Periodic chain of disks in a magnetic field: bulk states and edge states

An explicitly solvable model for periodic chain of coupled disks in orthogonal magnetic field is considered. The spectrum for the Hamiltonian is compared with the spectrum for the corresponding chain of circles. These models are used for the comparison of the bulk and edge states. It is found that for some range of the magnetic field values the lowest band for the circles system lies below the spectrum for the corresponding disks system, i.e. the edge band is below and is separated from the lowest bulk band.