Incommensurate nematic fluctuations in two dimensional metals

TL;DR

This paper investigates nematic fluctuations in two-dimensional metals, revealing how their strength and spatial modulation depend on electron filling and interactions, with implications for nematic phase formation.

Contribution

It provides a detailed calculation of the static d-wave polarization function, showing how nematic instabilities can lead to spatially modulated states in 2D metals.

Findings

Divergence of polarization at Van Hove filling at q=0

Finite wave vector peaks in polarization away from Van Hove filling

Modulation vector increases with distance from Van Hove filling

Abstract

To assess the strength of nematic fluctuations with a finite wave vector in a two-dimensional metal, we compute the static d-wave polarization function for tight-binding electrons on a square lattice. At Van Hove filling and zero temperature the function diverges logarithmically at q=0. Away from Van Hove filling the ground state polarization function exhibits finite peaks at finite wave vectors. A nematic instability driven by a sufficiently strong attraction in the d-wave charge channel thus leads naturally to a spatially modulated nematic state, with a modulation vector that increases in length with the distance from Van Hove filling. Above Van Hove filling, for a Fermi surface crossing the magnetic Brillouin zone boundary, the modulation vector connects antiferromagnetic hot spots with collinear Fermi velocities.