Unified Theoretical Approach to Electronic Transport from Diffusive to Ballistic Regimes

TL;DR

This paper presents a unified semiclassical framework that seamlessly describes electron transport across diffusive and ballistic regimes, bridging two classical models with a single analytical approach.

Contribution

The authors develop a comprehensive method integrating boundary conditions into the Boltzmann equation, unifying diffusive and ballistic transport descriptions in various dimensions.

Findings

Derived analytical formulas for conductance in 1D, 2D, and 3D.

Recovered classical models (Boltzmann-Drude and Landauer-Büttiker) in respective limits.

Applicable to charge and spin transport phenomena considering system size and impurity effects.

Abstract

We show that by integrating out the electric field and incorporating proper boundary conditions, a semiclassical Boltzmann equation can describe electron transport properties, continuously from the diffusive to ballistic regimes. General analytical formulas of the conductance in $D=1,2,3$ dimensions are obtained, which recover the Boltzmann-Drude formula and Landauer-B\"uttiker formula in the diffusive and ballistic limits, respectively. This intuitive and efficient approach can be applied to investigate the interplay of system size and impurity scattering in various charge and spin transport phenomena.