Centre for the Physics of Materials and Department of Physics, McGill University, Montreal, QC, H3A 2T8, Canada.
J Phys Condens Matter. 2011 Oct 19;23(41):415301. doi: 10.1088/0953-8984/23/41/415301. Epub 2011 Sep 27.
We report the development and an application of a symbolic tool, called SymGF, for analytical derivations of quantum transport properties using the Keldysh nonequilibrium Green's function (NEGF) formalism. The inputs to SymGF are the device Hamiltonian in the second quantized form, the commutation relation of the operators and the truncation rules of the correlators. The outputs of SymGF are the desired NEGF that appear in the transport formula, in terms of the unperturbed Green's function of the device scattering region and its coupling to the device electrodes. For complicated transport analysis involving strong interactions and correlations, SymGF provides significant assistance in analytical derivations. Using this tool, we investigate coherent quantum transport in a double quantum dot system where strong on-site interaction exists in the side-coupled quantum dot. Results obtained by the higher-order approximation and Hartree-Fock approximation are compared. The higher-order approximation reveals Kondo resonance features in the density of states and conductances. Results are compared both qualitatively and quantitatively to the experimental data reported in the literature.
我们报告了一种符号工具 SymGF 的开发和应用，该工具用于使用 Keldysh 非平衡格林函数（NEGF）形式主义进行量子输运性质的分析推导。SymGF 的输入是二次量子化形式的器件哈密顿量、算符的对易关系和相关函数的截断规则。SymGF 的输出是出现在输运公式中的所需的 NEGF，其形式为器件散射区域的未受扰格林函数及其与器件电极的耦合。对于涉及强相互作用和相关性的复杂输运分析，SymGF 在分析推导中提供了重要的帮助。使用这个工具，我们研究了在存在强局域相互作用的侧耦合量子点中的双量子点系统中的相干量子输运。比较了高阶近似和 Hartree-Fock 近似的结果。高阶近似揭示了在态密度和电导中存在的 Kondo 共振特征。结果与文献中报道的实验数据进行了定性和定量的比较。
