石墨烯纳米结构中输运性质的研究
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摘要
石墨烯是把两个等价碳原子交替排列在一个六角晶格上形成的一种二维结构的平面材料。它从发现之初就受到了广泛的关注,是因为石墨烯被证实了存在很多奇特的电子特性,比如在狄拉克点附件的线性色散关系,整数和半整数的量子霍尔效应,高的电子迁移率等等。所有的这些奇特性质使石墨烯成为半导体工业中硅的理想替代品。同时为了在石墨烯的能带结构上产生一个带隙,可以沿着特定的晶格方向对其进行切割,这样得到的石墨烯条带在狄拉克点附近存在一个能隙。与二维石墨烯相比,一维的石墨烯条带在输运性质上也发生了很大的改变。除了可以在狄拉克点产生带隙外,狄拉克点的另一个性质是位于布里渊区两端的两个狄拉克点是简并的(被视为一种赝自旋)。通过区分两个简并的狄拉克点,得到两个与赝自旋方向有关的电流,这种性质可以被用来制作成赝自旋电子器件。而量子抽运是一种非常有效的产生电流的方法。
本论文主要研究了一维双层扶手椅形石墨烯条带的输运性质和赝自旋方向有关的抽运电流。论文的内容主要包括以下这些方面。
第一章从四个方面讲述了论文的研究背景。首先实验室中几种常用的石墨烯制备方法被列举出来进行了比较。然后我们详细讨论了一些石墨烯的基本特点。因为在这里主要关注的是石墨烯的输运性质,所以紧跟着通过与宏观和微观系统比较,我们介绍了介观体系下的电子输运。本章的最后提到了石墨烯在工业领域上存在广泛的潜在应用,并且它已经开始逐步走进我们的生活。
第二章是理论部分,主要详细推导了计算过程中用到的各种公式。紧束缚近似模型,格林函数方法,散射矩阵是研究介观体系输运性质常用的方法。另一方面,量子抽运区别于它们也是一种常用的产生电流的方法。
在第三章我们研究发现了从单层石墨烯条带入射的电子,经过一个双层区域,电子的透射几率随着两层相对位置的变化出现周期震荡。这是因为一个基本单元中每个电子的几率密度不同,有大有小,当两个较大几率密度的电子存在相互作用时层间相互作用强。因此当两层有相对移动时,存在层间相互作用的原子发生变化,导致层间相互作用的强弱发生改变,从而影响了通过两层区域时电子透射几率的大小。透射几率出现周期性震荡的性质可以用来测量层间的相对位移,并且精度可以达到10-10这个量级。
第四章中用量子抽运的方法在一个局域拉伸的石墨烯中产生了一个纯赝自旋电流。完美石墨烯中K点和K’点是简并的,通过拉伸石墨烯可以消除简并。同时考虑两个反平行铁磁引起的矢量势,在一个由三个势垒构成的结构中就产生了一个与赝自旋指数有关的电流。因此这样的一种结构可以被用来制作赝自旋电子器件。
延续第四章中的工作,我们用带隙来解除K点和K’点的简并去产生一个纯的赝自旋电流。部分区域用BN作衬底可以产生一个与空间位置有关的带隙,在上一章中三个势垒的结构上再考虑两个平行的铁磁矢量势,就可以得到一个纯的赝自旋电流。
在本文的最后一章对各部分内容给出了一个总结。
Graphene, a two dimensional material which is formed by arranging carbon atoms in a hexagonal lattice, is attractive to researchers. It has been proved to have many unique properties, such as linear dispersion relation at the Dirac point, integer and half-integer quantum Hall effect, high electron mobility and so on. All of these properties make graphene become the ideal substitute for silicon in semi-conductor industry. In order to open a gap in graphene, we can confine the graphene along a special direction to form graphene ribbon. The confined direction and the width of the ribbon affect the value of the gap. The gap is opened at the Dirac points. As we already known that the Dirac points are degeneracy in graphene. Some researchers have focused on the transport property by differing the two degenerated Dirac points which is useful to make valleytronic device. On the other hand quantum pumping is a powerful method to research the transport in mesoscopic system. This thesis studied the transport property of the bilayer graphene ribbon and generated a pure valley current in graphene by using quantum pumping method. It contains the following chapters.
Chapter one gives an introduction of the research background and it included four parts. Firstly we present the widely used methods in laboratory to product graphene and point out the advantage part and disadvantage part of each method. Secondly some graphene properties are discussed in detail. Next the mesoscopic transport theory is explained by comparing with the transpirt theory in macroscopic and microscopic system. At last it is necessary to specify the potential applications of graphene in many aspects of real life.
Chapter two is the theory part where the formulas used in the calculation process are derived step by step. Tight-binding model, Green's function method, scattering matrix are all the favorite theories to the researchers when they solve the transport problem. Quantum pumping theory is different from previous ones where a current flow through the device without a bias.
In chapter three we investigate the oscillation property of the transmission probability of the bilayer graphene ribbon with two single layer leads. The DOS of each atom in a unit cell are different. Thus in the bilayer region when the top layer moves relative to the bottom layer, the interlayer interaction strength changes which results in the change of electron transmission probability through the bilayer region. This property can be used to detect the relative movement of the two layers in the order of A.
