Electron Correlations and Nematicity in the Iron-Based Superconductors

Introduction Superconductivity in the iron-based materials was first discovered in 2008 in fluorine-doped LaFeAsO, with a superconducting transition temperature Tc of 26 K [1]. Like most major discoveries in physics, this was a serendipitous discovery, in this case in the search for transparent semiconductors for flexible displays [2]. Very quickly, researchers across the world raced to synthesize and discover related iron-based superconductors (FeSCs), raising the Tc to 55 K [3,4] within a few months and launching what became known in the field as the “iron age”. As the second family of high-temperature superconductors after the dominance of the copper oxide superconductors, one of the first questions raised was whether the superconductivity in FeSCs was of similar or distinct origin as the cuprates. Having benefited from substantial development through the prior studies of cuprates and heavy fermion systems, the tool of angle-resolved photoemission spectroscopy (ARPES), with its capability to measure the single-particle spectral function in a momentumresolved fashion, became a unique and important technique to the study of this new family of superconductors [5]. In this work, we review two important aspects of the FeSCs contributed by synchrotron-based ARPES: orbital-selective correlation effects and nematicity, as well as the expansion of ARPES as a tool driven by these physics in the FeSCs. The common building block of any FeSC is a tetragonal iron-pnictogen or iron-chalcogen plane (Figure 1b) [7]. The pnictogens (As, P) or chalcogens (Se, Te) pucker alternatively above and below the iron-plane such that the true unit cell of the crystal structure is a 2-Fe unit cell— double that of the 1-Fe unit cell when considering only the iron plane. Different FeSCs can be built by simply stacking such layers, as is the case in FeSe, or by inserting alkaline-earth metal elements or alkali metals in between the layers, such as BaFe2As2 and NaFeAs (Figure 1a). The dominant density of states near the Fermi level are of Fe 3d orbitals, in particular the three t2g orbitals of dxz, dyz, and dxy [8,9]. Due to the common Fe plane amongst FeSCs, the electronic structure across the FeSC families is similar, consisting of three hole-like bands around the Brillouin zone (BZ) center (Γ) and two electron-like bands around the 2-Fe BZ corner (M). As shown in Figure 1c, these bands are dominated by different orbital characters, and form small Fermi pockets around the Γ and M points. Due to the presence of all three t2g orbitals at the Fermi level, EF, the multi-orbital nature of FeSCs manifests as a key aspect of their properties. ARPES, as one of the very few experimental techniques that can directly probe the orbital degree of freedom, has made important contributions to the understanding of both the normal state properties as well as the superconducting properties in the FeSCs [10–18]. Across the numerous members of the FeSCs, the phase diagrams also share strong similarities (Figure 1d). The undoped parent compounds of iron pnictides, including BaFe2As2 and NaFeAs, are often found to exhibit two strongly coupled symmetry-breaking phases, a collinear antiferromagnetic (AFM) order and a rotational-symmetry breaking nematic order [19–22]. The nematic order lowers the C4 rotational symmetry to C2, and is manifested on the phase diagram by a tetragonal to orthorhombic lattice distortion. The collinear AFM order forms either simultaneously with the nematic order or at a slightly lower temperature, inherits the C2 rotational symmetry, and further breaks translational symmetry with spins ferromagnetically aligned along the shorter Fe-Fe bond direction and antiferromagnetically aligned along the longer Fe-Fe bond direction. The in-plane component of the magnetic wavevector is (π, π) in the notation of the 2-Fe unit cell, with the out-of-plane component varying amongst different material families [23]. As this magnetic wavevector connects the hole Fermi pockets at the BZ center and the electron Fermi pockets at the BZ corner, this AFM order has also been referred to as a spin density wave (SDW) order. With charge carrier doping into the Fe-plane, the intertwined nematic order and SDW order can be suppressed, leading to the emergence of superconductivity in the form of a dome in the phase diagram (Figure 1d). Electron doping can be realized by replacing Fe with Co or Ni [24,25]. Hole doping can be realized by replacing Ba with K or Na [26,27]. Isovalent substitution of As by P, which is a form of chemical pressure, can also achieve a similar phase diagram [28], as can also by direct hydrostatic pressure [29]. In the iron chalcogenides, SDW order has not been found under ambient pressure [23, 30]. FeSe exhibits only a nematic order [31], which can be suppressed by either substitution by S or Te [32,33]. Under hydrostatic pressure, a magnetic order has been found in FeSe [34,35].