Low-energy microscopic models for iron-based superconductors: a review

Abstract

IntroductionThe discovery of a rich family of iron-based superconductors (FeSC) with a variety of different chemical compositions [1,2], such as LaFeAsO (1 1 1 1 material), BaFe 2 As 2 (1 2 2 mat erial), NaFeAs (1 1 1 material), and FeSe (1 1 material), opened a new route to study high-temperature superconductivity. Similarly to high-T c cuprates, which are made of coupled CuO 2 layers, FeSC are also layered systems made of coupled FeAs layers. In both cases, the Cu and Fe atoms form a simple square lattice.The phase diagrams of FeSC are also quite similar to those of the cuprates. Although details of the phase diagrams vary between different families of FeSC, most materials display the key Corresponding Editor Laura Greene AbstractThe development of sensible microscopic models is essential to elucidate the normal-state and superconducting properties of the iron-based superconductors. Because these materials are mostly metallic, a good starting point is an effective low-energy model that captures the electronic states near the Fermi level and their interactions. However, in contrast to cuprates, iron-based high-T c compounds are multi-orbital systems with Hubbard and Hund interactions, resulting in a rather involved 10-orbital lattice model. Here we review different minimal models that have been proposed to unveil the universal features of these systems. We first review minimal models defined solely in the orbital basis, which focus on a particular subspace of orbitals, or solely in the band basis, which rely only on the geometry of the Fermi surface. The former, while providing important qualitative insight into the role of the orbital degrees of freedom, do not distinguish between high-energy and low-energy sectors and, for this reason, generally do not go beyond mean-field. The latter allow one to go beyond mean-field and investigate the interplay between superconducting and magnetic orders as well as Ising-nematic order. However, they cannot capture orbital-dependent features like spontaneous orbital order. We then review recent proposals for a minimal model that operates in the band basis but fully incorporates the orbital composition and symmetries of the lowenergy excitations. We discuss the results of the renormalization group study of such a model, particularly of the interplay between superconductivity, magnetism, and spontaneous orbital order, and compare theoretical predictions with experiments on iron pnictides and chalcogenides. We also discuss the impact of the glide-plane symmetry on the low-energy models, highlighting the key role played by the spin-orbit coupling.

Order on Command

“…According to this scenario, the suppression of the nesting condition by the induced C 4 plaquette order will have a more drastic effect on superconductivity compared with switching between and C 4 orders that maintain the nesting conditions, as shown in the recent studies on Ba 1−x K x Fe 2 As 2 [17] and Ba 1−x Na x Fe 2 As 2 [18], where a more subtle T c reduction was observed. Among multiple theories of iron-based superconductivity based on spin fluctuations [36,37] and orbital fluctuations [38,39], our experimental results on this material seem to favor the former.…”

Order parameter fluctuation and ordering competition in Ba1−xKxFe2As2

“…A universal property shared by most known iron-based superconductors (FeSCs) is the bulk coexistence of two or even more distinct long-range orders [1][2][3][4][5][6][7][8][9][10][11][12], such as superconductivity, stripe-type spin-density-wave (SDW) order, nematic order, and other possible orders. The competition and coexistence of these orders leads to a very complicated global phase diagram [1][2][3][4][5][6][7][8][9][10][11][12].…”

“…The competition and coexistence of these orders leads to a very complicated global phase diagram [1][2][3][4][5][6][7][8][9][10][11][12]. Acquiring a detailed knowledge of the phase diagram is an important step towards a better understanding of FeSCs.…”

“…In most cases, the nematic order sets in at a temperature T n slightly higher than the critical temperature of magnetic order T m [4,6,10,18,19]. Usually, the magnetic order is generated by a stripe-type SDW, and possesses two characteristic vectors Q X = (π, 0) and Q Y = (0, π) in the Brillouin zone of the iron square lattice, which relate to the spin operator S(r) in the form S(r) = M X,Y e iQX,Y ·r [12,20]. This stripe SDW breaks the discrete lattice rotational symmetry by selecting out only one of the two characteristic vectors Q X and Q Y , preserving the C 2 symmetry [6,8,10,12].…”

“…Usually, the magnetic order is generated by a stripe-type SDW, and possesses two characteristic vectors Q X = (π, 0) and Q Y = (0, π) in the Brillouin zone of the iron square lattice, which relate to the spin operator S(r) in the form S(r) = M X,Y e iQX,Y ·r [12,20]. This stripe SDW breaks the discrete lattice rotational symmetry by selecting out only one of the two characteristic vectors Q X and Q Y , preserving the C 2 symmetry [6,8,10,12]. Because the nematic order and SDW order coexist over a large part of the global phase diagram, it is widely believed [3][4][5][6][8][9][10][11][12] that the nematic order is actually induced by the fluctuation of magnetic order.…”