Many-body effects due to the electron-electron interaction in silicene under an applied exchange field: The case of valley-spin coupling

We investigate the many-body effects induced by the electron-electron interaction in a valley-spin-polarized silicene under a perpendicularly applied exchange field. We calculate the real and imaginary parts of the self-energy within the leading order dynamical screening approximation where the screened interaction is obtained from the random phase approximation. Our study on the valley- and spin-dependent real and imaginary parts of the self-energy indicates that the different coupled valley-spin subbands may exhibit distinct characteristics. Moreover, we obtain the corresponding spectral functions and find that the plasmaron and quasiparticle peaks have different spectral weights and broadenings in all states. Interestingly, it seems that there are clear dependencies for the position and broadening of the peaks on valley-spin indexes. In addition, we study the effect of the electron-electron interaction on the renormalized velocity in the on-shell approximation and show that the renormalized velocity in gapped states becomes greater, and in gapless states, it becomes smaller as the wave vector grows.