[Paper Review] Out-of-plane momentum and symmetry dependent superconducting gap in Ba0.6K0.4Fe2As2

Y. Zhang, L. X. Yang+11 more|arXiv (Cornell University)|Jun 20, 2010

Iron-based superconductors research3 citations

TL;DR

This study uses high-resolution angle-resolved photoemission spectroscopy (ARPES) to reveal that the superconducting gap in Ba₀.₆K₀.₄Fe₂As₂ exhibits strong out-of-plane momentum (k_z) dependence and symmetry-dependent gap sizes. The authors identify three hole-like Fermi surfaces near Γ with distinct k_z dispersion and show that the gap on the β band varies significantly with k_z, while bands with different spatial symmetries (odd vs. even) display different gap magnitudes at the same in-plane momentum, challenging 2D theoretical models and highlighting the importance of 3D electronic structure and orbital symmetry in iron-based superconductors.

ABSTRACT

The three-dimensional band structure and superconducting gap of Ba0.6K0.4Fe2As2 are studied with high-resolution angle-resolved photoemission spectroscopy. In contrast to previous results, we have identified three hole-like Fermi surfaces near the zone center with sizable out-of-plane or kz dispersion. The superconducting gap on certain Fermi surface shows significant kz-dependence. Moreover, we found that the superconducting gap sizes are different at the same Fermi momentum for two bands with different spatial symmetries (one odd, one even). Our results provide further information on the rich superconducting gap structure in iron pnictides, and a distinct test for theories.

Motivation & Objective

• To resolve the long-standing controversy over the pairing symmetry and gap structure in iron-based superconductors by directly probing the 3D electronic structure.
• To investigate the role of out-of-plane momentum (k_z) dispersion in the superconducting gap, which has been largely unexplored in previous ARPES studies.
• To determine how orbital symmetry and Fermi surface topology influence gap size, particularly in multi-band, multi-orbital systems.
• To test the validity of 2D theoretical models against experimental data that reveal strong 3D character in the superconducting order parameter.
• To establish a comprehensive, 3D picture of the superconducting gap in Ba₀.₆K₀.₄Fe₂As₂, including symmetry-dependent and k_z-dependent behavior.

Proposed method

• High-resolution angle-resolved photoemission spectroscopy (ARPES) was performed on high-quality Ba₀.₆K₀.₄Fe₂As₂ single crystals at various photon energies to access different k_z regions.
• Photon energy-dependent ARPES measurements allowed the reconstruction of the 3D band structure and the mapping of k_z dispersion of the Fermi surfaces.
• Momentum-distribution curves (MDCs) at the Fermi level were extracted and used to identify three distinct hole-like Fermi surface sheets near the Γ point.
• Symmetrized energy distribution curves (EDCs) were fitted using a phenomenological superconducting spectral function to extract superconducting gap values at different k_z and momentum points.
• The k_z dependence of the gap was analyzed by comparing gap values across different photon energies, with a focus on the β band, which showed strong variation.
• A modified gap function Δ(k) = Δ₀|cos kₓ cos kᵧ|(1 + A cos k_z) was used to fit the k_z-dependent gap of the β band, yielding parameters Δ₀ ≈ 11.2 meV and A ≈ 0.24.

Experimental results

Research questions

• RQ1 How does the out-of-plane momentum (k_z) dependence of the superconducting gap influence the pairing mechanism in Ba₀.₆K₀.₄Fe₂As₂?
• RQ2 What is the true number of hole-like Fermi surface sheets near the Γ point, and how does their k_z dispersion affect the superconducting gap?
• RQ3 Why do bands with different spatial symmetries (odd vs. even) exhibit different superconducting gap sizes at the same in-plane momentum?
• RQ4 Can the observed k_z-dependent gap behavior be explained by conventional 2D models of s± pairing symmetry, or is a 3D description necessary?
• RQ5 How do orbital characters and 3D electronic structure influence the gap anisotropy and pairing symmetry in iron-based superconductors?

Key findings

• Three hole-like Fermi surface sheets were identified near the Γ point, contradicting previous reports of only two sheets.
• The superconducting gap on the β band exhibits strong k_z dependence, varying from 11.5 meV to 7 meV as k_z changes, indicating significant 3D character in the order parameter.
• At the same in-plane momentum, the α band (even symmetry) and β band (odd symmetry) show distinct gap sizes (7 meV vs. 11.5–7 meV), demonstrating symmetry-dependent gap behavior.
• The k_z dependence of the β band's gap cannot be explained by in-plane Fermi surface size changes alone, requiring inclusion of k_z in the gap function.
• A modified gap function Δ(k) = Δ₀|cos kₓ cos kᵧ|(1 + A cos k_z) with Δ₀ ≈ 11.2 meV and A ≈ 0.24 successfully fits the k_z-dependent gap of the β band.
• The results challenge 2D theoretical models and necessitate inclusion of out-of-plane pairing channels and orbital symmetry effects in microscopic theories of iron-based superconductors.