In chapter four we try to generate pure valley current in strain engineered graphene by quantum pumping. The K and K' valley are degenerate in clear graphene and are separated by the strain induced the vector potential. By adding two anti-parallel magnetic fields a pure valley current is pumped out in the structure. The proposed structure is easily realized in experiment and can be used to make valleytronics.
Following the work done in chapter4, we try to separate the two valleys in another method. In chapter five a pure valley current is obtained by using local gapped graphene which is achieved by using BN substrate in specific region. The FM stripes are necessary for pure valley current generation, but they should be in anti-parallel configuration.
本论文主要研究了一维双层扶手椅形石墨烯条带的输运性质和赝自旋方向有关的抽运电流。论文的内容主要包括以下这些方面。
第一章从四个方面讲述了论文的研究背景。首先实验室中几种常用的石墨烯制备方法被列举出来进行了比较。然后我们详细讨论了一些石墨烯的基本特点。因为在这里主要关注的是石墨烯的输运性质,所以紧跟着通过与宏观和微观系统比较,我们介绍了介观体系下的电子输运。本章的最后提到了石墨烯在工业领域上存在广泛的潜在应用,并且它已经开始逐步走进我们的生活。
第二章是理论部分,主要详细推导了计算过程中用到的各种公式。紧束缚近似模型,格林函数方法,散射矩阵是研究介观体系输运性质常用的方法。另一方面,量子抽运区别于它们也是一种常用的产生电流的方法。
在第三章我们研究发现了从单层石墨烯条带入射的电子,经过一个双层区域,电子的透射几率随着两层相对位置的变化出现周期震荡。这是因为一个基本单元中每个电子的几率密度不同,有大有小,当两个较大几率密度的电子存在相互作用时层间相互作用强。因此当两层有相对移动时,存在层间相互作用的原子发生变化,导致层间相互作用的强弱发生改变,从而影响了通过两层区域时电子透射几率的大小。透射几率出现周期性震荡的性质可以用来测量层间的相对位移,并且精度可以达到10-10这个量级。
第四章中用量子抽运的方法在一个局域拉伸的石墨烯中产生了一个纯赝自旋电流。完美石墨烯中K点和K’点是简并的,通过拉伸石墨烯可以消除简并。同时考虑两个反平行铁磁引起的矢量势,在一个由三个势垒构成的结构中就产生了一个与赝自旋指数有关的电流。因此这样的一种结构可以被用来制作赝自旋电子器件。
延续第四章中的工作,我们用带隙来解除K点和K’点的简并去产生一个纯的赝自旋电流。部分区域用BN作衬底可以产生一个与空间位置有关的带隙,在上一章中三个势垒的结构上再考虑两个平行的铁磁矢量势,就可以得到一个纯的赝自旋电流。
在本文的最后一章对各部分内容给出了一个总结。
Graphene, a two dimensional material which is formed by arranging carbon atoms in a hexagonal lattice, is attractive to researchers. It has been proved to have many unique properties, such as linear dispersion relation at the Dirac point, integer and half-integer quantum Hall effect, high electron mobility and so on. All of these properties make graphene become the ideal substitute for silicon in semi-conductor industry. In order to open a gap in graphene, we can confine the graphene along a special direction to form graphene ribbon. The confined direction and the width of the ribbon affect the value of the gap. The gap is opened at the Dirac points. As we already known that the Dirac points are degeneracy in graphene. Some researchers have focused on the transport property by differing the two degenerated Dirac points which is useful to make valleytronic device. On the other hand quantum pumping is a powerful method to research the transport in mesoscopic system. This thesis studied the transport property of the bilayer graphene ribbon and generated a pure valley current in graphene by using quantum pumping method. It contains the following chapters.
Chapter one gives an introduction of the research background and it included four parts. Firstly we present the widely used methods in laboratory to product graphene and point out the advantage part and disadvantage part of each method. Secondly some graphene properties are discussed in detail. Next the mesoscopic transport theory is explained by comparing with the transpirt theory in macroscopic and microscopic system. At last it is necessary to specify the potential applications of graphene in many aspects of real life.
Chapter two is the theory part where the formulas used in the calculation process are derived step by step. Tight-binding model, Green's function method, scattering matrix are all the favorite theories to the researchers when they solve the transport problem. Quantum pumping theory is different from previous ones where a current flow through the device without a bias.
In chapter three we investigate the oscillation property of the transmission probability of the bilayer graphene ribbon with two single layer leads. The DOS of each atom in a unit cell are different. Thus in the bilayer region when the top layer moves relative to the bottom layer, the interlayer interaction strength changes which results in the change of electron transmission probability through the bilayer region. This property can be used to detect the relative movement of the two layers in the order of A.
In chapter four we try to generate pure valley current in strain engineered graphene by quantum pumping. The K and K' valley are degenerate in clear graphene and are separated by the strain induced the vector potential. By adding two anti-parallel magnetic fields a pure valley current is pumped out in the structure. The proposed structure is easily realized in experiment and can be used to make valleytronics.
Following the work done in chapter4, we try to separate the two valleys in another method. In chapter five a pure valley current is obtained by using local gapped graphene which is achieved by using BN substrate in specific region. The FM stripes are necessary for pure valley current generation, but they should be in anti-parallel configuration.
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