Two-dimensional Bloch electrons under strong magnetic modulation

The band structure of a high-mobility two-dimensional electron gas patterned with a square lattice of holes (antidots) is studied theoretically under the influence of a magnetic modulation consisting of perpendicular magnetic flux tubes with the same period and nonzero net flux per unit cell. The magnetic field pierces the system through the patterned holes only, so that the coupling with the electrons is purely quantum mechanical. The model takes implicitly into account the coupling between the different Bloch bands. The flux-dependent energy structure exhibits a Hofstadter butterfly-type spectrum. Such a structure is repeated indefinitely without distortion with a period of one magnetic flux quantum through a lattice hole. Rectangular deviations from the square lattice are also studied. It is found that the number and width of the magnetic gaps decrease, and even disappear for large antidot filling fractions