Nematic fluctuations and their wave vector in two-dimensional metals

Abstract

We revisit the problem of electrons on a square lattice below half filling close to an Ising-nematic quantum critical point. For Fermi surfaces with sufficiently strong antinodal nesting, the static nematic susceptibility is maximal at the antinodal nesting wave vector within a simple RPA calculation. We present a detailed analysis of the nematic susceptibility within Eliashberg theory and show that the strong interaction between Fermions in the antinodal regions shifts the maximum of the nematic susceptibility to slightly larger wave vectors. The corresponding order is akin to the incommensurate charge-density wave with d-wave form factor found recently in some underdoped cuprate materials. At sufficiently high temperatures around $T/t\sim 0.1$ nematic fluctuations are strongest at zero wave vector.

arXiv commentrevised version, updated references

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• The special role of the first Matsubara frequency for superconductivity near a quantum-critical point -- the non-linear gap equation below $T_c$ and spectral properties in real frequencies
• The interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal
• Spin-fermion model with overlapping hot spots and charge modulation in cuprates
• Fluctuation effects at the onset of $2{\mathbf{k}}_{\mathbf{F}}$ density wave order with one pair of hot spots in two-dimensional metals
• Finite temperature scaling close to Ising-nematic quantum critical points in two-dimensional metals
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• Real space Eliashberg approach to charge order of electrons coupled to dynamic antiferromagnetic fluctuations
• Overlapping hot spots and charge modulation in cuprates
• Fluctuation effects at the onset of $2{\mathbf{k}}_{\mathbf{F}}$ density wave order with two pairs of hot spots in two-dimensional metals