Space‐Projected Conductivity and Spectral Properties of the Conduction Matrix

Abstract

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‐SiO1.3) 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.