[Paper Review] Hidden antiferro-nematic order in Fe-based superconductor BaFe$_2$As$_2$ and NaFeAs above $T_S$

Seiichiro Onari, Hiroshi Kontani|arXiv (Cornell University)|Nov 25, 2019

Iron-based superconductors research4 citations

TL;DR

This paper proposes that hidden antiferro-nematic order with wavevector $\bm{q} = (0,\pi)$ emerges at $T^*$ in Fe-based superconductors BaFe$_2$As$_2$ and NaFeAs, above the structural transition $T_S$, explaining the tiny but finite nematicity, pseudogap, and shadow bands. The order arises from inter-orbital nesting between $d_{xy}$-hole and electron pockets, driven by spin-fluctuation interference, and naturally accounts for $T$-linear nematicity and the absence of $T^*$ in FeSe.

ABSTRACT

In several Fe-based superconductors, slight $C_4$ symmetry breaking occurs at $T^*$, which is tens of Kelvin higher than the structural transition temperature $T_S$. In this "hidden" nematic state at $T_S

Motivation & Objective

• To resolve the long-standing mystery of the hidden nematic state in Fe-based superconductors above $T_S$ but below $T^*$, where a true second-order phase transition occurs despite tiny orthorhombicity.
• To explain the origin of the $T$-linear nematicity $\psi \propto T^* - T$ observed in BaFe$_2$As$_2$ and NaFeAs.
• To clarify why $T^*$ is absent in FeSe, which lacks the $d_{xy}$-orbital hole-pocket necessary for the proposed mechanism.
• To unify the explanation of pseudogap, band-folding, and nematicity within a single microscopic mechanism based on antiferro-bond (AFB) order.

Proposed method

• The study employs a two-dimensional eight-orbital $d$-$p$ Hubbard model with a tunable parameter $r$ to simulate BaFe$_2$As$_2$, NaFeAs, and FeSe.
• It uses the random phase approximation (RPA) and dynamical vertex (DW) approximation to compute spin and nematic susceptibilities, identifying dominant fluctuations at $\bm{q} = (0,\pi)$.
• The AFB order parameter is derived from the interplay of antiferro and ferro spin fluctuations, mediated by inter-orbital nesting between $d_{xy}$-hole and electron pockets.
• The form factor of the AFB order is calculated microscopically from the DW equation, enabling the construction of a $k$-dependent pairing interaction.
• The superconducting gap function is solved via the Eliashberg equation including RPA and DW-mediated interactions, with a cutoff energy $W_c = 0.02$ eV.
• The theory is validated in the cluster dynamical mean-field theory (CA) framework, confirming the dominance of AFB order over ferro-orbital order.

Experimental results

Research questions

• RQ1 What is the microscopic origin of the hidden nematic transition at $T^*$ in BaFe$_2$As$_2$ and NaFeAs, which occurs above $T_S$ and exhibits $T$-linear nematicity?
• RQ2 Why does the $T^*$ transition not occur in FeSe, despite similar electronic structure features?
• RQ3 How does the antiferro-bond (AFB) order with $\bm{q} = (0,\pi)$ explain the coexistence of pseudogap, band-folding, and tiny nematicity without disrupting the ferro-orbital order at $T_S$?
• RQ4 What is the role of inter-orbital nesting between $d_{xy}$-hole and electron pockets in driving the AFB order?
• RQ5 Can the AFB fluctuations mediate $s_{++}$-wave superconductivity, and how does this mechanism differ from conventional spin-fluctuation pairing?

Key findings

• The antiferro-bond (AFB) order with wavevector $\bm{q} = (0,\pi)$ emerges at $T^*$, explaining the hidden nematic transition in BaFe$_2$As$_2$ and NaFeAs.
• The AFB order arises from inter-orbital nesting between the $d_{xy}$-orbital hole-pocket and electron-pockets, driven by interference of antiferro and ferro spin fluctuations.
• The AFB order produces a pseudogap in the density of states and induces $T$-linear nematicity $\psi \propto T^* - T$, consistent with experiments in both BaFe$_2$As$_2$ and NaFeAs.
• The AFB order coexists with ferro-orbital (FO) order at $T_S$ because they have distinct orbital components, explaining the absence of strong anomalies in spin and nematic susceptibilities at $T^*$.
• The AFB fluctuations yield a large attractive pairing interaction $\bar{I}^{\bm{q}} \sim 9$ eV at $\bm{q} = (0,\pi)$, leading to a full-gap $s_{++}$-wave superconducting state.
• The mechanism explains the absence of $T^*$ in FeSe, which lacks the $d_{xy}$-orbital hole-pocket required for the inter-orbital nesting that drives AFB order.