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=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, exhibiting an unexpected divergence at a critical
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.
We theoretically consider Fermi surface anomalies manifesting in the temperature-dependent quasiparticle properties of two-dimensional (2D) interacting electron systems, comparing and contrasting with the corresponding three-dimensional (3D) Fermi liquid situation. In particular, employing microscopic many-body perturbative techniques, we obtain analytically the leading-order and the next-to-leading-order interaction corrections to the renormalized effective mass for three distinct physical interaction models: electron-phonon, electron-paramagnon, and electron-electron Coulomb coupling. We find that the 2D renormalized effective mass does not develop any Fermi surface anomaly due to electron-phonon interaction, manifesting
O(T2) temperature correction and thus remaining consistent with the Sommerfeld expansion of the noninteracting Fermi function, in contrast to the corresponding 3D situation where the temperature correction to the renormalized effective mass has the anomalous
T2logT behavior. In contrast, both electron-paramagnon and electron-electron interactions lead to the anomalous
O(T) corrections to the 2D effective mass renormalization in contrast to
T2logT behavior in the corresponding 3D interacting systems. We provide detailed analytical results, and comment on the conditions under which a
T2logT term could possibly arise in the 2D quasiparticle effective mass from electron-phonon interactions. We also compare results for the temperature-dependent specific heat in the interacting 2D and 3D Fermi systems, using the close connection between the effective mass and specific heat.
We consider a two-dimensional electron system with Coulomb interaction between particles at a finite temperature
T. We show that the dynamic Kohn anomaly in the response function at
2kF leads to a nonanalytic, linear-in-
T correction to the spin susceptibility, $\ensuremath{\delta}\ensuremath{\chi}(T)=aT$, the same as in systems with short-range interaction. We show that the singularity of the Coulomb interaction at
q=0 does not invalidate the expansion of the prefactor
a in powers of
rs, but makes the expansion nonanalytic.
We consider the nonanalytic terms in the spin susceptibility arising as a result of rescattering of pairs of quasiparticles. We emphasize the importance of rescattering in the Cooper channel for the analysis of the temperature dependences in the two-dimensional electron systems in the ballistic regime. In the calculation of the linear in
T term we use angular harmonics in the Cooper channel, because for each harmonic the interaction amplitude is renormalized independently. We observe, that as a consequence of strong renormalizations in the Cooper ladder, the temperature derivative of the spin susceptibility may change its sign at low temperatures.
We derive analytical expressions for the quasiparticle lifetime $\ensuremath{\tau}$, the effective mass
m∗, and the Green's function renormalization factor
Z for a two-dimensional Fermi liquid with electron-electron interaction in the presence of the Rashba spin-orbit interaction. We find that the modifications are independent of the Rashba band index $\ensuremath{\rho}$, and occur in second order of the spin-orbit coupling $\ensuremath{\alpha}$. In the derivation of these results, we also discuss the screening of the Coulomb interaction, as well as the susceptibility and the self-energy in small $\ensuremath{\alpha}$.
The exchange interaction and effective mass of fermionic excitation in a low-density (r S ≫ 1) system of two-dimensional electrons are estimated from simple considerations. For the ratio of effective (renormalized due to interaction) to band mass, the dependence % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVy0df9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lqpe0x% c9q8qqaqFn0dXdir-xcvk9pIe9q8qqaq-xir-f0-yqaqVeLsFr0-vr% 0-vr0xc8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcgaqaai% aad2gadaahaaWcbeqaaiaacQcaaaaakeaacaWGTbaaaiabg2da9iaa% cIcadaWcgaqaaiaadgeaaeaadaGcaaqaaiaadkhadaWgaaWcbaGaam% 4uaaqabaaabeaaaaGccaGGPaGaciyzaiaacIhacaGGWbGaaiikaGGa% aiab-f7aHnaakaaabaGaamOCamaaBaaaleaacaWGtbaabeaaaeqaaO% Gaaiykaaaa!49B6! $${{m^* } \mathord{\left/ {\vphantom {{m^* } m}} \right. \kern-\nulldelimiterspace} m} = ({A \mathord{\left/ {\vphantom {A {\sqrt {r_S } }}} \right. \kern-\nulldelimiterspace} {\sqrt {r_S } }})\exp (\alpha \sqrt {r_S } )$$ is obtained, where A and α are constants on the order of unity. The effective g factor is independent of r S and is larger than its bare value in the two-valley case (silicon). Comparison with experimental data shows a qualitative agreement with silicon.