石墨烯及其纳米带电磁输运性质研究
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摘要
石墨烯是一种新型二维平面碳纳米材料,其电子在狄拉克点附近的线性色散关系决定了它具有丰富而新奇的性质.自2004年底成功制备以来,迅速成为凝聚态物理、材料、化学、信息和生物技术等学科领域的交叉研究热点之一.本文分别采用狄拉克方程,紧束缚近似,非平衡态格林函数和第一原理等方法对石墨烯及其纳米带的电子输运和自旋输运性质进行了较系统的理论研究,为其在纳米电子器件,自旋量子器件等领域的应用提供理论指导.
全文共分为六章.第一章为绪论部分,简要介绍了石墨烯的发现及实验制备,石墨烯及其纳米带的应用背景.第二章,我们详细介绍了石墨烯及其纳米带的能带结构以及石墨烯的奇异物理性质.
第三章至第五章是我们自己的工作.第三章,我们利用狄拉克方程研究了单模式和多模式扶手椅型石果烯纳米带在外加方势垒下的输运性质.结果表明：对于金属扶手椅边缘石墨烯纳米带,最低子带对应的透射系数恒为1,其它子带的透射谱与半导体扶手椅纳米带系统中的子带类似.所有子带均敏感地依赖于扶手椅纳米带的宽度以及势垒的宽度和高度.此外,我们还研究了多模式金属和半导体型扶手椅纳米带的电导和Fano因子.结果表明：电导最小对应Fano因子最大,且Fano因子最大值大于石墨烯中Fano因子的普适值(1／3).
第四章是我们研究的重点内容.我们推导出了石墨烯和扶手椅石墨烯纳米带在动量空间中的推迟格林函数.利用非平衡格林函数方法,系统地研究了外加磁绝缘体下石墨烯的自旋输运性质.结果表明：在两铁磁平行分布的情况下,系统电子自旋向上(向下)的态密度随两铁磁电极极化强度的增大而减小(增加)：但系统的电导正好相反,电子自旋向上(向下)的电导随铁磁电极极化强度的增大而增加(减小).系统电子自旋向上和向下的电流在小偏压时呈现出线性行为,而在大偏压时则表现为非线性现象.有趣的是,当磁绝缘体在石墨烯中引起的交换劈裂能为0时,系统的TMR呈现出一个尖端结构,在0电压处出现极大值.而当交换劈裂能不为0时,这一尖端结构被强烈地抑制.此外,系统的自旋转矩随两铁磁电极磁矩的相对夹角呈正弦函数变化,而随电压的关系类似于系统的电流,且正比于两铁磁平行分布下自旋电流的大小,自旋转矩对交换劈裂能大小的变化不甚敏感.基于相同的方法,我们进一步研究了外加磁绝缘体下7-和8-扶手椅石果烯纳米带的自旋输运性质.研究结果表明,对于7-(8-)扶手椅理想条带，系统的态密度随电子入射能量的关系在费米能附近表现为对称的0平台(非0平台)；当电子入射能量远离费米能时,7-和8-扶手椅纳米带的电子自旋向上和向下的态密度均呈现出一系列尖峰结构.由于量子尺寸效应,线性电导、微分电导也呈现出一系列尖峰结构,且这些尖峰的位置随交换劈裂能而变化.有趣的是,在交换劈裂能为0时,7-和8-扶手椅纳米带的TMR在0电压附近均呈现出理想的平台结构；而当交换劈裂能不为0时,7-扶手椅纳米带的TMR的平台结构变窄,8-扶手椅纳米带的TMR在0电压附近出现一个更高的平台结构,其宽度正比于交换劈裂能的大小.通过进
-步研究,发现7-扶手椅纳米带的自旋转矩定量上要大于8-扶手椅纳米带；7-和8-扶手椅纳米带的自旋转矩随两铁磁电极磁矩的相对夹角变化与石墨烯系统类似；与石墨烯不同的是,7-和8-扶手椅型纳米带的自旋转矩随交换劈裂能呈振荡行为.
第五章,利用第一原理AtomisticToolkit程序包,计算了掺杂与非掺杂十字型石墨烯纳米结系统的电子输运性质.计算结果表明,十字型结的电子输运性质十分敏感于分支的高度、宽度等几何特性和惨杂的位置.例如,当氮(或硼)掺杂于两臂时,我们发现十字型石墨烯纳米结系统在低偏压情况下电流随偏压的增加基本保持为零；但当氮(或硼)掺杂于两干时,电流随偏压的增加显著增大.
