超均匀无序对带隙的影响

Jonas F. Karcher, Sarang Gopalakrishnan, Mikael C. Rechtsman
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引用次数: 0

摘要

半导体、绝缘体和光子晶体的特性是由它们的电子或光子带以及它们之间的间隙所决定的。当材料处于无序状态时,就会出现 Lifshitz 尾部:这是从带边分叉出来的局部状态,其作用是有效地关闭带隙。虽然当无序状态在空间上不相关时,人们对 Lifshitz 尾部有很好的理解,但最近人们对超均匀无序的情况产生了兴趣,即当无序波动高度相关,并在长长度尺度上趋近于零时。在本文中,我们采用路径积分和斯坦顿方法分析求解了超均匀系统的 Lifshitz 尾问题。我们发现了状态密度与带边能量差的函数形式。我们还研究了超均匀无序对不存在带隙的韦尔半金属的状态密度的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The effect of hyperuniform disorder on band gaps
The properties of semiconductors, insulators, and photonic crystals are defined by their electronic or photonic bands, and the gaps between them. When the material is disordered, Lifshitz tails appear: these are localized states that bifurcate from the band edge and act to effectively close the band gap. While Lifshitz tails are well understood when the disorder is spatially uncorrelated, there has been recent interest in the case of hyperuniform disorder, i.e., when the disorder fluctuations are highly correlated and approach zero at long length scales. In this paper, we analytically solve the Lifshitz tail problem for hyperuniform systems using a path integral and instanton approach. We find the functional form of the density-of-states as a function of the energy difference from the band edge. We also examine the effect of hyperuniform disorder on the density of states of Weyl semimetals, which do not have a band gap.
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