Origin of Orthorhombic Transition, Magnetic Transition, and Shear Modulus Softening in Iron Pnictide Superconductors: Analysis based on the Orbital Fluctuation Theory

TL;DR

This paper presents a unified orbital fluctuation theory explaining the orthorhombic transition, magnetic order, and shear modulus softening in iron pnictide superconductors, highlighting the role of orbital fluctuations and two-orbiton processes.

Contribution

It introduces a multiorbital Hubbard-Holstein model analysis showing orbital fluctuations cause structural and magnetic transitions in iron pnictides, unifying their phenomena.

Findings

Orbital fluctuations induce shear modulus softening.

FQ fluctuations trigger orthorhombic transition.

FQ order relates to stripe magnetic order.

Abstract

The main features in iron-pnictide superconductors are summarized as (i) the orthorhombic transition accompanied by remarkable softening of shear modulus, (ii) high-Tc superconductivity close to the orthorhombic phase, and (iii) stripe-type magnetic order induced by orthorhombicity. To present a unified explanation for them, we analyze the multiorbital Hubbard-Holstein model with Fe-ion optical phonons based on the orbital fluctuation theory. In the random-phase-approximation (RPA), a small electron-phonon coupling constant ($\lambda ~ 0.2$) is enough to produce large orbital (=charge quadrupole) fluctuations. The most divergent susceptibility is the $O_{xz}$-antiferro-quadrupole (AFQ) susceptibility, which causes the s-wave superconductivity without sign reversal (s_{++}-wave state). At the same time, divergent development of $O_{x2-y2}$-ferro-quadrupole (FQ) susceptibility is brought by the "two-orbiton process" with respect to the AFQ fluctuations, which is absent in the RPA. The derived FQ fluctuations cause the softening of $C_{66}$ shear modulus, and its long-range-order not only triggers the orthorhombic structure transition, but also induces the instability of stripe-type antiferro-magnetic state. In other words, the condensation of composite bosons made of two orbitons gives rise to the FQ order and structure transition. The theoretically predicted multi-orbital-criticality presents a unified explanation for abovementioned features of iron pnictide superconductors.