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arXiv:1801.06571 · Physical review. B./Physical review. B

Conditions for l=1 Pomeranchuk instability in a Fermi liquid

Yiming Wu, Avraham Klein, Andrey V. Chubukov

Published Apr 2, 2018• 21 citations
arXivHTMLPDF

Abstract

In a Fermi liquid, the stability of the Fermi surface to deformation is encoded in the angular moments of the interaction between quasiparticles via the Pomeranchuk criterion ${F}_{l}$ $\ensuremath{\ge}$ $-1$. Interestingly, charge and spin conservation prevent interactions from destabilizing the $l$=1 channel even when ${F}_{l}$ = -1, indicating that high-energy processes play a nontrivial role in the low-energy Fermi liquid dynamics. The authors identify, analytically and numerically, that conservation laws imply an equivalence between processes near and away from the Fermi surface, preventing $l$=1 instabilities. Then, they construct $l$=1 order parameters without this equivalence, identifying possible novel instabilities in strongly correlated electron systems.

DOI
10.1103/physrevb.97.165101

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In a Fermi liquid, the stability of the Fermi surface to deformation is encoded in the angular moments of the interaction between quasiparticles via the Pomeranchuk criterion Fl{F}_{l}Fl​ \ensuremath≥\ensuremath{\ge}\ensuremath≥ −1-1−1. Interestingly, charge and spin conservation prevent interactions from destabilizing the lll=1 channel even when Fl{F}_{l}Fl​ = -1, indicating that high-energy processes play a nontrivial role in the low-energy Fermi liquid dynamics. The authors identify, analytically and numerically, that conservation laws imply an equivalence between processes near and away from the Fermi surface, preventing lll=1 instabilities. Then, they construct lll=1 order parameters without this equivalence, identifying possible novel instabilities in strongly correlated electron systems.
Abstract This paper is a short review on the foundations and recent advances in the microscopic Fermi-liquid (FL) theory. We demonstrate that this theory is built on five identities, which follow from conservation of the total charge (particle number), spin, and momentum in a translationally and SU(2)-invariant FL. These identities allow one to express the effective mass and quasiparticle residue in terms of an exact vertex function and also impose constraints on the “quasiparticle” and “incoherent” (or “low-energy” and “high-energy”) contributions to the observable quantities. Such constraints forbid certain Pomeranchuk instabilities of a FL, e.g., towards phases with order parameters that coincide with charge and spin currents. We provide diagrammatic derivations of these constraints and of the general (Leggett) formula for the susceptibility in arbitrary angular momentum channel, and illustrate the general relations through simple examples treated in perturbation theory.
Electron-electron interactions can induce Fermi surface deformations which break the point-group symmetry of the lattice structure of the system. In the vicinity of such a "Pomeranchuk instability" the Fermi surface is easily deformed by anisotropic perturbations, and exhibits enhanced collective fluctuations. We show that critical Fermi surface fluctuations near a d-wave Pomeranchuk instability in two dimensions lead to large anisotropic decay rates for single-particle excitations, which destroy Fermi-liquid behavior over the whole surface except at the Brillouin zone diagonal.
Interactions in Fermi systems can induce a "Pomeranchuk instability" leading to orientational symmetry breaking, that is, nematic order. In a metallic system close to such an instability the Fermi surface is easily deformed by anisotropic perturbations, and exhibits enhanced collective fluctuations. We discuss electrons on a square lattice near a Pomeranchuk instability with d-wave symmetry. The strong response of such a system to a small orthorhombic perturbation can explain naturally the large in-plane anisotropy of electronic and magnetic properties observed in detwinned YBCO crystals. Fluctuations in a quantum critical regime near the instability provide a mechanism for non-Fermi liquid behavior. They lead to a singular forward scattering interaction, which destroys fermionic quasi-particles on the whole Fermi surface except at "cold spots" on the Brillouin zone diagonal. The decay rate for DC transport is linear in temperature except at the cold spots, where conventional Fermi liquid behavior survives. In clean systems this gives rise to a T 3/2 temperature dependence of the DC resistivity, as observed in some overdoped cuprates. In the presence of disorder, the resistivity is linear in T at low temperatures.