第六章,我们对本文的工作进行了总结和归纳,并对石墨烯及其条带的电磁输运性质这一研究领域的发展前景作了简要的展望.
Graphene is found to be exhibit many unusual and intriguing physical prop-erties due to its linear dispersion relation near the Dirac point. Since successful preparation at the end of 2004, graphene has been becoming one of the hot sys-tems in condensed matter physics, material science, chemistry, information and biology technologies. In this thesis, electronic and magnetic transport proper-ties have been theoretically investigated based on the Dirac equation method, the tight-binding method, the non-equilibrium Green function technique, and the first principles method which could provide theoretical guidancd for their applications in nano-electronci devices and spintronics devices.
The thesis is divided into six chapters. In the first chapter, we give a brief introduction about the discovery and fabrication techniques of graphene, the ap-plication background of graphene and its nanoribbons. In the second chapter, we give a detailed introduction about the electronic structure of graphene and its nanoribbons, and the unique physical properties in graphene.
Chapter three, four and five are our works. In the third chapter, based on the Dirac equation method, we theoretcally investigate the mode-dependent and mode-independent transmission probability through a rectanglar potential barrier embedded in armchair-edge graphene nanoribbons (AGNRs) of various widths. It is demonstrated that, the transmission probability for the lowest mode (mode crossing the Fermi level) of the metallic AGNRs is always equal to unity, and the other modes transmission probability for metallic AGNRs is similar to that for semiconducting AGNRs, which depends sensitively on the widths of AGNRs, the barrier height and its range. Besides, the both metallic and semiconducting AGNRs in the vicinity of barrier own a minimum conductance associated with the maximum Fano factor which is larger than universal value 1/3 for a short and wide graphene strip at zero carrier concentration.
Chapter four is our major works. Firstly, a momentum-space expression for the retard Green's function of graphene and AGNRs is derived. By using nonequilibrium Green's function techniques, we theoretically investigate the spin-dependent transport through a graphene sheet between two ferromagnetic leads with arbitrary polarization directions. A magnetic insulator is deposited on the graphene to induce an exchange splitting. It is noted that the density of states (DOS) decreases for spin-up and increases for spin-down when the polarization strength of the two leads in parallel alignment increases, while the conductance increases for spin-up but decreases for spin-down with an increase of the polar-ization. The currents for both spin-up and spin-down channels are found to be linearly proportional to the applied voltage at small bias, then grow nonlincarly as the bias increases. Interestingly, a pronounced cusp-like feature and the max-imum tunneling magnetoresistanec (TMR) value appear at zero bias without the exchange splitting, and the magnitude of TMR is dramatically suppressed with an increase of the exchange splitting. Furthermore, the current-induced spin transfer torque (STT) dependence on the relative angle between the magnetic moments of the two leads shows a sine-like behavior. The behavior of the bias dependent STT is similar to that of the current because the STT is proportional to the spin cur-rent for the two leads in parallel alignment, but it is not sensitive to the exchange splitting in graphene. In the same way, we also investigate the spin-dependent transport for the system of 7-and 8-AGNRs with a magnetic insulator deposited on the AGNRs. It is demonstrated that, a zero (nonzero) value plateau in DOS for 7-AGNR (8-AGNR) appears symmetrically with respect to the Fermi level. For larger electron incident energy, the DOS for the system of both 7-and 8-AGNRs shows an oscillation behavior with sharp peaks. Due to quantum size effect, the linear conductance and the differential conductance are demonstrated to an oscil-lation behavior with sharp peaks, the positions of the peaks for the system shift with the exchange field strength. Interestingly, a pronounced plateau for 7-and 8-AGNR systems appears at lower bias, the increase of the exchange spliitingΔsuppresses the amplitude of this structure for 7-AGNR system. However, the TMR is enhanced within bias range from-ΔtoΔfor 8-AGNR system. Similarly, the STT versus the angle shows a sine-like behavior for 7-and 8-AGNR systems, but it for 7-AGNR system is quantitatively larger than that for 8-AGNR system. In contrast to the STT of the FM/graphene/FM system, the STT with the exchange splitting displays a oscillation behavior for the 7-and 8-AGNR system.
