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 ${r}_{s}$ , exhibiting an unexpected divergence at a critical ${r}_{s}$ 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.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 ${r}_{s}$, exhibiting an unexpected divergence at a critical ${r}_{s}$ 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.

arXiv:cond-mat/0312565Physical Review BJan 18, 200542 citations

Leading Corrections to Fermi Liquid Behavior at Low Density in Two Dimensions

Jungsoo Kim, Dermot Coffey

APSMar 1, 19960 citations

Fermions in Two Dimensions: Scattering and Many-Body Properties

Alexander Galea, Tash Zielinski, Stefano Gandolfi +1 more

arXiv:1705.09310Journal of Low Temperature PhysicsAug 10, 20179 citations

Kohn-Luttinger effect in nested fermion liquids

H. Dharma Kwon

We study the Kohn-Luttinger effect in a two-dimensional (2D) nested fermion liquid with a repulsive interaction via the renormalization group method and identify the resulting order parameter symmetry. Using the band structure of the 2D Hubbard model close to half-filling as a prototype, we construct an effective low-energy theory. We use multidimensional bosonization to incorporate the zero-sound channel and find marginal Fermi liquid behavior in the absence of any instability. We show an analog of the Landau theorem in nested fermion liquids, which serves as the criterion of the BCS instability. Including repulsive or antiferromagnetic exchange interactions in the low-energy theory, we show that the ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$-wave BCS channel is renormalized to be the most attractive. Below half-filling, when the nesting is not perfect, there is competition between the spin-density-wave (SDW) and the BCS channels; when the SDW coupling is small enough, there occurs a ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$-wave superconducting instability at sufficiently low temperatures.We study the Kohn-Luttinger effect in a two-dimensional (2D) nested fermion liquid with a repulsive interaction via the renormalization group method and identify the resulting order parameter symmetry. Using the band structure of the 2D Hubbard model close to half-filling as a prototype, we construct an effective low-energy theory. We use multidimensional bosonization to incorporate the zero-sound channel and find marginal Fermi liquid behavior in the absence of any instability. We show an analog of the Landau theorem in nested fermion liquids, which serves as the criterion of the BCS instability. Including repulsive or antiferromagnetic exchange interactions in the low-energy theory, we show that the ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$-wave BCS channel is renormalized to be the most attractive. Below half-filling, when the nesting is not perfect, there is competition between the spin-density-wave (SDW) and the BCS channels; when the SDW coupling is small enough, there occurs a ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$-wave superconducting instability at sufficiently low temperatures.

arXiv:cond-mat/9610020Physical review. B, Condensed matterMar 1, 19973 citations

Three-body correlations in a two-dimensional SU(3) Fermi gas

Thomas Kirk, Meera M. Parish

We consider a three-component Fermi gas that has SU(3) symmetry and is confined to two dimensions (2D). For realistic cold atomic gas experiments, we show that the phase diagram of the quasi-2D system can be characterized using two 2D scattering parameters: the scattering length and the effective range. Unlike the case in three dimensions (3D), we argue that three-body bound states (trimers) in the quasi-2D system can be stable against three-body losses. Using a low-density expansion coupled with a variational approach, we investigate the fate of such trimers in the many-body system as the attractive interactions are decreased (or, conversely, as the density of particles is increased). We find that remnants of trimers can persist in the form of strong three-body correlations in the weak-coupling (high-density) limit.We consider a three-component Fermi gas that has SU(3) symmetry and is confined to two dimensions (2D). For realistic cold atomic gas experiments, we show that the phase diagram of the quasi-2D system can be characterized using two 2D scattering parameters: the scattering length and the effective range. Unlike the case in three dimensions (3D), we argue that three-body bound states (trimers) in the quasi-2D system can be stable against three-body losses. Using a low-density expansion coupled with a variational approach, we investigate the fate of such trimers in the many-body system as the attractive interactions are decreased (or, conversely, as the density of particles is increased). We find that remnants of trimers can persist in the form of strong three-body correlations in the weak-coupling (high-density) limit.

arXiv:1704.06772Physical Review ANov 10, 201721 citations

Many-body theories of density response for a strongly correlated Fermi gas

Hui Hui, Hu

物理学前沿：英文版Jan 1, 20120 citations

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

{r}_{s}

, exhibiting an unexpected divergence at a critical

{r}_{s}

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.