Session D39: Focus Session: Iron Based Superconductors: Theory I

A common thread linking the heavy-fermion, cuprate and iron superconductors

Is the pairing interaction which is responsible for superconductivity in the heavy-fermion, cuprate and iron-pnictide materials similar or different? These materials come in families which contain quasi-2D layers of correlated d or f electrons. Their phase diagrams show antiferromagnetism or SDW phases in close proximity or coexisting with superconductivity. The ratio of their superconducting transition temperatures Tc to the Fermi energy or coherence scale is similar and large relative to that of the traditional electron-phonon superconductors. The resonant peak observed in inelastic neutron scattering experiments in the superconducting phase provides a signature for an unconventional gap. Single and multi-band Hubbard models have been found to describe a number of the observed properties of these systems. Here, based on the experimental phenomenology and studies of the momentum and frequency dependence of the pairing interaction for Hubbard-like models, we suggest that spin-fluctuation mediated pairing is the common thread linking this broad class of superconducting materials.   

Quasiparticle self-energy in Fe-based superconductors

Novel iron-based superconductors with $T_c$ up to 55K present several challenges to the condensed matter community, including the question of electronic pairing in a multiband system consisting of nearly compensated electron and hole pockets. One unusual feature of these systems is that the quasiparticle scattering rates on hole and electron Fermi surface pockets are quite different [1,2]. We have calculated the scattering rate on different Fermi surface sheets within the framework of generalized spin-fluctuation theory with local interactions. The self-energy was approximated via the second-order diagrams with the effective interaction in the random phase approximation. We compare our results to recent experiments on the Fe-pnictide materials. [1]. B. Muschler \textit{et al.}, arXiv:0910.0898. [2]. L. Fang \textit{et al.}, Phys. Rev. B 80, 140508 (2009).   

Functional Renormalization Group Study of Iron-based Superconductors

We report functional renormalization group(FRG) results on iron-based superconductors, in particular LaFePO and Fe(Se,Te). Following the previous study by the same authors for LaFeAsO [Phys. Rev. Lett., 102, 047005 (2009)], we use tight-binding models of five Fe d-orbitals fit to the band structure calculations, and use on-site Kanamori interactions as initial condition for the RG flow. For both cases we found that the $s_{\pm}$ pairing is the leading instability, with opposite sign of pairing order parameters between electron and hole Fermi surfaces. The result of Fe(Se,Te) is a fully gapped $s_{\pm}$ pairing. However for LaFePO the gap has accidental nodes on electron Fermi surfaces, in sharp contrast to Fe(Se,Te) and the previous result of LaFeAsO. We propose several possible reasons for this nodal $s_{\pm}$ pairing in LaFePO. Comparison to and implication for experiments will be briefly discussed.   

Sensitivity of gap anisotropy to electronic structure in spin-fluctuation pairing models of Fe-pnictide superconductors

We discuss the dependence of gap anisotropy on doping and band structure in the framework of RPA spin-fluctuation calculations, computed within the framework of a 5-orbital model. Either doping or changes in electronic interactions may induce the creation of an additional Fermi surface pocket near $\pi,\pi$ in the unfolded zone. The additional nesting provided by this pocket stabilizes a nodeless state,allowing for a concrete description of possible nodal-gapped transitions. This mechanism works, however, only provided the character of the pocket is predominantly $d_{xy}$-orbital in character, consistent with the dominant intraorbital pairing in these systems. We discuss generally the orbital dependence of the pairing vertex, and the effect of electronic structure changes on the commensurability of the magnetic resonance observed in experiment. Our results offer a possible explanation for the proliferation of experimental results regarding the superconducting gap structure in the various Fe-pnictide materials.   

A diagonal 2-orbital ladder model for the Fe based superconductors

We study a diagonal 2-orbital ladder model for the Fe based superconductors using the density matrix renormalization group method. The diagonal geometry treats the $x$ and $y$ directions symmetrically, and therefore it is particularly suitable for addressing some of the outstanding problems of the field, such as nematic order and the competition between A$_{1,g}$ and B$_{1,g} $ pairing symmetries. At half filling, we find a close competition between a ``spin-striped'' state and a non-collinear ``spin-checkerboard'' state, as well as significant nematic correlations. Upon finite hole or electron doping, the dominant pairing correlations are found to have A$_{1,g}$ ($S-$wave) symmetry.   

Spectral information in the fluctuation induced superconducting state for iron based superconductors

Magnetic fluctuations in iron based superconductors have been considered as a plausible mediating glue that is responsible for pair formation. Based on a multiorbital model, we analyze the spectral function and the spin excitation spectrum in the superconducting state induced by spin fluctuation. We show the feature in the spectral function that is related to the electron collective-mode coupling observed in ARPES measurement and the spin resonance mode observed in inelastic neutron scattering measurement. We also show how the dispersion of the spin resonance mode can distinguish between s+- and d-wave paring symmetries.   

