Exact result for the Green’s function of a two-dimensional interacting electron gas withspin–orbit interaction in a perpendicular magnetic field

Abstract

An exact property is established for the Green’s function of a uniform two-dimensionalinteracting electron gas in a perpendicular magnetic field with spin–orbit interaction. It isshown that the spin-diagonal Green’s function is exactly diagonal in the Landaulevel index even in the presence of electron–electron interactions. For the Green’sfunction with different spin indexes, only that with adjacent Landau level indexes isnon-zero. This exact result should be helpful in calculating the Green’s functionapproximately.