Manipulating the electron current through a splitting

TL;DR

This paper develops a mathematical model for electron transport in quantum networks with splits, deriving an asymptotic scattering matrix formula to aid in designing devices that manipulate quantum current.

Contribution

It introduces a new asymptotic formula for the scattering matrix of quantum network splittings based on the properties of attached compact domains.

Findings

Derived an asymptotic formula for the scattering matrix.

Proposed device designs for manipulating quantum current.

Connected boundary conditions to physical device properties.

Abstract

The description of electron current through a splitting is a mathematical problem of electron transport in quantum networks. For quantum networks constructed on the interface of narrow-gap semiconductors the relevant scattering problem for the multi-dimensional Schoedinger equation may be substituted by the corresponding problem on a one-dimensional linear graph with proper selfadjoint boundary conditions at the nodes. However, realistic boundary conditions for splittings have not yet been derived. Here we consider some compact domain attached to a few semi-infinite lines as a model for a quantum network. An asymptotic formula for the scattering matrix for this object is derived in terms of the properties of the compact domain. This allows us to propose designs for devices for manipulating quantum current through a splitting.