Two exact properties of the perturbative expansion for the two-dimensional electron liquid with Rashba or Dresselhaus spin-orbit coupling

We have identified two useful exact properties of the perturbative expansion for the case of a two-dimensional electron liquid with Rashba or Dresselhaus spin-orbit interaction and in the absence of magnetic field. The results allow us to draw interesting conclusions regarding the dependence of the exchange and correlation energy and of the quasiparticle properties on the strength of the spin-orbit coupling which are valid to all orders in the electron-electron interaction.

Figure 1

Left: Interaction vertex, associated with a $\langle \mathbf{k}\mu |{\mathbf{k}}^{\prime }{\mu }^{\prime }\rangle$ factor. Right: Example of a fermionic loop.