Competing pairing symmetries in a generalized two-orbital model for the pnictide superconductors

Spin, orbital and topological order in models of strongly correlated electrons

Different types of order are discussed in the context of strongly correlated transition metal oxides, involving pure compounds and [Formula: see text] and [Formula: see text] hybrids. Apart from standard, long-range spin and orbital orders we observe also exotic noncollinear spin patterns. Such patters can arise in presence of atomic spin-orbit coupling, which is a typical case, or due to spin-orbital entanglement at the bonds in its absence, being much less trivial. Within a special interacting one-dimensional spin-orbital model it is also possible to find a rigorous topological magnetic order in a gapless phase that goes beyond any classification tables of topological states of matter. This is an exotic example of a strongly correlated topological state. Finally, in the less correlated limit of 4d ⁴ oxides, when orbital selective Mott localization can occur it is possible to stabilize by a 3d ³ doping one-dimensional zigzag antiferromagnetic phases. Such phases have exhibit nonsymmorphic spatial symmetries that can lead to various topological phenomena, like single and multiple Dirac points that can turn into nodal rings or multiple topological charges protecting single Dirac points. Finally, by creating a one-dimensional [Formula: see text] hybrid system that involves orbital pairing terms, it is possible to obtain an insulating spin-orbital model where the orbital part after fermionization maps to a non-uniform Kitaev model. Such model is proved to have topological phases in a wide parameter range even in the case of completely disordered 3d ² impurities. What more, it exhibits hidden Lorentz-like symmetries of the topological phase, that live in the parameters space of the model.

Orbital Symmetry and Orbital Excitations in High-Tc Superconductors

We discuss a few possibilities of high- T c superconductivity with more than one orbital symmetry contributing to the pairing. First, we show that the high energies of orbital excitations in various cuprates suggest a simplified model with a single orbital of x 2 − y 2 symmetry doped by holes. Next, several routes towards involving both e g orbital symmetries for doped holes are discussed: (i) some give superconductivity in a CuO 2 monolayer on Bi2212 superconductors, Sr 2 CuO 4 − δ , Ba 2 CuO 4 − δ , while (ii) others as nickelate heterostructures or Eu 2 − x Sr x NiO 4 , could in principle realize it as well. At low electron filling of Ru ions, spin-orbital entangled states of t 2 g symmetry contribute in Sr 2 RuO 4 . Finally, electrons with both t 2 g and e g orbital symmetries contribute to the superconducting properties and nematicity of Fe-based superconductors, pnictides or FeSe. Some of them provide examples of orbital-selective Cooper pairing.

Particle–Hole Transformation in Strongly-Doped Iron-Based Superconductors

An exact particle–hole transformation is discovered in a local-moment model for a single layer of heavily electron-doped FeSe. The model harbors hidden magnetic order between the iron d x z and d y z orbitals at the wavenumber ( π , π ) . It potentially is tied to the magnetic resonances about the very same Néel ordering vector that have been recently discovered in intercalated FeSe. Upon electron doping, the local-moment model successfully accounts for the electron-pocket Fermi surfaces observed experimentally at the corner of the two-iron Brillouin zone in electron-doped FeSe, as well as for isotropic Cooper pairs. Application of the particle–hole transformation predicts a surface-layer iron-based superconductor at strong hole doping that exhibits high T c, and that shows hole-type Fermi-surface pockets at the center of the two-iron Brillouin zone.

Magnetic Lifshitz transition and its consequences in multi-band iron-based superconductors

In this paper we address Lifshitz transition induced by applied external magnetic field in a case of iron-based superconductors, in which a difference between the Fermi level and the edges of the bands is relatively small. We introduce and investigate a two-band model with intra-band pairing in the relevant parameters regime to address a generic behaviour of a system with hole-like and electron-like bands in external magnetic field. Our results show that two Lifshitz transitions can develop in analysed systems and the first one occurs in the superconducting phase and takes place at approximately constant magnetic field. The chosen sets of the model parameters can describe characteristic band structure of iron-based superconductors and thus the obtained results can explain the experimental observations in FeSe and Co-doped BaFe₂As₂ compounds.

Competing superconducting channels in iron pnictides from the strong coupling theory with biquadratic spin interactions

We study the symmetry and strength of the superconducting pairing in a two-orbital [Formula: see text] model for iron pnictides using the slave boson strong coupling approach. We show that the nearest-neighbor biquadratic interaction [Formula: see text] strongly affects the superconducting pairing phase diagram by promoting the [Formula: see text] B _1g and the [Formula: see text] A _1g channels. The resulting phase diagram consists of several competing pairing channels, including the isotropic [Formula: see text] A _1g channel, an anisotropic [Formula: see text] B _1g channel, and two [Formula: see text] pairing channels. We have investigated the evolution of superconducting states with electron doping, and find that the biquadratic interaction plays a crucial role in stabilizing the [Formula: see text] and even pure d-wave pairing in the heavily electron- and hole-doped regimes. In addition, we identify a novel orbital-B _1g pairing channel, which has a s-wave form factor but a B _1g symmetry. This channel has a comparable pairing amplitude to the d-wave pairing, and may strongly influence the superconducting gap anisotropy of the system in the overdoped regime. These findings are crucial in understanding the doping evolution of the superconducting gap anisotropy observed by angle resolved photoemission spectroscopy in the iron pnictides and iron chalcogenides, including the heavily K-doped BaFe₂As₂ and K-doped FeSe films.

