Quantum transport in nanostructures: From computational concepts to spintronics in graphene and magnetic tunnel junctions
Quantum transport in nanostructures: From computational concepts to spintronics in graphene and magnetic tunnel junctions
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发表时间：
2009-12
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通讯作者：
M. Wimmer
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作者：
M. Wimmer
自旋电子学（利用载流子的自旋自由度）和石墨烯（单层石墨）领域都为未来的电子学提供了很好的前景。对这类系统输运性质的理论研究可能有助于确定新的物理效应和应用。然而，这种理论探索经常遇到不允许解析解决的复杂系统，需要先进的数值技术。因此，本论文有两个目标：第一，开发通用的数值输运算法；第二，研究磁隧道结和石墨烯纳米带中的自旋相关输运。本文分为两部分：第一部分致力于开发可应用于任何由紧密结合哈密顿量描述的系统的通用传输算法。为此，对非平衡格林\\\\\\\函数形式主义的教学回顾确定了在计算紧密结合系统的输运性质时出现的问题。然后用一种通用的方法解决这些问题，使用可以很容易地应用于任意紧密绑定系统的算法。特别地，本文提供了表面Green\\\\\\\引线函数的显式表达式的严格推导，以及计算该表达式的数值稳定方法。此外，一个广义的Fisher-Lee关系允许从延迟Green\\\\\\\函数计算散射矩阵。最后，基于图划分技术的矩阵重排序算法允许将最初为导线开发的成熟量子传输算法应用于任意几何甚至多终端系统。第二部分涉及磁性隧道结和石墨烯纳米带中的自旋相关输运，利用第一部分中开发的数值技术以及分析模型来捕捉基本物理。本文以一个典型的自旋电子学器件为例，研究了磁场对具有单一铁磁接触和外延半导体势垒的磁隧道结隧道各向异性磁电阻效应的影响。发现势垒中磁场的依赖关系受Dresselhaus自旋轨道耦合控制，数值模拟结果与实验结果吻合较好。此外，本文还讨论了石墨烯纳米带中的自旋相关输运。边缘态磁性的预测使之字形石墨烯纳米带成为石墨烯基自旋电子学的一个有前途的候选材料。本文讨论了在纯石墨烯器件中产生和检测自旋电流的方法。为此，对石墨烯各种模型中边缘态输运特性的深入讨论表明，边缘态输运的现实描述必须超越常用的最近邻紧密结合模型。这些结果为研究之字形石墨烯纳米带中的自旋电流奠定了基础。特别是，发现自旋电流波动是普遍的，并讨论了在石墨烯纳米带中检测自旋电流的可能实验装置。
Both the field of spintronics - utilizing the spin degree of freedom of charge carriers - as well as the field of graphene - a single layer of graphite - offer promising perspectives for a future electronics. Theoretical studies of transport properties in such systems may help identifying new physical effects and applications. Such theoretical explorations however often encounter complex systems that do not allow for an analytical solution, calling for advanced numerical techniques. Hence, this thesis has two objectives: First, to develop generic numerical transport algorithms and second, to investigate spin-dependent transport in magnetic tunnel junctions and in graphene nanoribbons. This thesis is organized in two parts: The first part is devoted to developing generic transport algorithms that can be applied to any system described by a tight-binding Hamiltonian. To this end, a pedagogical review of the non-equilibrium Green\\\\\\\'s function formalism identifies problems that arise in computing the transport properties of a tight-binding system. These problems are then solved in a generic way, employing algorithms that can be readily applied to arbitrary tight-binding systems. In particular, this thesis provides a rigorous derivation of an explicit expression for the surface Green\\\\\\\'s function of a lead, as well as a numerically stable way for evaluating this expression. In addition, a generalized Fisher-Lee relation allows for the calculation of the scattering matrix from the retarded Green\\\\\\\'s function. Finally, a matrix-reordering algorithm based on graph partitioning techniques allows for the application of well-established quantum transport algorithms, originally developed for wires, to arbitrary geometries and even multi-terminal systems. The second part deals with spin-dependent transport in magnetic tunnel junctions and graphene nanoribbons, making use of the numerical techniques developed in the first part as well as analytical models in order to capture the essential physics. As an example of a prototypical spintronics device, the thesis provides an investigation of magnetic field effects on the tunneling anisotropic magnetoresistance effect in a magnetic tunnel junction with a single ferromagnetic contact and an epitaxial semiconducting barrier. The magnetic field dependence is found to be governed by the Dresselhaus spin orbit coupling in the barrier, and numerical simulations show good quantitative agreement with experiments. In addition, this thesis discusses spin-dependent transport in graphene nanoribbons. The prediction of edge state magnetism makes zigzag graphene nanoribbons a promising candidate for graphene-based spintronics. This thesis discusses methods of generating and detecting spin currents in graphene-only devices. To this end, a thorough discussion of edge state transport properties within various models for graphene shows that a realistic description of edge state transport must go beyond the commonly used nearest-neighbor tight-binding model. These results are the basis for an investigation of spin currents in zigzag graphene nanoribbons. In particular, the spin current fluctuations are found to be universal, and possible experimental setups for detecting spin currents in graphene nanoribbons are discussed.