Local electric conductive property of Si nanowire models

Local electric conductive properties of Si nanowire models are investigated by using two local electric conductivity tensors, \documentclass[12pt]{minimal}\begin{document}${\mathop{\sigma }\limits^{\leftrightarrow} }_{\mathrm{ext}}(\vec{r})$\end{document}σ↔ ext (r⃗) and \documentclass[12pt]{minimal}\begin{document}${\mathop{\sigma }\limits^{\leftrightarrow} }_{\mathrm{int}}(\vec{r})$\end{document}σ↔ int (r⃗), defined in Rigged QED. It is emphasized that \documentclass[12pt]{minimal}\begin{document}${\mathop{\sigma }\limits^{\leftrightarrow} }_{\mathrm{int}}(\vec{r})$\end{document}σ↔ int (r⃗) is defined as the response of electric current to the actual electric field at a specific point and does not have corresponding macroscopic physical quantity. For the Si nanowire models, there are regions which show complicated response of electric current density to electric field, in particular, opposite and rotational ones. Local conductivities are considered to be available for the study of a negative differential resistance (NDR), which may be related to this opposite response. It is found that \documentclass[12pt]{minimal}\begin{document}${\mathop{\sigma }\limits^{\leftrightarrow} }_{\mathrm{int}}(\vec{r})$\end{document}σ↔ int (r⃗) shows quite different pattern from \documentclass[12pt]{minimal}\begin{document}${\mathop{\sigma }\limits^{\leftrightarrow} }_{\mathrm{ext}}(\vec{r})$\end{document}σ↔ ext (r⃗), local electric conductivity defined for the external electric field. The effects of impurities are also studied by using the model including a Ge atom, in terms of the local response to electric field. It is found that the difference from the pristine model is found mainly around the Ge atom.