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

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 Ӎ 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.

Many-body local fields theory of quasiparticle properties in a three-dimensional electron liquid

“…1 This caveat must be taken quite seriously since in the case of the two-dimensional electron liquid, for instance, a casual use of the OSA formula leads to a spurious divergence in the quasiparticle effective mass even for experimentally reasonable values of r s . 24 The formal origin of this dangerous pitfall is rather prosaic and can be readily appreciated by comparing the denominator of ͑ap-proximate͒ Eq. ͑6͒ with that of ͑exact͒ Eq.…”

Quasi-particle properties in a quasi-two-dimensional electron liquid

“…The QP effective mass enhancement is substantially smaller in the Dyson equation calculation than in the OSA, because of cancellations in the expression for the Dyson approach [18,30]. To clarify the effect of chargeand spin-density fluctuations we have also included the RPA results which do not take the spin fluctuations into account.…”

“…Previously [19] we studied a strictly 2D electron system and calculated the effects of correlations and disorder in the effective mass enhancement. More recently, we concentrated [18] on Q2D systems, but we had employed local-field factors which were built from the quantum Monte Carlo (QMC) data and were valid for strictly 2D systems. Local-field factors embody correlation effects beyond the random phase approximation (RPA) and constitute a significant input to our calculations at intermediate couplings.…”

“…As applied to the electron gas model this entails the calculation of effective electron-electron interactions which enter the many-body formalism allowing the calculation of various physical properties. A number of calculations considered the self-energy [15][16][17][18][19] from which density, spin polarization, and temperature dependence of effective mass are obtained. In these calculations the on-shell approximation [16,17] yields a diverging effective mass but the full solution of Dyson equation yields only a mild enhancement [18,19].…”

Quasiparticle mass enhancement and Fermi surface shape modification in oxide two-dimensional electron gases

“…Indeed, the full long-range of the Coulomb potential must be recognized in any theory of electron-electron interaction effects in semimetal or doped semiconductor small-Fermi-surface systems. The long-range Coulomb potential plays a critical role in the theory of plasmon oscillations [10][11][12][13] , quasiparticle effective mass [14][15][16] , angleresolved photoemission spectra 17,18 , and many other observables 19,20 .…”