[Paper Review] Spin fluctuations and superconductivity in KxFe{2-y}Se2

Andreas Kreisel, Yan Wang+3 more|arXiv (Cornell University)|Aug 26, 2013

Iron-based superconductors research4 citations

TL;DR

This study investigates spin-fluctuation-mediated superconductivity in KxFe2−ySe2 using a 3D, ten-orbital tight-binding model derived from density functional theory (DFT) bands, treating electron interactions via random-phase approximation (RPA). It finds a leading d-wave pairing instability with quasi-nodes on electron pockets that vary in topology (horizontal, looplike, or vertical), while spin-orbit coupling enhances hybridization of M-centered electron pockets and stabilizes subdominant s±-wave states with bonding-antibonding character.

ABSTRACT

Superconductivity in alkali-intercalated iron selenide, with T_c's of 30K and above, may have a different origin than that of the other Fe-based superconductors, since it appears that the Fermi surface does not have any holelike sheets centered around the Gamma point. Here we investigate the symmetry of the superconducting gap in the framework of spin-fluctuation pairing calculations using density functional theory bands downfolded onto a three-dimensional (3D), ten-orbital tight-binding model, treating the interactions in the random-phase approximation (RPA). We find a leading instability towards a state with d-wave symmetry, but show that the details of the gap function depend sensitively on electronic structure. As required by crystal symmetry, quasi-nodes on electron pockets always occur, but are shown to be either horizontal, looplike or vertical depending on details. A variety of other 3D gap structures, including bonding-antibonding s-symmetry states which change sign between inner and outer electron pockets are found to be subdominant. We then investigate the possibility that spin-orbit coupling effects on the one-electron band structure, which lead to enhanced splitting of the two M-centered electron pockets in the 2-Fe zone, may stabilize the bonding-antibonding s_+/- wave states. Finally, we discuss our results in the context of current phenomenological theories and experiments.

Motivation & Objective

• To determine the symmetry and structure of the superconducting gap in KxFe2−ySe2, where conventional s± pairing mechanisms are challenged by the absence of hole-like Fermi sheets.
• To assess the role of three-dimensional electronic structure and spin-orbit coupling in stabilizing unconventional superconducting states.
• To compare predictions from 3D RPA spin-fluctuation theory with 2D models and experimental observations, particularly regarding gap node topology.
• To evaluate how spin-orbit coupling modifies the Fermi surface and promotes bonding-antibonding s±-wave states in the absence of hole pockets.

Proposed method

• Constructs a 3D, ten-orbital tight-binding model from DFT bands using maximally localized Wannier functions, capturing full orbital and momentum-space structure.
• Applies the random-phase approximation (RPA) to electron-electron interactions to compute the spin-fluctuation pairing vertex in the superconducting channel.
• Solves the linearized gap equation to identify the leading superconducting instability and determine the gap function symmetry.
• Incorporates spin-orbit coupling via a phenomenological term λ³d_Fe ≈ 0.06 eV in the Hamiltonian, modifying the band structure near the Fermi level.
• Uses Wannier function projections and k-space sampling (up to 7500 k-points) to ensure convergence of band structure and Fermi surface calculations.
• Analyzes the impact of spin-orbit coupling on the hybridization of M-centered electron pockets and its effect on pairing symmetry.

Experimental results

Research questions

• RQ1 What is the dominant superconducting pairing symmetry in KxFe2−ySe2 when hole-like Fermi sheets are absent?
• RQ2 How does the topology of the superconducting gap nodes (e.g., horizontal, looplike, vertical) depend on the electronic structure details?
• RQ3 To what extent does spin-orbit coupling enhance the hybridization of M-centered electron pockets and stabilize s±-wave pairing?
• RQ4 How do the results from a full 3D ten-orbital model differ from those of simplified 2D models in predicting the gap structure?
• RQ5 Can the observed gap structure in experiments be explained by spin-fluctuation pairing in a 3D framework with realistic band parameters?

Key findings

• The leading superconducting instability is a d-wave state, with gap nodes on electron pockets whose topology (horizontal, looplike, or vertical) depends sensitively on the electronic structure.
• Bonding-antibonding s±-wave states, which change sign between inner and outer M-centered electron pockets, are found to be subdominant but stabilized by spin-orbit coupling.
• Spin-orbit coupling increases the splitting of the two M-centered electron pockets in the 2-Fe Brillouin zone, enhancing their hybridization and favoring s±-wave pairing.
• The DFT-based 3D ten-orbital tight-binding model successfully captures symmetry-protected quasi-node structures not accessible in 2D approximations.
• The Fermi surface and band structure remain qualitatively consistent with ARPES data, supporting the validity of the effective model for superconducting regions.
• The inclusion of spin-orbit coupling (λ³d_Fe ≈ 0.06 eV) leads to measurable band splitting near the Fermi level, which influences the pairing channel competition.