Direct observation of spin–orbit coupling in iron-based superconductors

Abstract

Spin-orbit coupling (SOC) is a fundamental interaction in solids which can induce a broad spectrum of unusual physical properties from topologically non-trivial insulating states to unconventional pairing in superconductors. In iron-based superconductors (IBS) its role has so far been considered insignificant with the models based on spin-or orbital fluctuations pairing being the most advanced in the field. Using angle-resolved photoemission spectroscopy we directly observe a sizeable spin-orbit splitting in all main families of IBS. We demonstrate that its impact on the lowenergy electronic structure and details of the Fermi surface topology is much stronger than that of possible nematic ordering. Intriguingly, the largest pairing gap is always supported exactly by SOCinduced Fermi surfaces.In the presence of spin-orbit coupling, the electron's spin quantized along any fixed axis is no longer a good quantum number, but its total angular momentum is. This basic fact alone or in combination with a particular symmetry breaking may lead to a splitting of otherwise degenerate energy bands and is the origin of fascinating phenomena such as spin Hall effects A special role has been played by SOC in the field of superconductors. In low-dimensional or noncentrosymmetric systems it can promote and stabilize superconductivity [6], allow ferromagnetism to coexist with superconductivity [7] or even rise T c [8]. If SOC is large, some superconductors can host an elusive Fulde-Ferrell-Larkin-Ovchinnikov state [9] or topological superconductivity [4]. It is anticipated that SOC could be a very important ingredient in describing the superconducting state in Sr 2 RuO 4 [10]. Since k-dependent spin-orbit splitting is larger than the superconducting gap in this material, the SOC-induced spin anisotropy together with the orbital mixing should directly influence the orbital and spin angular momentum of the Cooper pairs. Singlet and triplet states could be strongly mixed, blurring the distinction between spin-singlet and spintriplet pairing [11].In multiband iron-based superconductors, where the low energy electronic structure is composed of different orbitals, the situation is even more complicated because of the presence of the sizeable Hund's coupling. When the electronic structure near the Fermi energy is composed of different orbitals and spins mixed via spin-orbit coupling, determination of the pairing symmetry becomes non-trivial. However, up to now SOC in iron pnictides and chalcogenides was considered weak.We start with the example of LiFeAs, which is a special representative of iron-based family of superconductors [12]. This material is one of the most studied due to its stoichiometry and non-polar surfaces. Its electronic structure is believed to be well understood from numerous angle-resolved photoemission experiments (ARPES) and the parameterization of its electronic dispersions has been used to test the most developed theoretical approaches [13][14][15]. To detect spin-orbit coupling in LiFeAs experimentally we first ne...

Hund Interaction, Spin-Orbit Coupling, and the Mechanism of Superconductivity in Strongly Hole-Doped Iron Pnictides

“…ARPES measurements (Ref. [21]) extracted λ ∼ 10−20meV, comparable to µ. Without SO, the Cooper states at zero momentum can be classified according to their behavior separately under the crystal's point group operations and under spin SU (2) rotations.…”

“…The renormalization affects differently the prefactors in different terms in Eq. (21). In a generic case, H b changes to…”

Stabilizing the spin vortex crystal phase in two-dimensional iron-based superconductors

“…It has been shown that single electron spinorbit coupling in iron-based superconductors is strong 27 (approximately 10.7 meV), and neutron scattering experiments suggest that this single electron spinorbit coupling reveals itself in the magnetic excitation spectrum; a spin-space anisotropy exists to around 6-8 meV 28,29 . Additionally, our density-functional-theory calculations, discussed in Sec.…”

Distinguishing spin-orbit coupling and nematic order in the electronic spectrum of iron-based superconductors

“…As the system is doped towards its maximum superconducting transition temperature, both gaps decrease 16 . Meanwhile, an atomic-like spin-orbit coupling present in the system gives rise to splittings at the Γ point of the order of 10-30 meV in the band structure 17 without any broken-symmetry 13 .…”