Strongly correlated fermions with nonlinear energy dispersion and spontaneous generation of anisotropic phases

TL;DR

This paper investigates how band curvature and interactions in fermionic systems with nonlinear dispersion can lead to instabilities and the emergence of anisotropic phases such as nematic and hexatic states in dimensions greater than two.

Contribution

It introduces a bosonization approach for nonlinear dispersions in higher dimensions and analyzes the impact of band curvature on phase transitions and anisotropic phase formation.

Findings

Band curvature induces relevant interaction terms near instabilities.

The phase diagram includes isotropic, nematic, and hexatic phases.

Negative Landau parameters can trigger anisotropic phase transitions.

Abstract

Using the bosonization approach we study fermionic systems with a nonlinear dispersion relation in dimension d>2. We explicitly show how the band curvature gives rise to interaction terms in the bosonic version of the model. Although these terms are perturbatively irrelevant in relation to the Landau Fermi liquid fixed point, they become relevant perturbations when instabilities take place. Using a coherent state path integral technique we built up the effective action that governs the dynamics of the Fermi surface fluctuations. We consider the combined effect of fermionic interactions and band curvature on possible anisotropic phases triggered by negative Landau parameters. In particular we study in some detail the phase diagram for the isotropic/nematic/hexatic quantum phase transition.