Speaker
Description
The most common way of studying electrons in a lattice is to imagine that they simply hop instantaneously from one lattice site to another. When a magnetic field is involved, it is common to assume that the only way, in which it affects the electrons, is by attaching a gauge-dependent phase shift to their hops. This assumption, however, is only valid for relatively small magnetic field strengths. There are also well-established theories for when the magnetic field is very large, but they deal with very weak periodic potentials. In this work, we focus on two-dimensional systems and theoretically study the intermediate regime where both magnetic fields and periodic confining potentials are strong, thus, bridging the gap between the two limiting cases. We study the geometry of the wavefunctions and show that there are multiple topological phase transitions between the two limiting cases. Furthermore, we demonstrate how hopping models can be made more realistic in the presence of large magnetic fields.
