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arXiv:cond-mat/0406676 · Physical Review B

Quasiparticle self-energy and many-body effective mass enhancement in a two-dimensional electron liquid

Reza Asgari, B. Davoudi, Marco Polini, Gabriele F. Giuliani, M. P. Tosi, Giovanni Vignale

Published Jan 18, 2005• 64 citations
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Abstract

Motivated by a number of recent experimental studies we have revisited the problem of the microscopic calculation of the quasiparticle self-energy and many-body effective mass enhancement in an unpolarized two-dimensional electron liquid. Our systematic study is based on the many-body local field theory and takes advantage of the results of the most recent diffusion Monte Carlo calculations of the static charge and spin response of the electron liquid. We report extensive calculations of both the real and imaginary parts of the quasiparticle self-energy. We also present results for the many-body effective mass enhancement and the renormalization constant over a broad range of electron densities. In this respect we critically examine the relative merits of the on-shell approximation, commonly used in weak coupling situations versus the actual self-consistent solution of the Dyson equation. We show that already for ${r}_{s}\ensuremath{\simeq}3$ and higher, a solution of the Dyson equation proves necessary in order to obtain a well-behaved effective mass. Finally we find confirmation that the inclusion of both charge- and spin-density fluctuations beyond the random phase approximation is indeed crucial to get reasonable agreement with recent measurements.

DOI
10.1103/physrevb.71.045323

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We present a quantitative study of the quasiparticle properties of a three-dimensional electron Fermi liquid. Our approach is based on the theory of the many-body local field factors which we use to include vertex corrections associated with charge and spin fluctuations. Extensive use is made of the results of recent quantum Monte Carlo calculations. Several models for the wave-vector dependence of the spin-antisymmetric many-body local field factor ${G}_{\ensuremath{-}}$, for which no numerical results are currently available, are discussed and compared. Both the real and imaginary parts of the self-energy as well as the quasiparticle renormalization constant and the enhancement of the effective mass are calculated in the experimentally accessible range of electron densities. The results obtained by means of the on-shell approximation are critically compared with those given by a self-consistent solution of the Dyson equation. An ultraviolet catastrophe in the Coulomb-hole part of the self-energy is identified and a satisfactory resolution of this impasse is presented. The same many-body local field factors are also used to obtain the Landau interaction function. This allows us to obtain both the spin susceptibility and the proper compressibility of the system.
We present numerical calculations of the effect of electron-electron interactions on the quasiparticle properties such as the effective mass and the Land\'e ggg-factor in a GaAs∕AlGaAs\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}GaAs∕AlGaAs triangular quantum well from which the spin susceptibility is obtained. For this purpose, we consider quantum many-body effects associated with charge- and spin-density fluctuations induced many-body vertex corrections. The approach is based on the many-body local-field factors which are extracted from Fermi hypernetted-chain self-consistent calculation through the fluctuation-dissipation theorem. We find the spin susceptibility in good agreement with the recent experimental measurements and quantum Monte Carlo simulation data for such a system in the weak and intermediate coupling limits.
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We discuss the potential advantages of calculating the effective mass of quasiparticles in the interacting electron liquid from the low-temperature free energy vis-a-vis the conventional approach, in which the effective mass is obtained from approximate calculations of the self-energy, or from a quantum Monte Carlo evaluation of the energy of a variational ``quasiparticle wave function''. While raw quantum Monte Carlo data are presently too sparse to allow for an accurate determination of the effective mass, the values estimated by this method are numerically close to the ones obtained in previous calculations using diagrammatic many-body theory. In contrast to this, a recently published parametrization of quantum Monte Carlo data for the free energy of the homogeneous electron liquid yields effective masses that considerably deviate from previous calculations and even change sign for low densities, reflecting an unphysical negative entropy. We suggest that this anomaly is related to the treatment of the exchange energy at finite temperature.
We have carried out a comprehensive investigation of the quasiparticle properties of a two-dimensional electron gas, interacting via the long-range Coulomb interaction in the presence of bare mass anisotropy (i.e., with an elliptic noninteracting Fermi surface) by calculating the self-energy, the spectral function, the scattering rate, and the effective mass within the leading-order dynamical self-energy approximation. Our theory is exact in the high-density limit. We find anisotropic features of quasiparticle properties that are not captured by the commonly used isotropic approximation where the anisotropic effective mass is replaced by the isotropic averaged density-of-states mass. Some of these interesting results are as follows: (1) The many-body renormalization of the quasiparticle spectrum becomes highly anisotropic as the quasiparticle energy increases away from the Fermi energy; (2) the interaction-induced inelastic-scattering rate features a strong anisotropy, exhibiting an abrupt jump at different injected energies depending on the momentum direction of the injected electron; (3) the effective-mass enhancement is larger (smaller) for the light (heavy) mass, showing that the anisotropy is reduced by interactions. Our results and analysis show that the unjustified neglect of the mass anisotropy can lead to an incorrect description of quasiparticle properties of the anisotropic system and inaccurate estimates of physical quantities of interest although the use of an equivalent isotropic approximation using the density-of-states effective mass as is commonly and uncritically performed in the literature, works as a reasonable approximation in many situations. In addition to the complete random phase approximation theory for the anisotropic quasiparticles, we also provide a theory using the simpler plasmon-pole approximation, commenting on its validity for anisotropic self-energy calculations. We comment also on the interaction effect on the Fermi-surface topology, finding that the elliptic shape of the bare Fermi surface is preserved with suppressed ellipticity in the interacting system to a high degree of accuracy except in the very strongly interacting limit (and for very high bare mass anisotropy). Our theory provides a complete generalization of the existing isotropic many-body theory of interacting electrons to the corresponding anisotropic systems.