Herein, the Kubo–Greenwood formula is utilized to project the electronic conductivity into real space, and a Hermitian positive semidefinite matrix Γ is discussed, which is called the conduction matrix, that reduces the computation of spatial conduction activity to a diagonalization. It is shown that for low-density amorphous carbon, connected sp² rings and sp chains are conduction-active sites in the network. In amorphous silicon, transport involves hopping through tail states mediated by the defects near the Fermi level. It is found that for liquid silicon, thermal fluctuations induce spatial and temporal conductivity fluctuations in the material. The frequency-dependent absorption of light as a function of wavelength in an amorphous silicon suboxide (a-SiO_1.3) is also studied. It is shown that the absorption is strongly frequency dependent and selects out different oxygen vacancy subnetworks depending on the frequency. Γ is diagonalized to obtain conduction eigenvalues and eigenvectors, and it is shown that the density of states of the eigenvalues for FCC aluminum has an extended spectral tail that distinguishes metals from insulators and semiconductors. The method is easy to implement with any electronic structure code, providing suitable estimates for single-particle electronic states and energies.

中文翻译：

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传导矩阵的空间投影电导率和光谱特性

在此，利用 Kubo-Greenwood 公式将电子电导率投影到真实空间中，并讨论了 Hermitian 半正定矩阵Γ，称为传导矩阵，它将空间传导活动的计算减少到对角化。结果表明，对于低密度无定形碳，连接sp ²环和sp链是网络中的传导活性位点。在非晶硅中，传输涉及通过由费米能级附近的缺陷介导的尾态跳跃。发现对于液态硅，热波动会引起材料的空间和时间电导率波动。还研究了在无定形低氧化硅 (a-SiO _1.3 ) 中作为波长函数的光的频率相关吸收。结果表明，吸收与频率密切相关，并根据频率选择不同的氧空位子网络。Γ对角化以获得传导特征值和特征向量，并且表明 FCC 铝的特征值状态密度具有扩展的谱尾，可以将金属与绝缘体和半导体区分开来。该方法易于使用任何电子结构代码实现，为单粒子电子状态和能量提供合适的估计。