Vortex and anti-vortex patterns of the Integer Quantum Hall Effect

Abstract

The Integer Quantum Hall Effect transverse conductivity is derived assuming the electrons form a lattice described by the doubly periodic states of Rodrigues and Doria (2021). We consider the simplest scenario of one electron per Landau level in the unit cell to find complex electronic patterns revealing that besides the counter clockwise circulation set by the magnetic field, there is also clockwise circulation contrary to it. These circulations describe vortices and anti-vortices, thus there are novel topological excitations whose spatial distributions and individual vorticities are numerically calculated for the first eleven Landau levels. Although we work in a particular gauge, the Landau gauge, our results are gauge invariant as they hold for gauge invariant quantities, such as the wave function probability and the current density.