Magnetic breakdown investigated by means of the magnetic-field-containing relativistic tight-binding approximation method

We investigate the magnetic breakdown (MB) phenomena by means of the recently proposed magnetic- fieldcontaining relativistic tight-binding approximation (MFRTB) method [Phys. Rev. B 91, 075122 (2015)]. In the MFRTB method, the MB phenomena can be described as the electron hopping between adjacent semiclassical orbits. It is shown that a set of magnetic energy bands is generated by the MB in the cluster that corresponds to the semiclassical energy level. It is also found that magnetic energy bands originating from the MB and those originating from the semiclassical orbit lying on the constant energy surface are hybridized to each other. Such hybridization leads to various subclusters that correspond to energy states of the so- called forbidden orbits. Magnetic oscillations related to the MB occur when the subcluster changes from the occupied state to unoccupied one and vice versa