Thermodynamic electric quadrupole moments of nematic phases from first-principles calculation

TL;DR

This paper presents a first-principles calculation of thermodynamic electric quadrupole moments in nematic phases of iron-based and cuprate superconductors, revealing different underlying mechanisms for EQMs.

Contribution

The study introduces a first-principles method to compute thermodynamic EQMs in superconductors, clarifying their relation to orbital degeneracy and Fermi surface distortion.

Findings

EQMs in iron-based superconductors are mainly determined by wave function geometry.

In cuprates, EQMs are dominated by Fermi surface distortion.

First-principles calculations successfully characterize nematic order parameters.

Abstract

The electronic nematic phase emerging with spontaneous rotation symmetry breaking is a central issue of modern condensed matter physics. In particular, various nematic phases in iron-based superconductors and high-$T_{\rm c}$ cuprate superconductors are extensively studied recently. Electric quadrupole moments (EQMs) are one of the order parameters characterizing these nematic phases in a unified way, and elucidating EQMs is a key to understanding these nematic phases. However, the quantum-mechanical formulation of the EQMs in crystals is a nontrivial issue because the position operators are non-periodic and unbound. Recently, the EQMs have been formulated by local thermodynamics, and such {\it thermodynamic EQMs} may be used to characterize the fourfold rotation symmetry breaking in materials. In this paper, we calculate the thermodynamic EQMs in iron-based superconductors LaFeAsO and FeSe as well as a cuprate superconductor La$_2$CuO$_4$ by a first-principles calculation. We show that owing to the orbital degeneracy the EQMs in iron-based superconductors are mainly determined by the geometric properties of wave functions. This result is in sharp contrast to the cuprate superconductor, in which the EQMs are dominated by distortion of the Fermi surface.