Modeling Many-Body Physics with Slave-Spin Mean-Field: Mott and Hund’s Physics in Fe-Superconductors

Evidence for saddle point-driven charge density wave on the surface of heavily hole-doped iron arsenide superconductors

Unconventional superconductivity is known for its intertwining with other correlated states, making exploration of the intertwined orders important for understanding its pairing mechanism. In particular, spin and nematic orders are widely observed in iron-based superconductors; however, the presence of charge order is uncommon. Using scanning tunnelling microscopy, and through expanding the phase diagram of iron-arsenide superconductor Ba1-xKxFe2As2 to the hole-doping regime beyond KFe2As2 by surface doping, we demonstrate the formation of a charge density wave (CDW) on the arsenide surface of heavily hole-doped Ba1-xKxFe2As2. Its emergence suppresses superconductivity completely, indicating their direct competition. Notably, the CDW emerges when the saddle points approach the Fermi level, where its wavevector matches with those linking the saddle points, suggesting saddle-point nesting as its most probable formation mechanism. Our findings offer insights into superconductivity and intertwined orders, and a platform for studying them in iron-based superconductors close to the half-filled configuration.

Electronic stripe patterns near the fermi level of tetragonal Fe(Se,S)

FeSe1-xSx remains one of the most enigmatic systems of Fe-based superconductors. While much is known about the orthorhombic parent compound, FeSe, the tetragonal samples, FeSe1-xSx with x > 0.17, remain relatively unexplored. Here, we provide an in-depth investigation of the electronic states of tetragonal FeSe0.81S0.19, using scanning tunneling microscopy and spectroscopy (STM/S) measurements, supported by angle-resolved photoemission spectroscopy (ARPES) and theoretical modeling. We analyze modulations of the local density of states (LDOS) near and away from Fe vacancy defects separately and identify quasiparticle interference (QPI) signals originating from multiple regions of the Brillouin zone, including the bands at the zone corners. We also observe that QPI signals coexist with a much stronger LDOS modulation for states near the Fermi level whose period is independent of energy. Our measurements further reveal that this strong pattern appears in the STS measurements as short range stripe patterns that are locally two-fold symmetric. Since these stripe patterns coexist with four-fold symmetric QPI around Fe-vacancies, the origin of their local two-fold symmetry must be distinct from that of nematic states in orthorhombic samples. We explore several aspects related to the stripes, such as the role of S and Fe-vacancy defects, and whether they can be explained by QPI. We consider the possibility that the observed stripe patterns may represent incipient charge order correlations, similar to those observed in the cuprates.

Mott Quantum Critical Points at Finite Doping

We demonstrate that a finite-doping quantum critical point (QCP) naturally descends from the existence of a first-order Mott transition in the phase diagram of a strongly correlated material. In a prototypical case of a first-order Mott transition the surface associated with the equation of state for the homogeneous system is "folded" so that in a range of parameters stable metallic and insulating phases exist and are connected by an unstable metallic branch. Here we show that tuning the chemical potential, the zero-temperature equation of state gradually unfolds. Under general conditions, we find that the Mott transition evolves into a first-order transition between two metals, associated with a phase separation region ending in the finite-doping QCP. This scenario is here demonstrated solving a minimal multiorbital Hubbard model relevant for the iron-based superconductors, but its origin-the splitting of the atomic ground state multiplet by a small energy scale, here Hund's coupling-is much more general. A strong analogy with cuprate superconductors is traced.

Mott transition, magnetic and orbital orders in the ground state of the two-band Hubbard model using variational slave-spin mean field formalism

We study the ground state phase diagram of the degenerate two-band Hubbard model at integer fillings as a function of onsite Hubbard interactionUand Hund's exchange couplingJ. We use a variational slave-spin mean field method which allows symmetry broken states to be studied within the computationally less intensive slave-spin mean field formalism. The results show that at half-filling, the ground state at smallerUis a Slater antiferromagnet with substantial local charge fluctuations. AsUis increased, the antiferromagnetic (AF) state develops a Heisenberg behavior, finally undergoing a first-order transition to a Mott insulating AF state at a critical interactionU_cwhich is of the order of the bandwidth. Introducing the Hund's couplingJcorrelates the system more and reducesU_cdrastically. At quarter-filling with one electron per site, the ground state at smallerUis paramagnetic metallic. At finiteJ, as interaction is increased beyond a lower critical valueU_c1, it goes to a fully spin polarized ferromagnetic state coexisting with an antiferro-orbital order. Further increase inUbeyond a higher critical valueU_c2results in the Mott insulating state where local charge fluctuation vanishes.

Many-Body Effects in FeN4 Center Embedded in Graphene

We introduce a computational approach to study porphyrin-like transition metal complexes, bridging density functional theory and exact many-body techniques, such as the density matrix renormalization group (DMRG). We first derive a multi-orbital Anderson impurity Hamiltonian starting from first principles considerations that qualitatively reproduce generalized gradient approximation (GGA)+U results when ignoring inter-orbital Coulomb repulsion U ′ and Hund exchange J. An exact canonical transformation is used to reduce the dimensionality of the problem and make it amenable to DMRG calculations, including all many-body terms (both intra- and inter-orbital), which are treated in a numerically exact way. We apply this technique to FeN 4 centers in graphene and show that the inclusion of these terms has dramatic effects: as the iron orbitals become single occupied due to the Coulomb repulsion, the inter-orbital interaction further reduces the occupation, yielding a non-monotonic behavior of the magnetic moment as a function of the interactions, with maximum polarization only in a small window at intermediate values of the parameters. Furthermore, U ′ changes the relative position of the peaks in the density of states, particularly on the iron d z 2 orbital, which is expected to affect the binding of ligands greatly.

Hund's metal regimes and orbital selective Mott transitions in three band systems

We analyze the electronic properties of interacting crystal field split three band systems. Using a rotationally invariant slave boson approach we analyze the behavior of the electronic mass renormalization as a function of the intralevel repulsion U, the Hund's coupling J, the crystal field splitting, and the number of electrons per site n. We first focus on the case in which two of the bands are identical and the levels of the third one are shifted by [Formula: see text] with respect to the former. We find an increasing quasiparticle mass differentiation between the bands, for system away from half-filling (n  =  3), as the Hubbard interaction U is increased. This leads to orbital selective Mott transitions where either the higher energy band (for 4  >  n  >  3) or the lower energy degenerate bands (2  <  n  <  3) become insulating for U larger than a critical interaction [Formula: see text]. Away from the half-filled case [Formula: see text] there is a wide range of parameters for [Formula: see text] where the system presents a Hund's metal phase with the physics dominated by the local high spin multiplets. Finally, we study the fate of the n  =  2 Hund's metal as the energy splitting between orbitals is increased for different possible crystal distortions. We find a strong sensitivity of the Hund's metal regime to crystal fields due to the opposing effects of J and the crystal field splittings on the charge distribution between the bands.