Ground state of a spinless charged particle in a periodic magnetic field

The ground-state energy of a two-dimensional, spinless, charged particle in a periodic magnetic field is studied by an exact quantum-mechanical wave-packet propagation method. The periodic magnetic-field modulation removes the degeneracy of the lowest Landau level, and a cluster of states appears both above and below ℏω_c, the homogeneous field lowest Landau level. With two magnetic flux units threading through each magnetic unit cell, the lowest Landau level splits into two separate subbands, with three magnetic flux units the lowest Landau level splits into three separate subbands, and so forth. When a spin energy term is added to the Hamiltonian of the charged particle in the periodic magnetic field, the lowest Landau level becomes unaffected by the periodic magnetic field modulation, in agreement with Dubrovin and Novikov.