Boltzmann transport theory for metal-insulator transitions

Introducing both weak-localization corrections and electron-electron interactions of elastic scattering channels into the framework of Boltzmann transport theory, we construct a Wölfle–Vollhardt self-consistent equation for the diffusion coefficient and investigate metal-insulator transitions at finite temperatures. Here, we focus on two dimensional metal-insulator transitions and compare them with those in three dimensions, considering the diffusion constant as a function of both disorder strength and bath temperature. As a result, we find that renormalization of the diffusion constant in two dimensions strongly depends on the bare value of the dephasing rate, introduced to regularize the IR divergence of the weak-localization kernel in two dimensions while the renormalized diffusion coefficient does not rely on the bare value of the dephasing rate much in three dimensions, free from the IR divergence. This result implies that the role of dephasing in renormalization of the diffusion constant is more complex in two dimensions than that in three dimensions, where higher-order interaction corrections for the dephasing rate should be taken into account in the framework of the Boltzmann transport theory. Graphical abstract