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Journal of Physics C Solid State Physics

A study of the self-energy of quasiparticles in an electron liquid

H Suehiro, Y Ousaka, Hiroshi Yasuhara

Published Dec 30, 1984• 6 citations
Publisher

Abstract

The self-energy of an electron liquid is studied by including the infinite series of particle-hole and particle-particle ladder interactions beyond the RPA. The effects of these two local-field corrections on the quasiparticle dispersion, the chemical potential mu , the quasiparticle renormalisation factor z F and the effective-mass ratio m*/m have been numerically examined in the metallic density region.

DOI
10.1088/0022-3719/17/36/022

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The self-energy of an electron liquid is studied by including the infinite series of particle-hole and particle-particle ladder interactions beyond the RPA. The effects of these two local-field corrections on the quasiparticle dispersion, the chemical potential mu , the quasiparticle renormalisation factor z F and the effective-mass ratio m*/m have been numerically examined in the metallic density region.
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Within the infinite series of ring (or bubble) diagram approximation for the electronic self-energy as appropriate for the long-range Coulomb interaction, we calculate the density-dependent T=0T=0T=0 Fermi-liquid quasiparticle effective-mass renormalization in two-dimensional (2D) electron systems in the random-phase approximation. We find that the quasiparticle effective mass increases very strongly with increasing rs{r}_{s}rs​, exhibiting an unexpected divergence at a critical rs{r}_{s}rs​ value ($\ensuremath{\sim}16$ in the ideal 2D system). We discuss the possibility for and the consequences of such an interaction-induced effective-mass divergence as the electron density decreases and critically comment on the likely theoretical scenarios which could lead to such a low-density effective-mass divergence in electron liquids.
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We present a method for calculating the effective mass and quasiparticle weight of a Landau Fermi liquid using time-ordered Green’s functions and a Wick rotation to the imaginary frequency axis. This technique simplifies the evaluation of self-energy derivatives by ensuring analytic properties compatible with contour deformations. We apply the method to the electron gas in both two and three spatial dimensions within the random phase approximation (RPA), and derive explicit expressions for the static and dynamic contributions to the self-energy. Our results confirm known limits at weak coupling and offer an accurate and transparent route to evaluate effective mass and quasiparticle weight, with clear extensions possible for systems including vertex corrections or local-field effects and band-gap renormalization.