Session Z22: Focus Session: Fe-based Superconductors - Orbital Order and Chalcogenides

Orbital Order and Orthorhombic Anisotropy in Iron Pnictides

Orthorhombic anisotropy has been reported in iron-pnictide superconductors by a broad range of experiments, including neutron scattering, transport measurements, and a variety of spectroscopies. We explore the idea that these observed anisotropies of broken tetragonal symmetry stem from an ordering of the partially-filled iron d-orbitals. In particular, we will consider a model Hamiltonian that couples the spin and orbital variables, and show that this spin-orbital model captures several observed behaviors in the iron-pnictide materials. We will conclude the talk by discussing x-ray absorption linear dichroism and other recent experiments supportive of theories highlighting the orbital degrees of freedom.   

Orbital ordering in Ba(Fe$_{1-x}$Co$_{x})_{2}$As$_{2}$ revealed by X-ray absorption Spectroscopy

Recently, anomalous in-plane anisotropy was observed by various experiment in iron pnictide systems. To explain the anomalous in-plane anisotropic behavior observed in iron pnictide system, orbital ordering was suggested as an origin of it. Among the various possible ordering, Ferroorbital ordering was proposed which occurs unequal occupation number of d$_{yz}$ and d$_{zx}$ orbital. it was theoretically predicted that such orbital ordering could be observed by performing X-ray Linear Dichroism experiment. To figure out, we performed the experiment on the most studied iron pnictide system, Ba(Fe$_{1-x}$Co$_{x})_{2}$As$_{2}$. We obtained linear dichroism signal which indicates different occupation number for different orbital. And we observed temperature and doping dependence of the dichroism signal. Our results support the existence of ferro-orbital ordering.   

Non-Fermi Liquid due to Orbital Fluctuations in Iron Pnictide Superconductors

We propose that the quantum fluctuations associated with quasi-1D $d_{xz}$ and $d_{yz}$ bands could result in a non-Fermi liquid behaviour in iron-pnictide superconductors. Using a five orbital tight binding model with generalized Hubbard on-site interactions, we find that within a one-loop treatment, a branch of overdamped collective modes develops at low frequency in channels associated with quasi-1D $d_{xz}$ and $d_{yz}$ bands. When the critical point for the $C_4$ symmetry broken phase (structural phase transition) is approached, the overdamped collective modes soften, and acquire increased spectral weight, leading to a non-Fermi liquid behavior at the Fermi surface. We argue that this non-Fermi liquid behavior is responsible for the recently observed zero-bias enhancement in the tunneling signal in quantum point contact spectroscopy. A key experimental test of this proposal is the absence of the non-Fermi liquid behaviour in the hole-doped materials. Our result suggests that quantum criticality plays an important role in understanding the normal state properties of iron-pnictide superconductors.   

Spin and orbital characters of excitations in iron arsenide superconductors revealed by simulated resonant inelastic x-ray scattering

We theoretically examine the orbital excitations coupled to the spin degree of freedom in the parent state of the iron-arsenide superconductor, based on the calculation in a five-band itinerant model [1]. The calculated Fe L$_3$-edge resonant inelastic x-ray scattering (RIXS) spectra disclose the presence of spin-flip excitations involving several specific orbitals. Magnon excitations predominantly composed of a single orbital component can be seen in experiments, although its spectral weight is smaller than spin-flipped interorbital high-energy excitations. The detailed polarization and momentum dependence is also discussed with predictions for the experiments. [1] E. Kaneshita, K. Tsutsui, and T. Tohyama, Phys. Rev. B {\bf 84}, 020511(R) (2011)   

Orbital fluctuation mediated superconductivity and structure transition in iron-based superconductors

The main features in Fe-based superconductors are summarized as (i) orthorhombic transition accompanied by remarkable softening of the shear modulus $C_{66}$, (ii) high-$T_{\rm c}$ superconductivity close to the orthorhombic phase, and (iii) stripe-type magnetic order induced by orthorhombicity. To understand them, we analyze the multiorbital Hubbard-Holstein model with Fe-ion optical phonons. In the random-phase-approximation (RPA), a small electron-phonon coupling constant ($\lambda\sim0.2$) is enough to produce large orbital (=charge quadrupole) fluctuations. The most divergent susceptibility is the $O_{xz}$-antiferro-quadrupole (AFQ) susceptibility, which causes the $s$-wave superconductivity without sign reversal ($s_{++}$-wave state). \footnote{H. Kontani and S. Onari, Phys. Rev. Lett. {\bf 104}, 157001 (2010).} The $_{s++}$-wave state is robust against impurities, \footnote{S. Onari and H. Kontani, Phys. Rev. Lett. {\bf 103}, 177001 (2009).} consistently with experimental observations. At the same time, divergent development of $O_{x^2-y^2}$-ferro-quadrupole (FQ) susceptibility is brought by the ``two-orbiton process'' with respect to the AFQ fluctuations.   

