Thermodynamic electric quadrupole moments in iron-based superconductors and a cuprate superconductor from first principles

Nematic phases in iron-based and cuprate superconductors are interesting exotic material phases. In these phases, electric quadrupole moments (EQMs) are candidates of the order parameter.
Quantum-mechanical formulation of multipole moments in materials with the C4 symmetry breaking has not been completed, in contrast to C4-preserving cases [1, 2]. Recently, the thermodynamic approach to the formulation of EQMs [3] has been proposed. These formulations are unit cell independent and gauge invariant. Thus, it is now possible to evaluate EQMs-related properties[3] and discuss their origin.
In this work, we analyze thermodynamic EQMs in three materials: LaFeAsO, FeSe, and La2CuO4 which show nematic phases, using a multiband tight-binding models constructed by a first-principles calculation. We discuss thermodynamic EQMs arising from an orbital order and/or bond order. Based on the results, we discuss the difference between iron-based superconductors and cuprate superconductors` EQMs.

[1] Wladimir A. Benalcazar, B. Andrei Bernevig, and Taylor L. Jughes, Science. 357 61 (2017)
[2] Wladimir A. Benalcazar, B. Andrei Bernevig, and Taylor L. Jughes, Phys. Rev. B. 96 245115 (2017)
[3] A. Daido, A. Shitade, and Y. Yanase, arXiv:2010.13999 (2020)