User:YohanesPramudya
Introduction
The study of electron transport is at the very heart of condensed matter physics. Band theory explains the physical properties of numerous materials, such as simple insulators, metals, and semiconductors. In metal, the electrons can move freely even at zero temperature because the conduction band is partially filled. On the other hand, insulators and semiconductor have fully filled valence band separated by an energy gap from an empty conduction band.
According to band theory, electrons in a perfectly periodic array of ions experience no collisions at all. However, some transition metal oxides with partially filled or bands (predicted to be a metal) are poor conductors or even insulators. The reason for the absence of carrier mobility is electron localization. The first fundamental mechanism of electron localization is the random scattering of mobile electrons caused by impurities or defect (disorder), which is called Anderson localization. The transition from metal into insulator occurs when the mean free path becomes smaller than the De Broglie wavelength. Based on scaling theory of localization by Abraham, Anderson, et.al. [3], the metal-insulator transition (MIT) exists for non-interacting electrons in three dimensions (3D). In addition, the system is an insulator if the Fermi energy is smaller than the characteristic amplitude of the disorder potential. According to this theory, there is no true metallic behavior in two dimensions (2D) and one dimensions (1D) system with non interacting electron.
The second fundamental mechanism in MIT is caused by electron-electron interaction. One of the simplest examples for interaction driven localization is Wigner crystallization. In this system, each electron is confined not by an ionic potential, but due to the formation of a deep potential well produced by repulsion from other electrons embedded in a positive charge background.