A Monte Carlo simulation study of phase transitions in spin-orbital models for iron pnictides

The common phase diagrams of superconducting iron pnictides show interesting material specificities in the structural and magnetic phase transitions. In some cases the two transitions are separate and second order, while in others they appear to happen concomitantly as a single first order transition. We explore these differences using Monte Carlo simulations of a two-dimensional Hamiltonian with coupled Heisenberg-spin and Ising-orbital degrees of freedom. In this spin-orbital model, the finite-temperature orbital-ordering transition results in a tetragonal-to-orthorhombic symmetry reduction and is associated with the structural transition in the iron-pnictide materials. With a zero or very small spin space anisotropy, the magnetic transition separates from the orbital one in temperature, and the orbital transition is found to be in the Ising universality class. With increasing anisotropy, the two transitions rapidly merge together and tend to become weakly first order. We also study the case of a single-ion anisotropy and propose that the preferred spin-orientation along the antiferromagnetic direction in these materials is driven by orbital order.   

Local Quantum Criticality of an Iron-Pnictide Tetrahedron

Motivated by the close correlation between transition temperature ($T_c$) and the tetrahedral bond angle of the As-Fe-As layer observed in the iron-based superconductors, we study the interplay between spin and orbital physics of an isolated iron-arsenide tetrahedron embedded in a metallic environment. Whereas the spin Kondo effect is suppressed to low temperatures by Hund's coupling, the orbital degrees of freedom are expected to quantum mechanically quench at high temperatures, giving rise to an overscreened, non-Fermi liquid ground-state. Translated into a dense environment, this critical state may play an important role in the superconductivity of these materials.   

Hint of a condensate in K$_{\mathbf{0.8}}$Fe$_{\mathbf{2-y}}$Se$_{\mathbf{2}}$

The optical properties of the iron-chalcogenide superconductor K$_{0.8}$Fe$_{2-y}$Se$_2$ with a critical temperature $T_c = 31$~K have been measured over a wide frequency range in the {\em a-b} planes above and below $T_c$. The conductivity is incoherent at room temperature, but becomes coherent (Drude-like) with $\omega_{p,D}\simeq 430 \pm 20$~cm$^{-1}$ and $1/\tau_D \simeq 70\pm 5$~cm$^{-1}$ at $T\simeq T_c$; however, $\omega_{p,D}$ is an order of magnitude smaller than what is observed in other iron-based superconductors. The highly anisotropic nature of these materials suggests that the transport is best described by a sheet resistance $R_\Box = \rho_{dc}/d \simeq 64$~k$\Omega$ (per sheet), well above the threshold for the superconductor-insulator transition at $R_\Box = h/4e^2 \simeq 6.9$~k$\Omega$. Below $T_c$, $\omega_{p,S} \simeq 220\pm 20$~cm$^{-1}$ resulting in a superfluid density $\rho_{s0} \equiv \omega_{p,S}^2 \simeq 48 \times 10^3$~cm$^{-2}$, placing this material on the scaling line $\rho_{s0}/8 \simeq 4.4\, \sigma_{dc}\, T_c$ observed for the cuprates, but in a region associated with Josephson coupling, suggesting this material is inhomogeneous and constitutes a Josephson phase.\footnote{C. C. Homes {\em et al.}, arXiv:1110.5529}   

Optical spectroscopy of K$_{x}$Fe$_{2-y}$Se$_{2-z}$S$_{z}$ superconductors

We measured the temperature dependent optical reflectivity $R(\omega$) and extracted the complex optical conductivity $\sigma(\omega)$ of the K$_{x}$Fe$_{2-y}$Se$_{2-z}$S$_{z}$ superconductors. At room temperature, both $R(\omega$) and $\sigma_{1}(\omega)$ have semiconducting behavior. Upon cooling, at temperatures depending on the S-concentration, the low frequency reflectivity increases in absolute value and shows a sharp upturn, consistent with metallic behavior. The phonon spectrum of $\sigma_{1}(\omega)$, which is very different from similar Fe-based superconductors and also doping dependent will be explained in terms of the changes in occupancy of the Fe-sites with doping. An anomalous feature in optical reflectivity is observed in the superconducting state and its possible origin and association with the condensation of free carriers will be discussed.   

