Landau levels in quasicrystals

TL;DR

This paper investigates the emergence and properties of Landau levels in two-dimensional quasicrystals with commensurate plaquettes, analyzing their spectrum, effective dispersion, and broadening mechanisms under a perpendicular magnetic field.

Contribution

It introduces a detailed analysis of Landau levels in quasicrystals, linking their existence to an effective dispersion relation and identifying key broadening mechanisms.

Findings

Landau levels appear near band edges in quasicrystals.

The broadening of Landau levels follows a nonuniversal algebraic behavior.

An underlying periodic crystal explains the effective dispersion relation.

Abstract

Two-dimensional tight-binding models for quasicrystals made of plaquettes with commensurate areas are considered. Their energy spectrum is computed as a function of an applied perpendicular magnetic field. Landau levels are found to emerge near band edges in the zero-field limit. Their existence is related to an effective zero-field dispersion relation valid in the continuum limit. For quasicrystals studied here, an underlying periodic crystal exists and provides a natural interpretation to this dispersion relation. In addition to the slope (effective mass) of Landau levels, we also study their width as a function of the magnetic flux per plaquette and identify two fundamental broadening mechanisms: (i) tunneling between closed cyclotron orbits and (ii) individual energy displacement of states within a Landau level. Interestingly, the typical broadening of the Landau levels is found to behave algebraically with the magnetic field with a nonuniversal exponent.