A Rigorous Formalism of Unconventional Symmetry Breaking in Fermi Liquid Theory and Its Application to Nematicity in FeSe

TL;DR

This paper introduces a rigorous formalism for unconventional symmetry breaking in Fermi liquids using a generalized order parameter, applied to explain nematicity in FeSe and related phenomena.

Contribution

It develops a formalism based on the Luttinger-Ward theory to describe nonlocal order parameters and applies it to FeSe, providing a theoretical foundation for understanding nematic order in correlated metals.

Findings

Explanation of Lifshitz transition in FeSe below Tc

Curie-Weiss behavior and deviations in nematic susceptibility

Scaling of specific heat jump with T_c

Abstract

Unconventional symmetry breaking due to nonlocal order parameters has attracted considerable attention in many strongly correlated metals. Famous examples are the nematic order in Fe-based superconductors and the star-of-David charge density order in kagome metals. Such exotic symmetry breaking in metals is a central issue of modern condensed matter physics, while its theoretical foundation is still unclear in comparison with the well-established theory of superconductivity. To overcome this difficulty, here we introduce the "form factor" that generalizes the nonlocal order parameter into the Luttinger-Ward (LW) Fermi liquid theory. We then construct a rigorous formalism of the "density-wave equation" that gives the thermodynamically stable form factor, similarly to the superconducting-gap equation. In addition, a rigorous expression of the Ginzburg-Landau free-energy for the unconventional order is presented to calculate various thermodynamic properties. In the next stage, we apply the derived formalism to a typical Fe-based superconductor FeSe, by using the one-loop LW function that represents the free-energy gain due to the interference among paramagnons. The following key experiments are naturally explained: (i) Lifshitz transition (=disappearance of an electron-pocket) due to the bond+orbital order below $T_c$. (ii) Curie-Weiss behavior of the nematic susceptibility at higher T, and the deviation from the Curie-Weiss behavior at lower T near the nematic quantum-critical-point. (iii) Scaling relation of the specific heat jump at $T_c$, $\Delta C/T_c \propto T_c^b$ with $b \sim 3$. (Note that b=0 in the BCS theory.) These results lead to a conclusion that the nematicity in FeSe is the bond+orbital order due to the "paramagnon interference mechanism". The present theory paves the way for solving various unconventional phase transition systems.