Conductance of a nanowire with nonlinear electrostatics

Conductance of a nanowire with nonlinear electrostatics

Benedysiuk, Piotr (TU Delft Applied Sciences)

Akhmerov, A.R. (mentor)
van Gijzen, M.B. (mentor)
Wimmer, M.T. (mentor)

Delft University of Technology

Applied Mathematics | Applied Physics

2019-04-02

The electrostatics has effect on conductance of nanowire devices. In this model electrostatics are described by nonlinear coupling of the Poisson and the Schr¨odinger equations. In presence of magnetic and electric field and spin-orbit interaction, conductance develops a feature called the helical gap. This gap is characterised by a drop of conductance and is the main focus of the research. The solver is based around an Anderson mixing scheme, and specific class of points has been discovered for which the solver performs poorly. For those points, an temperature annealing subroutine has been put in place to speed up convergence. This subroutine efficiently solves the system for some small finite temperature. The solver has also been expanded to solve systems for magnetic field pointed in any direction of the y, z plane. As a result, it is now possible to perform simulations for different magnitudes and directions of magnetic field, which are a handy tool for understanding the behaviour of conductance as a function of VG in real nanowires. The relation between energy and conductance has been researched. The size of helical gap is found to scale linearly with the Zeeman energy EZ, while other features of conductance scale nonlinearly

Electrostatics
Nanowire
Poisson equation
Nonlinear

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Student theses

bachelor thesis

© 2019 Piotr Benedysiuk