Density of states and Fermi level of a periodically modulated two-dimensional electron gas

Explicit analytic expressions are obtained for the density of states D(E) and Fermi energy E_F of a two-dimensional electron gas in the presence of a weak and periodic unidirectional electric or magnetic modulation and of a uniform perpendicular magnetic field B. The Landau levels broaden into bands and their width, proportional to the modulation strength, oscillates with B and gives rise to Weiss oscillations in D(E), E_F and the transport coefficients. When both electric and magnetic modulations are present the position of the resulting oscillations depends on the ratio δ between the two modulation strengths. When the modulations are out of phase there is no shift in the position of the oscillations when δ varies and for a particular value of δ the oscillations are suppressed.