Landau levels in the case of two degenerate coupled bands: kagome lattice tight-binding spectrum

TL;DR

This paper investigates the unique Landau level spectrum in a kagome lattice, revealing paramagnetic lowest levels and unequal spacings due to degenerate bands, with implications for superconducting wire networks.

Contribution

It provides a general analysis of Landau levels in systems with two degenerate bands and applies this to the kagome lattice, linking theoretical insights to experimental superconducting systems.

Findings

Lowest Landau levels are paramagnetic, decreasing with magnetic field.

Level spacings are unequal, contrasting typical Landau levels.

Degeneracy of zero-field bands explains the unusual Landau level structure.

Abstract

The spectrum of charged particles hopping on a kagome lattice in a uniform transverse magnetic field shows an unusual set of Landau levels at low field. They are unusual in two respects: the lowest Landau levels are paramagnetic so their energies decrease linearly with increasing field magnitude, and the spacings between the levels are not equal. These features are shown to follow from the degeneracy of the energy bands in zero magnetic field. We give a general discussion of Landau levels in the case of two degenerate bands, and show how the kagome lattice tight-binding model includes one special case of this more general problem. We also discuss the consequences of this for the behavior of the critical temperature of a kagome grid superconducting wire network, which is the experimental system that originally motivated this work.