Energy bands splitting in the Kohmoto model

TL;DR

This paper investigates how energy bands split in the Kohmoto model under a magnetic field, revealing effects on the Peierls gap and electron localization, supported by numerical analysis.

Contribution

It introduces analysis of energy band splitting in the Kohmoto model, highlighting the impact on Peierls gap and charge carrier localization in a magnetic field.

Findings

Energy bands split due to the Kohmoto potential.

Peierls gap expands at the metal-insulator transition.

Electrons localize while holes delocalize near the Fermi level.

Abstract

Peierls gap is analyzed in case of a two-dimensional lattice under the influence of a magnetic field, in a tight-binding approximation. By using a non-analytic class of potentials, such as the Kohmoto potential in the Harper model, splitting effect occurs in the energy bands. In the metal-insulator transition point, the charge carriers become separated due to their energy, releasing and expanding the Peierls gap. As a result, the energy bands around the Fermi level become localized in case of the electrons and delocalized corresponding to the holes, since their energy become lowered. These facts are supported by numerical investigations.