By the first principle (Atomistic Toolkit software packet) calculations, chap-ter five investigates the electronic transport property for a crossed junction of graphene nanoribbons with and without impurity doping. It is demonstrated that the transport property of the junctions very sensitively depends on their dopant positions and gcometic features, including the width and height of the branches. For example, the current is about zero for junction with N(B)-doped shoulder under small bias voltage, but increases notably with N(B)-doped stems.
In chapter six, a summary of the work and a outlook of this topic are given.
全文共分为六章.第一章为绪论部分,简要介绍了石墨烯的发现及实验制备,石墨烯及其纳米带的应用背景.第二章,我们详细介绍了石墨烯及其纳米带的能带结构以及石墨烯的奇异物理性质.
第三章至第五章是我们自己的工作.第三章,我们利用狄拉克方程研究了单模式和多模式扶手椅型石果烯纳米带在外加方势垒下的输运性质.结果表明：对于金属扶手椅边缘石墨烯纳米带,最低子带对应的透射系数恒为1,其它子带的透射谱与半导体扶手椅纳米带系统中的子带类似.所有子带均敏感地依赖于扶手椅纳米带的宽度以及势垒的宽度和高度.此外,我们还研究了多模式金属和半导体型扶手椅纳米带的电导和Fano因子.结果表明：电导最小对应Fano因子最大,且Fano因子最大值大于石墨烯中Fano因子的普适值(1／3).
第四章是我们研究的重点内容.我们推导出了石墨烯和扶手椅石墨烯纳米带在动量空间中的推迟格林函数.利用非平衡格林函数方法,系统地研究了外加磁绝缘体下石墨烯的自旋输运性质.结果表明：在两铁磁平行分布的情况下,系统电子自旋向上(向下)的态密度随两铁磁电极极化强度的增大而减小(增加)：但系统的电导正好相反,电子自旋向上(向下)的电导随铁磁电极极化强度的增大而增加(减小).系统电子自旋向上和向下的电流在小偏压时呈现出线性行为,而在大偏压时则表现为非线性现象.有趣的是,当磁绝缘体在石墨烯中引起的交换劈裂能为0时,系统的TMR呈现出一个尖端结构,在0电压处出现极大值.而当交换劈裂能不为0时,这一尖端结构被强烈地抑制.此外,系统的自旋转矩随两铁磁电极磁矩的相对夹角呈正弦函数变化,而随电压的关系类似于系统的电流,且正比于两铁磁平行分布下自旋电流的大小,自旋转矩对交换劈裂能大小的变化不甚敏感.基于相同的方法,我们进一步研究了外加磁绝缘体下7-和8-扶手椅石果烯纳米带的自旋输运性质.研究结果表明,对于7-(8-)扶手椅理想条带，系统的态密度随电子入射能量的关系在费米能附近表现为对称的0平台(非0平台)；当电子入射能量远离费米能时,7-和8-扶手椅纳米带的电子自旋向上和向下的态密度均呈现出一系列尖峰结构.由于量子尺寸效应,线性电导、微分电导也呈现出一系列尖峰结构,且这些尖峰的位置随交换劈裂能而变化.有趣的是,在交换劈裂能为0时,7-和8-扶手椅纳米带的TMR在0电压附近均呈现出理想的平台结构；而当交换劈裂能不为0时,7-扶手椅纳米带的TMR的平台结构变窄,8-扶手椅纳米带的TMR在0电压附近出现一个更高的平台结构,其宽度正比于交换劈裂能的大小.通过进
-步研究,发现7-扶手椅纳米带的自旋转矩定量上要大于8-扶手椅纳米带；7-和8-扶手椅纳米带的自旋转矩随两铁磁电极磁矩的相对夹角变化与石墨烯系统类似；与石墨烯不同的是,7-和8-扶手椅型纳米带的自旋转矩随交换劈裂能呈振荡行为.
第五章,利用第一原理AtomisticToolkit程序包,计算了掺杂与非掺杂十字型石墨烯纳米结系统的电子输运性质.计算结果表明,十字型结的电子输运性质十分敏感于分支的高度、宽度等几何特性和惨杂的位置.例如,当氮(或硼)掺杂于两臂时,我们发现十字型石墨烯纳米结系统在低偏压情况下电流随偏压的增加基本保持为零；但当氮(或硼)掺杂于两干时,电流随偏压的增加显著增大.
第六章,我们对本文的工作进行了总结和归纳,并对石墨烯及其条带的电磁输运性质这一研究领域的发展前景作了简要的展望.
