Effects of the electron-electron interaction on the surface of three-dimensional topological insulators

In the GW approximation, it has been shown that, owing to the electron-electron interaction, plasma satellites appear in the spectral function of a two-dimensional electron system on the surface of a topological insulator. They are due to the resonance plasmon-hole scattering. The contribution of satellites to the single-electron density of states is responsible for the downward energy shift of the minimum of the density, which is compared to the Dirac point in the experiment. To analyze the effect of vertex corrections on the resulting spectrum, a method has been proposed that goes beyond the GW approximation by summing ladder diagrams in the expansion of both the polarization function and self-energy. It has been shown with this method that the multiple electron-hole scattering hardly changes the resulting spectrum.