Nematic fluctuations and their wave vector in two-dimensional metals

TL;DR

This paper investigates nematic fluctuations in two-dimensional metals near an Ising-nematic quantum critical point, analyzing how Fermi surface nesting influences the wave vector dependence of nematic susceptibility.

Contribution

It provides a detailed Eliashberg theory analysis showing how strong antinodal interactions shift nematic susceptibility maxima, linking to incommensurate charge-density wave phenomena.

Findings

Nematic susceptibility peaks at antinodal nesting wave vector for certain Fermi surfaces.

Strong interactions shift susceptibility maxima to larger wave vectors, indicating incommensurate order.

At high temperatures, nematic fluctuations are strongest at zero wave vector.

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.