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

Abstract

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

Exact and quasiclassical Green's functions of two-dimensional electron gas with Rashba–Dresselhaus spin–orbit interaction in parallel magnetic field

“…Normaly using the GF in the form of a multiple integral is extremely uncomfortable both for analytical analysis and for numerical computations. Therefore the search of exact, simplified and asymptotic results for GFs attracts the constant attention of theorists and mathematicians (see, for example, [3][4][5]).…”