Transport in semiconductor nanowire superlattices described by coupled quantum mechanical and kinetic models

In this paper we develop a kinetic model for the analysis of semiconductor superlattices, accounting for quantum effects. The model consists of a Boltzmann-Poisson type system of equations with simplified Bhatnagar-Gross-Krook collisions, obtained from the general time-dependent Schrödinger-Poisson model using Wigner functions. This system for superlattice transport is supplemented by the quantum mechanical part of the model based on the Ben-Daniel-Duke form of the Schrödinger equation for a cylindrical superlattice of finite radius. The resulting energy spectrum is used to characterize the Fermi-Dirac distribution that appears in the Bhatnagar-Gross-Krook collision, thereby coupling the quantum mechanical and kinetic parts of the model. The kinetic model uses the dispersion relation obtained by the generalized Kronig-Penney method, and allows us to estimate radii of quantum wire superlattices that have the same miniband widths as in experiments. It also allows us to determine more accurately the time-dependent characteristics of superlattices, in particular their current density. Results, for several experimentally grown superlattices, are discussed in the context of self-sustained coherent oscillations of the current density which are important in an increasing range of current and potential applications.

Nonlinear Ginzburg-Landau-type approach to quantum dissipation

We formally derive two nonlinear Ginzburg-Landau type models starting from the Wigner-Fokker-Planck system, which rules the evolution of a quantum electron gas interacting with a heat bath in thermodynamic equilibrium. These models mainly consist of a quantum, dissipative O(Planck 3) hydrodynamic/O(Planck 4) stochastic correction to the frictional (Caldeira-Leggett-)Schrödinger equation. The main ingredient lies in the use of the hydrodynamic/stochastic fluid model approach associated with the quantum Fokker-Planck equation and the identification of the associated pressure field. Then, Madelung transformations set the problem in the Schrödinger picture of dissipative quantum mechanics. We also describe the stationary dynamics associated with both systems.