论文标题
在电子传输的Su-Schrieffer-Heeger模型上：Mellin Transform低温光电率
On the Su-Schrieffer-Heeger model of electron transport: low-temperature optical conductivity by the Mellin transform
论文作者
论文摘要
我们描述了低温光导率作为沿聚合物链跳跃的量子机械系统的频率的函数。为此，我们调用了Su-Schrieffer-Heeger \ emph {tight-Binting} hamiltonian在一维（1D）晶格上使用无旋转的无旋转电子。我们的目标是通过渐近学显示该系统的频带间电导率的行为，因为最小的能量带隙倾向于关闭。我们的分析方法包括：（i）由于显微镜碰撞而导致非零阻尼的光导率的久保型公式； （ii）将此公式的减少为一维动量在布里群区域内不可或缺； （iii）通过三维Mellin转换对关键物理参数以及随后在相应复杂空间的区域中的反转来评估该积分的基础函数。我们的方法揭示了电导率与其梅林转化的特定奇异性的亲密联系。分析结果与直接数值计算非常吻合。
We describe the low-temperature optical conductivity as a function of frequency for a quantum-mechanical system of electrons that hop along a polymer chain. To this end, we invoke the Su-Schrieffer-Heeger \emph{tight-binding} Hamiltonian for non-interacting spinless electrons on a one-dimensional (1D) lattice. Our goal is to show via asymptotics how the interband conductivity of this system behaves as the smallest energy bandgap tends to close. Our analytical approach includes: (i) the Kubo-type formulation for the optical conductivity with a nonzero damping due to microscopic collisions; (ii) reduction of this formulation to a 1D momentum integral over the Brillouin zone; and (iii) evaluation of this integral in terms of elementary functions via the three-dimensional Mellin transform with respect to key physical parameters and subsequent inversion in a region of the respective complex space. Our approach reveals an intimate connection of the behavior of the conductivity to particular singularities of its Mellin transform. The analytical results are found in good agreement with direct numerical computations.