Graphene is found to be exhibit many unusual and intriguing physical prop-erties due to its linear dispersion relation near the Dirac point. Since successful preparation at the end of 2004, graphene has been becoming one of the hot sys-tems in condensed matter physics, material science, chemistry, information and biology technologies. In this thesis, electronic and magnetic transport proper-ties have been theoretically investigated based on the Dirac equation method, the tight-binding method, the non-equilibrium Green function technique, and the first principles method which could provide theoretical guidancd for their applications in nano-electronci devices and spintronics devices.
The thesis is divided into six chapters. In the first chapter, we give a brief introduction about the discovery and fabrication techniques of graphene, the ap-plication background of graphene and its nanoribbons. In the second chapter, we give a detailed introduction about the electronic structure of graphene and its nanoribbons, and the unique physical properties in graphene.
Chapter three, four and five are our works. In the third chapter, based on the Dirac equation method, we theoretcally investigate the mode-dependent and mode-independent transmission probability through a rectanglar potential barrier embedded in armchair-edge graphene nanoribbons (AGNRs) of various widths. It is demonstrated that, the transmission probability for the lowest mode (mode crossing the Fermi level) of the metallic AGNRs is always equal to unity, and the other modes transmission probability for metallic AGNRs is similar to that for semiconducting AGNRs, which depends sensitively on the widths of AGNRs, the barrier height and its range. Besides, the both metallic and semiconducting AGNRs in the vicinity of barrier own a minimum conductance associated with the maximum Fano factor which is larger than universal value 1/3 for a short and wide graphene strip at zero carrier concentration.
Chapter four is our major works. Firstly, a momentum-space expression for the retard Green's function of graphene and AGNRs is derived. By using nonequilibrium Green's function techniques, we theoretically investigate the spin-dependent transport through a graphene sheet between two ferromagnetic leads with arbitrary polarization directions. A magnetic insulator is deposited on the graphene to induce an exchange splitting. It is noted that the density of states (DOS) decreases for spin-up and increases for spin-down when the polarization strength of the two leads in parallel alignment increases, while the conductance increases for spin-up but decreases for spin-down with an increase of the polar-ization. The currents for both spin-up and spin-down channels are found to be linearly proportional to the applied voltage at small bias, then grow nonlincarly as the bias increases. Interestingly, a pronounced cusp-like feature and the max-imum tunneling magnetoresistanec (TMR) value appear at zero bias without the exchange splitting, and the magnitude of TMR is dramatically suppressed with an increase of the exchange splitting. Furthermore, the current-induced spin transfer torque (STT) dependence on the relative angle between the magnetic moments of the two leads shows a sine-like behavior. The behavior of the bias dependent STT is similar to that of the current because the STT is proportional to the spin cur-rent for the two leads in parallel alignment, but it is not sensitive to the exchange splitting in graphene. In the same way, we also investigate the spin-dependent transport for the system of 7-and 8-AGNRs with a magnetic insulator deposited on the AGNRs. It is demonstrated that, a zero (nonzero) value plateau in DOS for 7-AGNR (8-AGNR) appears symmetrically with respect to the Fermi level. For larger electron incident energy, the DOS for the system of both 7-and 8-AGNRs shows an oscillation behavior with sharp peaks. Due to quantum size effect, the linear conductance and the differential conductance are demonstrated to an oscil-lation behavior with sharp peaks, the positions of the peaks for the system shift with the exchange field strength. Interestingly, a pronounced plateau for 7-and 8-AGNR systems appears at lower bias, the increase of the exchange spliitingΔsuppresses the amplitude of this structure for 7-AGNR system. However, the TMR is enhanced within bias range from-ΔtoΔfor 8-AGNR system. Similarly, the STT versus the angle shows a sine-like behavior for 7-and 8-AGNR systems, but it for 7-AGNR system is quantitatively larger than that for 8-AGNR system. In contrast to the STT of the FM/graphene/FM system, the STT with the exchange splitting displays a oscillation behavior for the 7-and 8-AGNR system.
By the first principle (Atomistic Toolkit software packet) calculations, chap-ter five investigates the electronic transport property for a crossed junction of graphene nanoribbons with and without impurity doping. It is demonstrated that the transport property of the junctions very sensitively depends on their dopant positions and gcometic features, including the width and height of the branches. For example, the current is about zero for junction with N(B)-doped shoulder under small bias voltage, but increases notably with N(B)-doped stems.
In chapter six, a summary of the work and a outlook of this topic are given.
引文
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