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arXiv:2101.07815 · Physical review. B./Physical review. B

Presence versus absence of two-dimensional Fermi surface anomalies

Donovan L. Buterakos, DinhDuy Vu, Jiabin Yu, S. Das Sarma

Published May 28, 2021• 4 citations
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Abstract

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 $\mathcal{O}({T}^{2})$ 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 ${T}^{2}logT$ behavior. In contrast, both electron-paramagnon and electron-electron interactions lead to the anomalous $\mathcal{O}(T)$ corrections to the 2D effective mass renormalization in contrast to ${T}^{2}logT$ behavior in the corresponding 3D interacting systems. We provide detailed analytical results, and comment on the conditions under which a ${T}^{2}logT$ 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.

DOI
10.1103/physrevb.103.205154

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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.
We calculate the momentum distribution of the Fermi-liquid phase of the homogeneous two-dimensional electron gas. We show that close to the Fermi surface, the momentum distribution of a finite system with NNN electrons approaches its thermodynamic limit slowly, with leading-order corrections scaling as ${N}^{\ensuremath{-}1/4}$. These corrections dominate the extrapolation of the renormalization factor ZZZ and the single-particle effective mass ${m}^{\ensuremath{\ast}}$ to the infinite system size. We show how convergence can be improved using analytical corrections. In the range $1\ensuremath{\le}{r}_{s}\ensuremath{\le}10$, we get a lower renormalization factor ZZZ and a higher effective mass ${m}^{\ensuremath{\ast}}>m$ compared to the perturbative random-phase approximation values.
We revisit the issue of the leading nonanalytic corrections to the temperature dependence of the specific heat coefficient, $\ensuremath{\gamma}(T)=C(T)∕T$, for a system of interacting fermions in three dimensions. We show that the leading temperature dependence of the specific heat coefficient $\ensuremath{\gamma}(T)\ensuremath{-}\ensuremath{\gamma}(0)\ensuremath{\propto}{T}^{3}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}T$ comes from two physically distinct processes. The first process involves a thermal excitation of a single particle-hole pair, whose components interact via a nonanalytic dynamic vertex. The second process involves an excitation of three particle-hole pairs which interact via the analytic static fixed-point vertex. We show that the single-pair contribution is expressed via the backscattering amplitude of quasiparticles at the Fermi surface. The three-pair contribution does not have a simple expression in terms of scattering in particular directions. We clarify the relation between these results and previous literature on both 3D and 2D systems, and discuss the relation between the nonanalyticities in $\ensuremath{\gamma}$ and those in spin susceptibilities.
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We calculate, using perturbative calculations and Ward identities, the basic parameters of the Fermi liquid: the scattering vertex, the Landau interaction function, the effective mass, specific heat, and physical susceptibilities for a model of two-dimensional (2D) fermions with a short-ranged interaction at nonzero temperature. The leading temperature dependence of the spin components of the scattering vertex, the Landau function, and the spin susceptibility is found to be linear. We find that the standard T=0T=0T=0 relationships for a Galilean-invariant Fermi liquid are violated by finite-temperature terms. The coefficients in the temperature corrections to these relationships involve a subtle interplay between contributions from small and large $(\ensuremath{\sim}{2k}_{F})$ momentum processes. A connection with previous studies of the 2D Fermi-liquid parameters is discussed. We conclude that the linear leading temperature dependence of the parameters is a generic feature of the 2D Fermi liquid.