Splitting of the spectrum of fermionic excitations in a topological insulator by charge fluctuations

It is shown that the intersite Coulomb interaction of electrons in a topological insulator leads to the splitting of the initial energy structure and to the induction of two bands of fluctuation states. As a result, the total spectrum of Fermi excitations of the topological insulator has a four-band structure. The dielectric gap is determined by the energy interval between the bottom of the band of fluctuation states of conduction electrons and the top of the valence band of fluctuation states. Since the band of fluctuation states is narrow, quasiparticles with different effective masses appear.