Orbital magnetization of the electron gas on a two-dimensional kagome lattice under a perpendicular magnetic field

TL;DR

This paper theoretically investigates the orbital magnetization of electrons on a 2D kagome lattice under a magnetic field, revealing oscillatory behavior linked to the Hofstadter spectrum and fractal structures, with finite-temperature effects considered.

Contribution

It introduces a detailed analysis of the Berry-phase and conventional contributions to magnetization in a kagome lattice, highlighting the fractal oscillations and their relation to the Hofstadter spectrum.

Findings

Oscillatory magnetization curves vary with electron filling.

Fractal structures emerge in magnetic oscillations near specific flux values.

Finite-temperature effects influence the magnetization behavior.

Abstract

The orbital magnetization of the electron gas on a two-dimensional kagome lattice under a perpendicular magnetic field is theoretically investigated. The interplay between the lattice geometry and magnetic field induce nontrivial $k$-space Chern invariant in the magnetic Brillouin zone, which turns to result in profound effects on the magnetization properties. We show that the Berry-phase term in the magnetization gives a paramagnetic contribution, while the conventional term brought about by the magnetic response of the magnetic Bloch bands produces a diamagnetic contribution. As a result, the superposition of these two components gives rise to a delicate oscillatory structure in the magnetization curve when varying the electron filling factor. The relationship between this oscillatory behavior and the Hofstadter energy spectrum is revealed by selectively discussing the magnetization and its two components at the commensurate fluxes of $f$=1/4, 1/3, and 1/6, respectively. In particular, we reveal as a typical example the fractal structure in the magnetic oscillations by tuning the commensurate flux around $f$=1/4. The finite-temperature effect on the magnetization is also discussed.