Magnetic breakdown in an array of overlapping Fermi surfaces A.M. Kadigrobov a,b , D. Radić a,n , A. Bjeliš a Q1 a Department of Physics, Faculty of Science, University of Zagreb, POB 331, HR-10001 Zagreb, Croatia b Theoretische Physik III, Ruhr-Universität Bochum, D-44801 Bochum, Germany article info Keywords: Magnetic breakdown Graphene abstract 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, in- augurated 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 re- lated 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 break- down induced density wave instability at the highest possible critical temperature. & 2014 Published by Elsevier B.V. 1. Introduction Since its discovery in sixties, magnetic breakdown (MB) theory [1] has been an important tool in understanding the influence of magnetic field on the electronic properties of conductors and semiconductors with rather small gaps at the Fermi surface. In the series of earlier works we have analyzed the MB mechanisms for electron bands of reduced dimensionality, more specifically the possibility of the stabilization of density wave (DW) ordering in the external magnetic field through the gain of band energy in- duced by MB. This kind of DW is possible already in the so-called anti-nesting regime in quasi-one-dimensional materials [2], in which MB takes place between equivalent pockets much larger than the characteristic surface for a quantum of magnetic flux, σ ≡ eH c /  [3]. Here H is the strength of magnetic field, and ℏ, e, and c are Planck constant, electron charge and velocity of light re- spectively. Even more favorable appears to be the ordering with touching Fermi sheets and largest possible pockets, having a more subtle mechanism of tunneling due to the internal structure of the MB barrier [4]. In this work we use previously developed form- alism to investigate the MB properties of two-dimensional iso- tropic band dispersions with circular Fermi surfaces. Assuming the presence of uniaxial periodic potential which induces the forma- tion of an array of slightly overlapping Fermi surfaces, we calculate the MB scattering matrix and ensuing electron spectrum, and apply the general results to the Dirac type of band dispersion characterizing honeycomb structures in the graphene and inter- calated graphite compounds. 2. Model The problem will be here illustrated by a simplified model of two-dimensional conducting band with a set of circular electronic orbits encircling the Fermi surface with a radius p F (see Fig. 1(a)). The extensions to more general band dispersions do not alter the main conclusions of present analysis. Further on, we assume the presence of a weak periodic potential with the uniaxial periodicity, = V Vx r () (), defined by the wave vector = Q Q ( , 0). Here we are interested in the range of values of the wave number Q of the lattice periodic modulation for which there is a presumably slight overlap between closed Fermi surfaces from neighboring new Brillouin zones, leading to the formation of the continuous chain of overlapping electron orbits in the momentum space [5], as shown in Fig. 1(a). Simultaneously, the periodic potential lifts the degeneracy at the crossing points of this chain, by opening gaps, so that the initial chain is converted into a set of small closed 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/physb Physica B http://dx.doi.org/10.1016/j.physb.2014.11.082 0921-4526/& 2014 Published by Elsevier B.V. n Corresponding author. Fax: þ385 1 4680336. E-mail address: dradic@phy.hr (D. Radić). Please cite this article as: A.M. Kadigrobov, et al., Physica B (2014), http://dx.doi.org/10.1016/j.physb.2014.11.082i Physica B ∎ (∎∎∎∎) ∎∎∎–∎∎∎