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arXiv:cond-mat/0308203

Divergence of the effective mass near a density wave instability in a MOSFET system

Victor M. Galitski, VICTOR A. KHODEL

Published Aug 11, 2003• 1 citation
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Abstract

We study the renormalization of the Fermi-liquid parameters in the vicinity of a density wave quantum phase transition, which should occur in MOSFET systems at low densities. First, using a perturbative RPA treatment of fluctuations, we calculate the electronic self-energy and show that the effective mass diverges at the density wave transition point. Second, we go beyond perturbation theory, making use of the exact Pitaevskii identities. Within this exact analysis, we also find a divergence of the effective mass, which occurs at higher densities in the fluctuation region, as compared to the perturbation theory. This result signals the break-down of conventional Fermi-liquid description in the vicinity of the transition point. The divergence of the effective mass gives rise to a singular behavior of the electronic compressibility. We suggest that the experimentally observed enhancement of the effective mass is a precursor to a second order thermodynamic phase transition into a glassy density wave state.

DOI
10.48550/arxiv.cond-mat/0308203

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We study the renormalization of the Fermi-liquid parameters in the vicinity of a density wave quantum phase transition, which should occur in MOSFET systems at low densities. First, using a perturbative RPA treatment of fluctuations, we calculate the electronic self-energy and show that the effective mass diverges at the density wave transition point. Second, we go beyond perturbation theory, making use of the exact Pitaevskii identities. Within this exact analysis, we also find a divergence of the effective mass, which occurs at higher densities in the fluctuation region, as compared to the perturbation theory. This result signals the break-down of conventional Fermi-liquid description in the vicinity of the transition point. The divergence of the effective mass gives rise to a singular behavior of the electronic compressibility. We suggest that the experimentally observed enhancement of the effective mass is a precursor to a second order thermodynamic phase transition into a glassy density wave state.
We study the quantum critical behavior in an isotropic Fermi liquid in the vicinity of a zero-temperature density-wave transition at a finite wave vector qc{q}_{c}qc​. We show that, near the transition, the Landau damping of the soft bosonic mode yields a crossover in the fermionic self-energy from $\ensuremath{\Sigma}(k,\ensuremath{\omega})\ensuremath{\approx}\ensuremath{\Sigma}(k)$ to $\ensuremath{\Sigma}(k,\ensuremath{\omega})\ensuremath{\approx}\ensuremath{\Sigma}(\ensuremath{\omega})$, where kkk and $\ensuremath{\omega}$ are momentum and frequency. Because of this self-generated locality, the fermionic effective mass diverges right at the quantum critical point, not before; i.e., the Fermi liquid survives up to the critical point.
The behavior of Fermi systems that approach the fermion condensation quantum phase transition (FCQPT) from the disordered phase is considered. We show that the quasiparticle effective mass M * diverges as M * ∝ 1/¦ x − x FC ¦, where x is the system density and x FC is the critical point at which FCQPT occurs. Such behavior is of general form and takes place in both three-dimensional (3D) and two-dimensional (2D) systems. Since the effective mass M * is finite, the system exhibits the Landau Fermi liquid behavior. At ¦ x − x FC ¦/ x FC ≪1, the behavior can be viewed as highly correlated, because the effective mass is large and strongly depends on the density. In the case of electronic systems, the Wiedemann-Franz law is valid and the Kadowaki-Woods ratio is preserved. Beyond the region ¦ x – x FC ¦/ x FC ≪1, the effective mass is approximately constant and the system becomes a conventional Landau Fermi liquid.
The behavior of Fermi systems which approach the fermion condensation quantum phase transition (FCQPT) from the disordered phase is considered. We show that the quasiparticle effective mass M ∗ diverges as M ∗ ∝ 1/|x − xFC | where x is the system density and xFC is the critical point at which FCQPT occurs. Such a behavior is of general form and takes place in both three dimensional (3D) systems and two dimensional (2D) ones. Since the effective mass M ∗ is finite, the system exhibits the Landau Fermi liquid behavior. At |x −xFC|/xFC ≪ 1, the behavior can be viewed as a highly correlated one, because the effective mass is large and strongly depends on the density. In case of electronic systems the Wiedemann-Franz law is held and Kadowaki-Woods ratio is preserved. Beyond the region |x−xFC|/xFC ≪ 1, the effective mass is approximately constant and the system becomes conventional Landau Fermi liquid.
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.
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 analyze quantum fluctuation effects at the onset of incommensurate 2 k F charge- or spin-density-wave order in two-dimensional metals for a model in which the ordering wave vector Q connects a single pair of hot spots on the Fermi surface with a vanishing Fermi surface curvature. The tangential momentum dependence of the bare dispersion near the hot spots is proportional to | k t | α with α > 2 . We first compute the order parameter susceptibility and the fermion self-energy in a random phase approximation (RPA). Logarithmic divergences are subsequently treated by a renormalization-group analysis. The coupling between the order parameter fluctuations and the fermions vanishes logarithmically in the low-energy limit. As a consequence, the logarithmic divergences found in the RPA do not sum up to anomalous power laws. Instead, only logarithmic corrections to Fermi liquid behavior are obtained. In particular, the quasiparticle weight and the Fermi velocity vanish logarithmically at the hot spots. Published by the American Physical Society 2024