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

The spectrum of charged particles hopping on a kagomé 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 kagomé 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 kagomé grid superconducting wire network, which is the experimental system that originally motivated this work.