Magnetic breakdown in an array of overlapping Fermi surfaces

We develop a theoretical framework for a magnetic breakdown in an array of circular two-dimensional bands with a finite overlap of neighboring Fermi surfaces due to the presence of a presumably weak periodic potential, and apply the obtained results to the electron bands in carbon honeycomb structures of doped graphene and intercalated graphite compounds. In contrast to the standard treatment, inaugurated more than fifty years ago by Slutskin and Kadigrobov, with electron semiclassical trajectories encircling significantly overlapping Fermi surfaces, we examine a configuration in which bands are related in a way that the Fermi surfaces only slightly overlap, forming internal band pockets with areas of the size comparable to the area of the quantum magnetic flux for a given external magnetic field. Such band configuration has to be treated quantum mechanically. The calculation leads to the results for magnetic breakdown coefficients comprising an additional large factor with respect to the standard results, proportional to the ratio of the Fermi energy and the cyclotron energy. Also, these coefficients show oscillating dependence on energy, as well as on the wave number of periodic potential. Both mentioned elements enable the adjustment of the preferred wave vector of possible magnetic breakdown induced density wave instability at the highest possible critical temperature.