理論預(yù)言依然存在較大的差異，所以，這一實驗證據(jù)的物理起源仍然存在大量爭論。因此，，探索馬約拉納束縛態(tài)的特征輸運性質(zhì)是當(dāng)前理論研究的重要課題。針對此課題，我們研究了含馬約拉納束縛態(tài)的T型結(jié)構(gòu)的輸運特性，采用散射矩陣方法推導(dǎo)出了微分電導(dǎo)的峰值與零溫時散粒噪聲Fano因子的關(guān)系式。研究表明，微分電導(dǎo)的峰值和零偏壓時的散粒噪聲Fano因子具備線性關(guān)系，這一普適結(jié)果與馬約拉納束縛態(tài)和左右兩端電極的耦合強(qiáng)度的相對大小無關(guān)。這一特點在不需要考慮耦合細(xì)節(jié)的條件下為探測馬約拉納束縛態(tài)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.
【學(xué)位授予單位】：東華大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：TB383.1

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