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arXiv 2009.12249cond-mat.mtrl-scicond-mat.str-elphysics.optics
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无序金属复电导率的数值外推方法

A numerical extrapolation method for complex conductivity of disordered metals

S. Kern, P. Neilinger, D. Manca, J. Greguš, S. Volkov, M. Grajcar

摘要:

最近,无序金属的光学电导率的量子校正到紫外区域被观察到。虽然这种电导率随频率的增加,也称为反德鲁德行为,应该在电子碰撞频率消失,这种转变从未被观察到或理论上描述过。因此,在很宽的频率范围内的光学电导率的知识是非常感兴趣的。众所周知,复电导率的外推是不适定的-对于有限精度的数据,解析延拓问题的解不是唯一的。然而,我们发现,假设物理上适当的属性的搜索功能$σ(ω)$,如:对称性,平滑性,和渐近解的低和高频率,可以显着限制的解决方案。我们提出了一个简单的数值方法,利用径向基函数近似和模拟退火,合理地外推的光学电导率从可见光频率范围下到远红外和紫外区域。MoC和NbN薄膜上获得的外推通过在宽的频率范围内的透射测量来检查。

英文摘要:

Recently, quantum corrections to optical conductivity of disordered metals up to the UV region were observed. Although this increase of conductivity with frequency, also called anti-Drude behaviour, should disappear at the electron collision frequency, such transition has never been observed or described theoretically. Thus, the knowledge of optical conductivity in a wide frequency range is of great interest. It is well known that the extrapolation of complex conductivity is ill-posed - a solution of the analytic continuation problem is not unique for data with finite accuracy. However, we show that assuming physically appropriate properties of the searched function $σ(ω)$, such as: symmetry, smoothness, and asymptotic solution for low and high frequencies, one can significantly restrict the set of solutions. We present a simple numerical method utilizing the radial basis function approximation and simulated annealing, which reasonably extrapolates the optical conductivity from visible frequency range down to far infrared and up to ultraviolet region. Extrapolation obtained on MoC and NbN thin films was checked by transmission measurement across a wide frequency range.

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