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arXiv:cond-mat/0507532 · Physical Review B

Fermi surface fluctuations and single electron excitations near Pomeranchuk instability in two dimensions

Luca Dell’Anna, Walter Metzner

Published Jan 27, 2006• 125 citations
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Abstract

A metallic electron system near an orientational symmetry breaking Pomeranchuk instability is characterized by a ``soft'' Fermi surface with enhanced collective fluctuations. We analyze fluctuation effects in a two-dimensional electron system on a square lattice in the vicinity of a Pomeranchuk instability with $d$-wave symmetry, using a phenomenological model which includes interactions with a small momentum transfer only. We compute the dynamical density correlations with a $d$-wave form factor for small momenta and frequencies, the dynamical effective interaction due to a fluctuation exchange, and the electron self-energy. At the quantum critical point the density correlations and the dynamical forward scattering interaction diverge with a dynamical exponent $z=3$. The singular forward scattering leads to large self-energy corrections, which destroy Fermi liquid behavior over the whole Fermi surface except near 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 maxima in the spectra flattens strongly near those portions of the Fermi surface which are remote from the zone diagonal. The contribution from classical fluctuations to the self-energy spoils $(\ensuremath{\omega}∕T)$ scaling in the quantum critical regime.

DOI
10.1103/physrevb.73.045127

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A metallic electron system near an orientational symmetry breaking Pomeranchuk instability is characterized by a ``soft'' Fermi surface with enhanced collective fluctuations. We analyze fluctuation effects in a two-dimensional electron system on a square lattice in the vicinity of a Pomeranchuk instability with ddd-wave symmetry, using a phenomenological model which includes interactions with a small momentum transfer only. We compute the dynamical density correlations with a ddd-wave form factor for small momenta and frequencies, the dynamical effective interaction due to a fluctuation exchange, and the electron self-energy. At the quantum critical point the density correlations and the dynamical forward scattering interaction diverge with a dynamical exponent z=3z=3z=3. The singular forward scattering leads to large self-energy corrections, which destroy Fermi liquid behavior over the whole Fermi surface except near 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 maxima in the spectra flattens strongly near those portions of the Fermi surface which are remote from the zone diagonal. The contribution from classical fluctuations to the self-energy spoils (\ensuremathω∕T)(\ensuremath{\omega}∕T)(\ensuremathω∕T) scaling in the quantum critical regime.
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.
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.
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 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 quantum fluctuation effects at the onset of charge or spin density wave order in two-dimensional metals with an incommensurate 2kF2{k}_{F}2kF​ wave vector connecting a single pair of hot spots on the Fermi surface. We compute the momentum and frequency dependence of the fermion self-energy near the hot spots to leading order in a fluctuation expansion (one loop). Non-Fermi liquid behavior with anomalous frequency scaling and a vanishing quasiparticle weight is obtained. The momentum dependence yields a divergent renormalization of the Fermi velocity and a flattening of the Fermi surface near the hot spots. Going beyond the leading-order calculation, we find that the one-loop result is not self-consistent. We show that any momentum-independent self-energy with a non-Fermi liquid frequency exponent wipes out the peak of the polarization function at the 2kF2{k}_{F}2kF​ wave vector, and thus destroys the mechanism favoring 2kF2{k}_{F}2kF​ density waves over those with generic wave vectors. However, a 2kF2{k}_{F}2kF​ density wave quantum critical point might survive in presence of a sufficiently flat renormalized Fermi surface.
We study the effects of Fermi-surface fluctuations on the single-particle lifetime near the diagonal electronic nematic phase on a two-dimensional square lattice. It has been shown that there exists a quantum critical point between the diagonal nematic and isotropic phases [H. Doh et al., Phys. Rev. B 73, 125117 (2006)]. We study the longitudinal fluctuations of the order parameter near the critical point, where the singular forward scattering leads to a non-Fermi-liquid behavior over the whole Fermi surface except along the kx{k}_{x}kx​ and ky{k}_{y}ky​ directions. We will also discuss the temperature and chemical potential dependences of the single-particle decay rate.