Origin of the lattice structure sensitivity of the superconductivity in the iron pnictides

For the iron pnictide superconductors, we construct a five orbital model from first principles calculations [1], to which we apply random phase approximation to investigate spin fluctuation mediated pairing. In both 1111 and 122 materials, we show that the appearance/disappearance of the hole Fermi surface arising from the $d_{X^2-Y^2}$ orbital is sensitive to the pnictogen height measured from the iron planes, which in turn affects superconductivity [2]. In particular, the superconducting gap has a fully gapped sign reversing s-wave symmetry when the pnictogen height is high, while they tend to have nodes when the height is low. We also discuss some differences between 1111 and 122 materials.\\[4pt] [1] K. Kuroki et al., Phys. Rev. Lett. 101 (2008) 087004, erratum: Phys. Rev. Lett. 102 (2009) 109902(E).\\[0pt] [2] K. Kuroki et al., Phys. Rev. B 79 (2009) 224511.   

Simple Real-Space Picture for the Gap Functions in Iron Pnictide Superconductors

We propose a simple way to parameterize the gap function in iron pnictides. The key idea is to use orbital representation, not band representation, and to assume real-space short-range pairing. Our parameterization reproduces fairly well the structure of gap function obtained in microscopic calculation like random phase approximation (RPA). At the same time the present parameterization is simple enough to obtain an intuitive picture and to develop a phenomenological theory. We also discuss simplification of the treatment of the superconducting state. Furthermore, we calculate nuclear magnetic relaxation rate $1/T_1$ in superconducting phase using the introduced representation, and we discuss the experimentally observed variety of $1/T_1$ from the calculated results.   

Spin-density-wave and superconductivity in iron-pnictide based superconductors

We study theoretically the coexistence of the spin-density-wave (SDW) and superconductivity in electron-doped iron-pnictide superconductors based on the two orbital model and Bogoliubov- de Gennes equations. The phase diagram is mapped out and the evolution of the Fermi surface as the doping varies is presented. The local density of states has also been calculated from low to high doping. We show that the strength of the superconducting coherent peak at the positive energy gets enhanced and the one at the negative energy is suppressed by the SDW order in the underdoped region. Several features of our results are in good agreement with the experiments.   

Three-Band Superconductivity and Time-Reversal Symmetry Breaking Order Parameter

Following the discovery of iron pnictide family of materials, the multiband superconductivity has migrated to the forefront of condensed matter physics. When ``multi'' means ``more than two'', an additional wealth of possibilities emerges, going beyond the possible sign-switched state of the two-gap models. We consider a simple model in which three bands are connected via repulsive interband pairing terms. In this case there are generically three possible superconducting states. While two of them are a straightforward generalization of the two-gap order parameter, the third one has a time-reversal symmetry breaking order parameter, even for fully isotropic interactions. This novel state appears due to the frustration between different superconducting gaps when all interactions are comparable in strength. We construct the phase diagram of the model and discuss its relevance to iron pnictides.   

Impurity bound states in multiband extended s-wave superconductors: analysis of iron pnictides

We examine the effect of a single, non-magnetic impurity on the density of states in an extended $s$-wave superconductor with both electron and hole Fermi surfaces (FS). We consider $\pm s$ symmetry of the superconducting gap and extend our treatment to include deep gap minima and gap nodes on the electron FS, both suggested for the Fe-pnictides. We use the $T$-matrix approximation to compare the semi-analytical results for a two-band continuum model with the numerical analysis of the multiband tight-binding model on a lattice. We determine the criteria for the existence of in-gap resonances and find that low-energy resonances occur only for strong scattering with comparable contributions from the intraband and interband scattering components. We also map the local density of states in the vicinity of the impurity, highlighting the clear differences between the cases of deep minima and gap nodes. We show that spatial-imaging of the impurity-induced resonance state by scanning tunneling microscopy can distinguish among the various superconducting gap symmetries.   

Impurity-induced bound states in Iron Pnictides with $s_{\pm}$ pairing symmetry

Using both the Bogoliubov-de Gennes and $T$-matrix approaches, we study the in-gap bound states induced by a single impurity in FeAs superconductors, with emphasis of the signatures associated with the sign-changed s-wave pairing symmetry. For a non-magnetic impurity, we find that there are two in-gap bound states, symmetric with respect to zero energy, only in the sign-changed s-wave pairing state, not in the sign-unchanged case, while for a magnetic impurity, we find that there exist only bound state solutions carrying one of the spin polarizations around the impurity. As increasing the scattering strength, the system undergoes a quantum phase transition from a spin-unpolarized ground state to a spin-polarized one. Although the results for the magnetic impurity are qualitatively similar in both the sign-changed and sign-unchanged s-wave pairing states, the bound states in the former case are more robust and there is no $\pi$ phase shift of the SC gap near the impurity in the strong scattering regime. The model dependence of our results is also discussed.   

Statistics of subgap states in superconductors with sign-changing order parameter

There is a strong theoretical reasoning in favor of the $s_{\pm}$ superconducting state in new iron-based superconductors. The order parameter in such a state has different signs in the electron and hole Fermi pockets. In this situation scattering between different pockets by impurities has pair-breaking effect and introduces states inside the gap which strongly influence low-temperature behavior of superconducting parameters. We solve numerically the two-band Bogolyubov equations for the $s_\pm$ superconductor and explore behavior of density of states and localization properties at different scattering parameters and concentration of impurities. We found that the commonly used self-consistent T-matrix approximation is incomplete and not very accurate in describing subgap states.