Collective mode at Lifshitz transition in iron-pnictide superconductors

We obtain the exact low-energy spectrum of two mobile holes in a t-J model for an isolated layer in an iron-pnictide superconductor. The minimum d xz and d yz orbitals per iron atom are included, with no hybridization between the two. After tuning the Hund coupling to a putative quantum critical point (QCP) that separates a commensurate spin-density wave from a hidden-order antiferromagnet at half filling, we find an s-wave hole-pair groundstate and a d-wave hole-pair excited state. Near the QCP, both alternate in sign between hole Fermi surface pockets at the Brillouin zone center and emergent electron Fermi surface pockets at momenta that correspond to commensurate spin-density waves (cSDW). The dependence of the energy splitting with increasing Hund coupling yields evidence for a true QCP in the thermodynamic limit near the putative one, at which the s-wave and d-wave Cooper pairs are degenerate. A collective s-to-d-wave oscillation of the macroscopic superconductor that couples to orthorhombic shear strain is also identified. Its resonant frequency is predicted to collapse to zero at the QCP in the limit of low hole concentration. This implies degeneracy of Cooper pairs with s, d and [Formula: see text] symmetry in the corresponding quantum critical state. We argue that the critical state describes Cooper pairs in hole-doped iron superconductors at the Lifshitz transition, where electron bands first rise above the Fermi level. We thereby predict that the s-to-d-wave collective mode observed by Raman spectroscopy in Ba1-x K x Fe2As2 at optimal doping should also be observed at higher doping near the Lifshitz transition.

The magnetic moment enigma in Fe-based high temperature superconductors

The determination of the most appropriate starting point for the theoretical description of Fe-based materials hosting high-temperature superconductivity remains among the most important unsolved problem in this relatively new field. Most of the work to date has focused on the pnictides, with LaFeAsO, BaFe(2)As(2) and LiFeAs being representative parent compounds of three families known as 1111, 122 and 111, respectively. This topical review examines recent progress in this area, with particular emphasis on the implication of experimental data which have provided evidence for the presence of electron itinerancy and the detection of local spin moments. In light of the results presented, the necessity of a theoretical framework contemplating the presence and the interplay between itinerant electrons and large spin moments is discussed. It is argued that the physics at the heart of the macroscopic properties of pnictides Fe-based high-temperature superconductors appears to be far more complex and interesting than initially predicted.

Magnetic and pairing properties of a two-orbital model for the pnictide superconductors: a quantum Monte Carlo study

Using the constrained-path Monte Carlo method, a two-orbital model for the pnictide superconductors is studied at half filling and in both the electron- and hole-doped cases. At half filling, a stable (π, 0)/(0, π) magnetic order is explicitly observed and the system tends to be in an orthomagnetic order rather than the striped antiferromagnetic order on increasing the Coulomb repulsion U. In the electron-doped case, the (π, 0)/(0, π) magnetic order is enhanced upon doping and suppressed eventually and a s(±) pairing state dominates all the possible nearest-neighbour-bond pairings. Whereas in the hole-doped case, the magnetic order is straightforwardly suppressed and two nearly degenerate A(1g) and B(1g) intraband pairings become the dominant ones.

Variable range hopping conductivity and spin glass behavior in spin-ladder Ba0.6K0.4Fe2Se3 single crystals

Ba0.6K0.4Fe2Se3 (BKFS) single crystals were investigated by means of measurements of powder x-ray diffraction, temperature-dependent resistivity, anisotropic dc magnetization, ac magnetic susceptibility and specific heat. The powder x-ray diffraction indicates staggered iron displacements along the ladders with short and long Fe-Fe bond lengths (2.64(2) and 2.91(2) Å) variation. The resistivity of BKFS exhibits variable range hopping behavior with ln(ρ) ~ T(-1/2) at low temperature. The magnetic susceptibility χ(T) exhibits a sharp cusp at around 20 K in a zero-field-cooled process. The frequency-dependent ac magnetic susceptibility reveals that the cusp feature is attributable to spin glass behavior. The anisotropic ac magnetic susceptibility indicates that BKFS is probably an anisotropic Heisenberg-like spin glass with its easy magnetization plane perpendicular to the chain direction. The specific heat also supports an insulating and spin glass ground state. Extended Curie-Weiss behavior above 40 K was observed with a reduced effective moment (μ(eff) = 1.66 μ(B)/Fe for H is perpendicular to b and μ(eff) = 1.82 μB/Fe for H is parallel to b) in BKFS, which is close to the spin-only magnetism with S=1/2.

Spin fluctuations and pairing symmetry in AxFe₂-ySe₂: dual effect of the itinerant and the localized nature of electrons

We investigate the spin fluctuations and the pairing symmetry in AxFe2-ySe2 by the fluctuation exchange approximation. Besides the on-site interactions, the next-nearest-neighbor antiferromagnetic coupling J2 is also included. We find that both the itinerant and the localized natures of electrons are important to describe recent experimental results on the spin fluctuations and the pairing symmetry. In particular, a small J2 coupling can change the pairing gap from the d-wave symmetry to the extended s-wave symmetry. We have also studied the real-space structures of the gap functions for different orbits in order to gain more insight into the nature of the pairing mechanism.

Anomalous superconducting state in LiFeAs implied by the 75As Knight shift measurement

(75)As NMR investigation of a single crystal of superconducting LiFeAs is presented. The Knight shift and the in situ ac susceptibility measurements as a function of temperature and external field are indicative of two superconducting (SC) transition temperatures, each of which is associated with its own upper critical field. Strikingly, the Knight shift maintains its normal state value over a temperature range in the SC state before it drops abruptly, being consistent with spin-singlet pairing. Together with our previous NMR study, the anomalous SC state featuring the constant Knight shift is attributed to the extremely sensitive SC properties of LiFeAs, probably stemming from its proximity to a critical instability.