Particle - particle interactions in graphene force charge carriers to behave as viscous liquid. In this report we model and study such a system in the framework of molecular dynamics. Two interaction regimes are studied, Dirac regime with negative interaction potential and Fermi regime with positive potential. We report on numerical stability condition in both regimes, qualitative liquid like behavior within the Dirac regime and quantitative conductance of typical experimental device within the Fermi regime.

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