We analyze the behavior of an itinerant two-dimensional Fermi system near a charge nematic (n=2)(n=2)(n=2) Pomeranchuk instability in terms of the Landau Fermi-liquid (FL) theory. A key object of our study is the fully renormalized vertex function ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$, related to the Landau interaction function. We derive ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$ for a model case of the long-range interaction in the nematic channel. Already within the random-phase approximation (RPA), the vertex is singular near the instability. The full vertex, obtained by resumming the ladder series composed of the RPA vertices, differs from the RPA result by a multiplicative renormalization factor ${Z}_{\ensuremath{\Gamma}}$, related to the single-particle residue ZZZ and effective-mass renormalization ${m}^{\ensuremath{\ast}}/m$. We employ the Pitaevski-Landau identities, which express the derivatives of the self-energy in terms of ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$, to obtain and solve a set of coupled nonlinear equations for ${Z}_{\ensuremath{\Gamma}}$, ZZZ, and ${m}^{\ensuremath{\ast}}/m$. We show that near the transition the system enters a critical FL regime, where ${Z}_{\ensuremath{\Gamma}}\ensuremath{\sim}Z\ensuremath{\propto}{(1+{g}_{c,2})}^{1/2}$ and ${m}^{\ensuremath{\ast}}/m\ensuremath{\approx}1/Z$, where gc,2{g}_{c,2}gc,2​ is the n=2n=2n=2 charge Landau component which approaches $\ensuremath{-}1$ at the instability. We construct the Landau function of the critical FL and show that all but gc,2{g}_{c,2}gc,2​ Landau components diverge at the critical point. We also show that in the critical regime the one-loop result for the self-energy $\ensuremath{\Sigma}(K)\ensuremath{\propto}\ensuremath{\int}dPG(P)D(K\ensuremath{-}P)$ is asymptotically exact if one identifies the effective interaction DDD with the RPA form of ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$.
Interactions in Fermi systems can generate a Pomeranchuk instability leading to orientational symmetry breaking, that is, nematic order. In a metallic system close to such an instability the Fermi surface is easily deformed by anisotropic perturbations and exhibits enhanced collective fluctuations. We analyze fluctuation effects in the quantum critical regime near a d-wave Pomeranchuk instability in two dimensions. Density correlations with a d-wave form factor and the dynamical forward scattering interaction diverge near the instability. The singular forward scattering leads to large self-energy contributions, which destroy Fermi liquid behavior over the whole Fermi surface except at “cold spots” on the Brillouin zone diagonal. The decay rate of single-particle excitations, which is related to the width of the peaks in the spectral function, exceeds the excitation energy in the low-energy limit. The dispersion of the spectra flattens strongly near those portions of the Fermi surface which are remote from the zone diagonal. The decay rate for DC transport is linear in temperature except at the cold spots. We discuss the possible relevance of d-wave Fermi surface fluctuations for the “strange metal” behavior observed in the normal phase of cuprates.
We address at the mean field level the emergence of a Pomeranchuk instability in a uniform Fermi liquid with central particle-particle interactions. We find that Pomeranchuk instabilities with all symmetries except l=1l=1l=1 can take place if the interaction is repulsive and has a finite range r0{r}_{0}r0​ of the order of the interparticle distance. We demonstrate this by solving the mean field equations analytically for an explicit model interaction, as well as numerical results for more realistic potentials. We find in addition to the Pomeranchuk instability other, subtler phase transitions in which the Fermi surface changes topology without rotational symmetry breaking. We argue that such interaction-driven topological transitions may be as generic to such systems as the Pomeranchuk instability.