Fermi liquid parameters in two dimensions with spin-orbit interaction

We derive analytical expressions for the quasiparticle lifetime $\tau$, the effective mass $m^{*}$, and the Green’s function renormalization factor $Z$ for a two-dimensional Fermi liquid with electron-electron interaction in the presence of the Rashba spin-orbit interaction. We find that the modifications are independent of the Rashba band index $\rho$, and occur in second order of the spin-orbit coupling $\alpha$. In the derivation of these results, we also discuss the screening of the Coulomb interaction, as well as the susceptibility and the self-energy in small $\alpha$.

Figure 1

The diagramatic representation of the self-energy ${\Sigma }_{\rho }\left(k\right)$ (23) in RPA. The full lines denote the electron Green’s functions (6), the dashed lines the Coulomb interaction, the circles are the susceptibility bubble diagram (18), and the double dashed line is the screened Coulomb interaction (17). The Rashba bands are denoted by the $\rho$’s, and yield the overlap factor ${\mathcal{F}}^{\prime }$ (19).