Electron-phonon interaction in two dimensions: Variation of ImΣ(εp,ω) with increasing ωD/EF

Abstract

The interaction between phonons and a two-dimensional (2D) electron gas is studied beyond the Migdal approximation. The analysis of the vertex function leads to the relative correction of ‖ImΣ(${\mathrm{\epsilon }}_{\mathit{p}}$,ω)‖ which is of the order of λ(${\mathrm{\Omega }}_{\mathrm{ph}}$+aT)${\mathit{E}}_{\mathit{F}}^{\mathrm{-}1}$ln(${\mathit{E}}_{\mathit{F}}$/${\mathrm{\Omega }}_{\mathrm{ph}}$). Here, ${\mathrm{\Omega }}_{\mathrm{ph}}$ is the average phonon frequency, and a(∼1) is the ratio between coupling constants for low-frequency and high-frequency phonon modes. For ‖ω‖≫${\mathrm{\Omega }}_{\mathrm{ph}}$ the correction is ‖ω‖/${\mathit{E}}_{\mathit{F}}$. The physically relevant result is that significant corrections are present only when ‖ω‖≲${\mathrm{\Omega }}_{\mathrm{ph}}$,‖ω-${\mathrm{\epsilon }}_{\mathit{p}}$‖≲${\mathrm{\Omega }}_{\mathrm{ph}}$ and they increase with temperature as ${\mathit{T}}^{\mathrm{\delta }}$ with δ≤1 in the entire frequency region. Also, our results strongly suggest that the quasiparticle picture for a 2D electron gas in a 3D lattice has to be corrected by many-particle effects even at small ${\mathrm{\omega }}_{\mathit{D}}$/${\mathit{E}}_{\mathit{F}}$.