Density modulation and electrostatic self-consistency in a two-dimensional electron gas subject to a periodic quantizing magnetic field

We calculate the single-particle states of a two-dimensional electron gas (2DEG) in a perpendicular quantizing magnetic field, which is periodic in one direction of the electron layer. We discuss the modulation of the electron density in this system and compare it with that of a 2DEG in a periodic electrostatic potential. We take account of the induced potential within the Hartree approximation, and calculate self-consistently the density fluctuations and effective energy bands. The electrostatic effects on the spectrum depend strongly on the temperature and on the ratio between the cyclotron radius ${R}_{c}$ and the length scale ${a}_{\ensuremath{\delta}\ensuremath{\rho}}$ of the density variations. We find that ${a}_{\ensuremath{\delta}\ensuremath{\rho}}$ can be equal to the modulation period $a$, but also much smaller. For ${R}_{c}\ensuremath{\sim}{a}_{\ensuremath{\delta}\ensuremath{\rho}}$ the spectrum in the vicinity of the chemical potential remains essentially the same as in the noninteracting system, while for ${R}_{c}\ensuremath{\ll}{a}_{\ensuremath{\delta}\ensuremath{\rho}}$ it may be drastically changed by the Hartree potential: For noninteger filling factors the energy dispersion is reduced, like in the case of an electrostatic modulation, whereas for even-integer filling factors, on the contrary, the dispersion may be amplified.