Decoherence due to contacts in ballistic nanostructures

TL;DR

This paper develops a theoretical framework to describe contact-induced decoherence in ballistic nanostructures, using open systems theory and Markovian approximations, and applies it to model transport properties including resonant features.

Contribution

It introduces a Markovian model for contact-induced decoherence in ballistic nanostructures, derived from non-Markovian dynamics via coarse-graining, and applies it to analyze transport characteristics.

Findings

Derived a general Markovian map for open quantum systems with memoryless environments.

Formulated a model for contact-active region interaction in ballistic nanostructures.

Applied the model to a double-barrier tunneling structure, reproducing resonant I-V features.

Abstract

The active region of a ballistic nanostructure is an open quantum-mechanical system, whose nonunitary evolution (decoherence) towards a nonequilibrium steady state is determined by carrier injection from the contacts. The purpose of this paper is to provide a simple theoretical description of the contact-induced decoherence in ballistic nanostructures, which is established within the framework of the open systems theory. The active region's evolution in the presence of contacts is generally non-Markovian. However, if the contacts' energy relaxation due to electron-electron scattering is sufficiently fast, then the contacts can be considered memoryless on timescales coarsened over their energy relaxation time, and the evolution of the current-limiting active region can be considered Markovian. Therefore, we first derive a general Markovian map in the presence of a memoryless environment, by coarse-graining the exact short-time non-Markovian dynamics of an abstract open system over the environment memory-loss time, and we give the requirements for the validity of this map. We then introduce a model contact-active region interaction that describes carrier injection from the contacts for a generic two-terminal ballistic nanostructure. Starting from this model interaction and using the Markovian dynamics derived by coarse-graining over the effective memory-loss time of the contacts, we derive the formulas for the nonequilibrium steady-state distribution functions of the forward and backward propagating states in the nanostructure's active region. On the example of a double-barrier tunneling structure, the present approach yields an I-V curve with all the prominent resonant features. The relationship to the Landauer-B\"{u}ttiker formalism is also discussed, as well as the inclusion of scattering.