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

• Published in: Physica. B, Condensed matter Condensed matter, 2024-04, Vol.678, p.415716, Article 415716
• Main Authors: Rodrigues, Edinardo I.B., Doria, Mauro M.
• Format: Article
• Language: English
• Subjects: Doubly periodic states; Integer Quantum Hall Effect; Topological excitations; Vortices
• ISSN: 0921-4526; 1873-2135
• DOI: 10.1016/j.physb.2024.415716

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. •The topological properties of the IQHE are fixed by the integer N associated with the transverse conductivity plateaus, Ne2/h, N is the number of filled Landau levels (n=0,…,N−1). Here we find that N does not describe all the topological properties of the IQHE thanks to the use of the doubly periodic functions obtained by Rodrigues and Doria (2021).•The treatment developed in details in the present paper, is for the case of one electron per Landau level in the unit cell (p=1), where the number of trapped magnetic flux, and also the vorticity in the unit cell, is one.•Novel topological properties of the IQHE are shown here, as besides the counter clockwise circulation set by the magnetic field, there is also clockwise circulation contrary to it in each Landau level above the fundamental one.•We explicitly obtain the spatial distributions of vortices and anti-vortices and their individual vorticities in the unit cell for the first time.•The present approach also provides a straightforward description of the IQHE solely based on bulk properties without any appeal to the use of boundaries, and so, proves that edge states are not fundamental to the description of the IQHE.