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arXiv:1801.04885 · Physical review. B./Physical review. B

Fluctuation effects at the onset of the 2kF density wave order with one pair of hot spots in two-dimensional metals

Jáchym Sýkora, Tobias Holder, Walter Metzner

Published Apr 30, 2018• 14 citations
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Abstract

We analyze quantum fluctuation effects at the onset of charge or spin density wave order in two-dimensional metals with an incommensurate $2{k}_{F}$ 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 $2{k}_{F}$ wave vector, and thus destroys the mechanism favoring $2{k}_{F}$ density waves over those with generic wave vectors. However, a $2{k}_{F}$ density wave quantum critical point might survive in presence of a sufficiently flat renormalized Fermi surface.

DOI
10.1103/physrevb.97.155159

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We analyze quantum fluctuation effects at the onset of charge or spin-density wave order in two-dimensional metals with an incommensurate nesting (2kF2{k}_{F}2kF​) wave vector connecting two pairs of hot spots on the Fermi surface. We first compute the momentum and frequency dependence of the fermion self-energy near the hot spots to leading order in a perturbation expansion (one loop). Non-Fermi liquid behavior with a linear (in energy) quasiparticle decay rate and a logarithmically vanishing quasiparticle weight is obtained. The momentum dependence of the self-energy entails only finite renormalizations of the Fermi velocity and the Fermi-surface curvature at the hot spots. The perturbative one-loop result is not self-consistent and casts doubt on the stability of the 2kF2{k}_{F}2kF​ quantum critical point. We construct a self-consistent solution of the one-loop equations with self-energy feedback, where the quantum critical point is stabilized rather than being destroyed by fluctuations, while the non-Fermi liquid behavior as found in the perturbative one-loop calculation is confirmed.
We analyze quantum fluctuation effects at the onset of charge- or spin-density wave order with a 2kF2{k}_{F}2kF​ wave vector Q\mathbf{Q}Q in two-dimensional metals, for the special case where Q\mathbf{Q}Q connects a pair of hot spots situated at high symmetry points of the Fermi surface with a vanishing Fermi surface curvature. We compute the order parameter susceptibility and the fermion self-energy in one-loop approximation. The susceptibility has a pronounced peak at Q\mathbf{Q}Q, and the self-energy displays non-Fermi liquid behavior at the hot spots, with a linear frequency dependence of its imaginary part. The real part of the one-loop self-energy exhibits logarithmic divergencies with universal prefactors as a function of both frequency and momentum, which may be interpreted as perturbative signatures of power laws with universal anomalous dimensions. As a result, one obtains a non-Fermi liquid metal with a vanishing quasiparticle weight at the hot spots, and a renormalized dispersion relation with anomalous algebraic momentum dependencies near the hot spots.
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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
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We revisit the problem of two-dimensional metals in the vicinity of a quantum phase transition to incommensurate Q=2kF\mathbf{Q}=2{k}_{F}Q=2kF​ charge-density-wave order, where the order-parameter wave vector Q\mathbf{Q}Q connects two hot spots on the Fermi surface with parallel tangents. Earlier theoretical works argued that such critical points are potentially unstable, if the Fermi surface at the hot spots is not sufficiently flat. Here we perform a controlled, perturbative renormalization-group analysis and find a stable fixed point corresponding to a continuous quantum phase transition, which exhibits a strong dynamical nesting of the Fermi surface at the hot spots. We derive scaling forms of correlation functions at the critical point and discuss potential implications for experiments with transition-metal dichalcogenides and rare-earth tellurides.