[Paper Review] Orbital-Parity Distinct Superconducting Pairing Structures of Fe-based Superconductors under Glide Symmetry

Chia‐Hui Lin, Chung-Pin Chou+2 more|arXiv (Cornell University)|Mar 14, 2014

Iron-based superconductors research3 citations

TL;DR

This paper proposes that glide symmetry in iron-based superconductors (FeSCs) induces orbital-parity-distinct superconducting pairing, where intra-orbital pairs exhibit different gap structures based on parity, while inter-orbital pairs form finite-momentum (π,π,0) η-pairs with odd form factors that break time-reversal symmetry. This explains the observed angular modulation contrast in ARPES and STS data on hole pockets.

ABSTRACT

We investigate an unusual symmetry of Fe-based superconductors (FeSCs) and find novel superconducting pairing structures. FeSCs have a minimal translational unit cell composed of two Fe atoms due to the staggered positions of anions with respect to the Fe plane. We study the physical consequences of the additional glide symmetry that further reduces the unit cell to have only one Fe atoms. In the regular momentum space, it not only leads to a particular orbital parity separated spectral function but also dictates orbital parity distinct pairing structures. Furthermore, it produces accompanying Cooper pairs of $(π,π,0)$ momentum, which have a characteristic extit{odd} form factor and break time reversal symmetry. Such novel pairing structures explain the unusual angular modulations of the superconducting gaps on the hole pockets in recent ARPES and STS experiments.

Motivation & Objective

• To resolve the long-standing puzzle of angularly modulated superconducting gaps in hole pockets of Ba_xK_1-xFe_2As_2 and LiFeAs.
• To clarify the physical consequences of glide symmetry (P_z T_∥) in FeSCs, which reduces the unit cell to one Fe atom and modifies momentum space structure.
• To explain why conventional momentum-space analysis fails in FeSCs due to broken in-plane translational symmetry from anion staggering.
• To identify novel Cooper pairing states—particularly inter-orbital-parity η-pairs with finite total momentum and broken time-reversal symmetry—arising from glide symmetry.
• To provide a unified framework for interpreting recent ARPES and STS data showing out-of-phase angular modulations between inner and outer hole pockets.

Proposed method

• Analyzes the FeSC Hamiltonian under glide symmetry (P_z T_∥), which introduces sign-changing hopping integrals via Θ = (−1)^{i_x+i_y} and (p_n' p_n)^{θ_i} factors.
• Uses a pseudo-crystal momentum representation to separate even- and odd-parity orbital contributions into distinct physical momenta, resolving the breakdown of standard momentum quantum numbers.
• Derives the anomalous Green’s function and pairing amplitudes, identifying intra-parity zero-momentum pairs and inter-parity η-pairs with total momentum Q = (π,π,0).
• Constructs the gap function as a sum of terms: Δ_s±, Δ_s++, and Δ_s, with orbital-parity-dependent angular modulations (4ϕ) and amplitudes.
• Applies the form factor Φ̃(k̃) = ϕ_e(−k̃)ϕ_o(k̃), which is purely imaginary and odd under k̃ → −k̃, indicating time-reversal symmetry breaking.
• Performs simulations using Eq. (6) and (7) to fit ARPES and STS data, showing fair agreement with experimental angular modulations and out-of-phase features.

Experimental results

Research questions

• RQ1 How does glide symmetry in Fe-based superconductors alter the momentum space structure and quasiparticle definition?
• RQ2 Why do hole pockets in Ba_xK_1-xFe_2As_2 show contrasting angular modulations of superconducting gaps in ARPES and STS?
• RQ3 What novel pairing states emerge from the interplay between orbital parity and glide symmetry?
• RQ4 Can the observed time-reversal-symmetry-breaking pairing be explained within a BCS framework without requiring extreme correlations?
• RQ5 How do intra- and inter-orbital-parity pairing channels coexist and contribute to the observed gap anisotropy?

Key findings

• Glide symmetry splits quasiparticle states into distinct even- and odd-parity contributions at different physical momenta, invalidating standard momentum-space analysis in FeSCs.
• Intra-orbital-parity Cooper pairs at zero momentum exhibit different gap structures depending on orbital parity, with even-parity orbitals showing stronger 4ϕ angular modulation and potential nodes.
• Inter-orbital-parity pairs form a novel finite-momentum (π,π,0) η-pairing state with an odd form factor, breaking time-reversal symmetry and carrying a purely imaginary pairing amplitude.
• The η-pairing amplitude |Φ̃(k̃)| is significant on electron pockets, particularly along the XM direction, and is maximized where d_xz/d_yz and d_xy orbitals hybridize strongly.
• Simulations based on the gap function Δ(k̃) = 4Δ_s± ± 4Δ_s++ + Δ_s reproduce the observed angular modulations in ARPES (Ba_xK_1-xFe_2As_2) and the out-of-phase behavior in STS (LiFeAs).
• The proposed pairing mechanism naturally explains the experimental contrast between hole pockets without requiring competing pairing symmetries or fine-tuned parameters.