Electronic Structure of K$_{0.8}$Fe$_2$Se$_2$ High Temperature Superconductor

Since the synthesis of the first ones in 2008, iron-based high temperature superconductors have been the subject of many studies. This great interest is partly due to their higher, upper magnetic field, smaller Fermi surface around the $\Gamma $ point, and a larger coherence length. This work is focused on A$_{x}$Fe$_{2}$Se$_{2}$ structural superconductor (FeSe, 11 hierarchy; A=K, Cs) as recently observed. ARPES data show novel, electronic structure and a hole-free Fermi surface which is different from previously observed Fermi surface images. \textit{Ab initio} density functional theory GW method was used to simulate the electronic structure of the novel superconductor A$_{x}$Fe$_{2}$Se$_{2}$. We compare this electronic structure with those of other Fe-based superconductors. Possible explanations for the hole-free Fermi surface were discussed.   

ARPES studies of the AFe2Se2 (A=K, Rb, Cs) iron-based superconductors

The AFe2Se2 (A=K, Rb, Cs) family is one of the newest iron-based superconductors that has attracted considerable attention in the pnictide community due to its many differences with the other iron pnictide compounds, including a very large magnetic moment indicative of strong electron correlation, insulating behavior in non-superconducting compounds, and even in superconducting compounds resistivity shows a bad metallic behavior that crosses over into insulating behavior at higher temperatures. Despite such marked differences with the other pnictides, Tc in AFe2Se2 can be as high as 30K. Such interesting properties suggest that the AFe2Se2 superconductors may be close to a Mott insulating state, and many theoretical efforts have followed in this regard. Here we present detailed angle-resolved photoemission studies of AFe2Se2 to address the issue of whether these materials are indeed close to a Mott insulating state.   

One-Fe versus Two-Fe Brillouin Zone of Fe-Based Superconductors: Creation of the Electron Pockets via Translational Symmetry Breaking

We investigate the physical effects of translational symmetry breaking in Fe-based high-temperature superconductors due to alternating anion positions [1]. In the representative parent compounds, including the newly discovered Fe-vacancy-ordered $\mathrm{K_{0.8}Fe_{1.6}Se_2}$, an unusual change of orbital character is found across the one-Fe Brillouin zone upon unfolding the first-principles band structure and Fermi surfaces [2], suggesting that covering a larger one-Fe Brillouin zone is necessary in experiments. Most significantly, the electron pockets (critical to the magnetism and superconductivity) are found only created with the broken symmetry, advocating strongly its full inclusion in future studies, particularly on the debated nodal structures of the superconducting order parameter. [1] C.-H. Lin et al, arXiv:1107.1485 (2011). [2] Wei Ku et al, Phys. Rev. Lett. {\bf 104}, 216401 (2010).   

Metal-to-Insulator Transition in Multi-Orbital Models for A$_x$Fe$_y$Se$_2$

The degree of electron correlations remains a central issue in the iron-based superconductors. Compared to other compounds, the newly discovered A$_x$Fe$_y$Se$_2$ family is unique in some aspects: the Fermi surface consists of only electron pockets, while T$_c$ is as high as 30 K ; the superconducting compound is close to an antiferromagnetically insulating phase with a large magnetic moment. These features suggest that the A$_x$Fe$_y$Se$_2$ system contains stronger electron correlations than pnictides.To investigate the correlation effects in A$_x$Fe$_y$Se$_2$, we study the metal-to-insulator transition in multi-orbital models for this system using slave-spin mean-field method. We show that when electron correlations are tuned, the system undergoes a metal-to-Mott-insulator transition at commensurate electron filling. We also find that the Mott insulator is close to an orbital-selective Mott phase in the phase diagram.