Interplay between parallel and diagonal electronic nematic phases in interacting systems

TL;DR

This paper explores how parallel and diagonal electronic nematic phases interact in square lattice systems, revealing their competition, coexistence, and the influence of Fermi surface topology on phase transitions.

Contribution

It provides a mean field theory analysis of the interplay between two distinct nematic phases and identifies conditions for their coexistence and quantum critical points.

Findings

Nematic phases compete and coexist depending on parameters.

Quantum critical point exists between diagonal nematic and isotropic phases.

Fermi surface topology affects phase diagram and critical points.

Abstract

An electronic nematic phase can be classified by a spontaneously broken discrete rotational symmetry of a host lattice. In a square lattice, there are two distinct nematic phases. The parallel nematic phase breaks $x$ and $y$ symmetry, while the diagonal nematic phase breaks the diagonal $(x+y)$ and anti-diagonal $(x-y)$ symmetry. We investigate the interplay between the parallel and diagonal nematic orders using mean field theory. We found that the nematic phases compete with each other, while they coexist in a finite window of parameter space. The quantum critical point between the diagonal nematic and isotropic phases exists, and its location in a phase diagram depends on the topology of the Fermi surface. We discuss the implication of our results in the context of neutron scattering and Raman spectroscopy measurements on La$_{2-x}$Sr$_x$CuO$_4$.