What I am really excited about - Flakes of artificial graphene in magnetic fields

Last physic's friday before holiday season - and today I will write about something which is not directly connected to finance. Me and my colleague and friend Esa from the university of Tampere will write about Flakes of artificial graphene in magnetic fields.

Artificial graphene (AG) is a man-made nanomaterial that can be constructed by arranging molecules on a metal surface or by fabricating a quantum-dot lattice in a semiconductor heterostructure. In both cases, AG resembles graphene in many ways, but it also has additional appealing features such as tunability with respect to the lattice constant, system size and geometry, and edge configuration.

Designer Dirac fermions and topological phases in molecular graphene. Gomes et al.
NATURE | VOL 483 | 15 MARCH 2012

Here we solve numerically the electronic states of various hexagonal AG flakes. The next picture shows our results  when calculating the electron density for such a system. It is amazing how the experiment and the simulation coincidence.

What are we going to do next: In particular, we demonstrate the formation of the Dirac point as a function of the lattice size and its response to an external, perpendicular magnetic field. Secondly,we examine the complex behaviour of the energy levels as functions of both the system size and magnetic field. Eventually, we find the formation of "Hofstadter butterfly"-type patterns in the energy spectrum. I will report about our findings as soon as they are published.

What is the connection to finance: Although not obvious the numerical methods to solve equations like the Schrödinger equation extremely fast and efficient help us to improve our numerical finance codes. Algorithms and methods used in UnRisk have proofed to work also in the fields of physics and industrial mathematics for years.