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arXiv:1908.08957 · Physical review. B./Physical review. B

Coupled electron-impurity and electron-phonon systems as trivial non-Fermi liquids

Donovan Buterakos, S. Das Sarma

Published Dec 30, 2019• 7 citations
arXivHTMLPDF

Abstract

We consider an electron gas, both in two (2D) and three (3D) dimensions, interacting with quenched impurities and phonons within leading order finite-temperature many-body perturbation theories, calculating the electron self-energies, spectral functions, and momentum distribution functions at finite temperatures. The resultant spectral function is in general highly non-Lorentzian, indicating that the system is not a Fermi liquid in the usual sense. The calculated momentum distribution function cannot be approximated by a Fermi function at any temperature, providing a rather simple example of a non-Fermi liquid with well-understood properties.

DOI
10.1103/physrevb.100.235149

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We consider an electron gas, both in two (2D) and three (3D) dimensions, interacting with quenched impurities and phonons within leading order finite-temperature many-body perturbation theories, calculating the electron self-energies, spectral functions, and momentum distribution functions at finite temperatures. The resultant spectral function is in general highly non-Lorentzian, indicating that the system is not a Fermi liquid in the usual sense. The calculated momentum distribution function cannot be approximated by a Fermi function at any temperature, providing a rather simple example of a non-Fermi liquid with well-understood properties.
We calculate the Green's function, particle-hole susceptibility and Cooper pair susceptibility of a 2D electron gas with long range current-current interactions, using Haldane bosonization scheme. We find Luttinger Liquid properties of weakly decaying power-law tails in the spectral function and a Kohn anomaly in the 2$k\sb{F}$ particle-hole susceptibility. At finite temperature, the system exhibits more radical departure from Fermi Liquid. The specific heat was determined being linearly proportional to temperature. The strong correlations of spins and holes are demonstrated in the 2D t-J model of spin-boson and hole-fermion, through the instability against charge ordering we find from our charge susceptibility calculation of bubble and ladder diagrams. We calculate the linear-T dependence of resistivity from the hole self-energy to the second order. The excitation spectra of holon and spinon found from the self-energy calculations agree with the mean-field results to that order.
The momentum distribution function of a one-dimensional interacting many electron-phonon system is calculated analytically within the framework of the Luttinger model. We have shown that, even a small electron-electron interaction destroys the fermi surface and in the presence of the electron-phonon interaction the residual fermi surface vanishes completely and the function becomes a continuous function of the wave vector as we increase the coupling strength. It shows that in one dimension, the Fermi liquid theory breaks down completely, if we include the electron-phonon interactions along with the electron-electron interaction.
An exactly soluble one-dimensional model of electrons interacting with order-parameter fluctuations associated with short-range order is considered. The energy and momentum dependence of the electronic self-energy and spectral function are calculated and found to exhibit non-Fermi-liquid features similar to that seen for the two-dimensional Hubbard model: a pseudogap, shadow bands, anomalies in the self-energy, and breakdown of the quasiparticle picture. Deviations from Fermi-liquid behavior are largest close to the Fermi surface and as the correlation length increases.
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)\mathcal{O}({T}^{2})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{T}^{2}logTT2logT behavior. In contrast, both electron-paramagnon and electron-electron interactions lead to the anomalous O(T)\mathcal{O}(T)O(T) corrections to the 2D effective mass renormalization in contrast to T2logT{T}^{2}logTT2logT behavior in the corresponding 3D interacting systems. We provide detailed analytical results, and comment on the conditions under which a T2logT{T}^{2}logTT2logT 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.
Landau theory of Fermi liquids is the foundational concept behind our understanding of conventional metals. Its basic postulate is that the low-energy physics can be described by weakly interacting quasiparticles --- a dressed but effectively free version of electrons formally represented by poles of the single-particle Green's function. However, this concept notoriously fails for strongly interacting systems such as high-Tc{T}_{c}Tc​ cuprate superconductors, and our understanding of properties of these ``non-Fermi'' quantum liquids is far from complete. One well-known candidate theory for non-Fermi liquids is Hertz-Millis theory: a finite-density fermion system coupled to a massless critical boson. In (2+1) dimensions, this theory is strongly interacting at low energies, but as of yet there is no controlled insight in this regime; conventional perturbation theory fails. In this article, the authors show that in the so-called quenched approximation the fermionic spectrum can be computed exactly to all orders in the coupling constant. They show extensive detailed analysis that, in this quenched limit, the nonperturbative low-energy dynamics are indeed that of a non-Fermi liquid. Instead of coherent quasiparticles one finds the emergence of critical fermionic excitations described by branch cuts in the single particle Green's function.
Despite the fact that the low energy behavior of the basic Kondo model cannot be studied perturbatively it was eventually shown by Wilson, Anderson, Nozieres and others to have a simple "local Fermi liquid theory" description. That is, electronic degrees of freedom become effectively non-interacting in the zero energy limit. However, generalized versions of the Kondo model involving more than one channel or impurity may exhibit low energy behavior of a less trivial sort which can, nonetheless, be solved exactly using either Bethe ansatz or conformal field theory and bosonization techniques. Now the low energy limit exhibits interacting many body behavior. For example, processes in which a single electron scatters off the impurity into a multi electron-hole state have a non-vanishing (and sometimes large) amplitude at zero energy. This corresponds to a rare solveable example of non-Fermi liquid behavior. Essential features of these phenomena are reviewed.