Session A11: Pairing Interaction and Gap Symmetry in Fe-based Superconductors

Glide-Plane Symmetry and Superconducting Gap Structure of Iron-Based Superconductors

This talk will provide a review [1] of the implications of the glide plane symmetry of a single Fe-pnictide/chalcogen plane on the structure of the superconducting gap. It will be shown that “$\eta$-pairing” with non-zero total momentum occurs inevitably in this system, but that its contribution to the superconducting condensate has the usual even parity symmetry and time reversal symmetry is preserved. I will demonstrate that for a single plane the gap function, which appears in physical quantities, is identical to that found in 1 Fe per unit cell pseudo-crystal momentum calculations and discuss the effects of the symmetry breaking out-of-plane hopping integrals in three dimensions. [1] Y. Wang, T. Berlijn, P. J. Hirschfeld, D. J. Scalapino, T. A. Maier, Phys. Rev. Lett. 114, 107002 (2015).   

Robust measurement of superconducting gap sign changes via quasiparticle interference: an application to 111 compounds

While quasiparticle interference (QPI) measurements based on scanning tunneling spectroscopy are often proposed as definitive tests of gap structure, the analysis typically relies on details of the model employed. Here using the simplified two-band model system we propose, that the temperature dependence of momentum-integrated QPI data can be used to identify gap sign changes in a qualitative way, and present an illustration for $s_{\pm}$ and $s_{++}$ states in a system with typical Fe-pnictide Fermi surface. Using ARPES derived band structures within 10 orbital model Hamiltonian we analyze the QPI spectra in LiFeAs and Co-doped NaFeAs compounds and show that the sign-changing gap can be clearly identified using non-magnetic impurity scattering.   

Features of Superconducting Gaps Revealed by STM/STS in Iron Based Superconductors With and Without Hole Pockets

The pairing mechanism and gap structure in iron based superconductors (IBS) remains unresolved. We have conducted extensive STM/STS study on the Na(Fe$_{\mathrm{1-x}}$T$_{\mathrm{x}})$As (T$=$Co, Cu, Mn)[1], Ba$_{\mathrm{1-x}}$K$_{\mathrm{x}}$Fe$_{\mathrm{2}}$As$_{\mathrm{2}}$[2], KFe$_{\mathrm{2}}$As$_{\mathrm{2}}$[3], and Li$_{\mathrm{1-x}}$Fe$_{\mathrm{x}}$OHFeSe[4] single crystals. We found the clear evidence of the in-gap quasi-particle states induced by the non-magnetic Cu impurities in Na(Fe$_{\mathrm{0.97-}}_{x}$Co$_{\mathrm{0.03}}$Cu$_{x})$As, giving strong evidence of the S$^{\mathrm{\pm }}$ pairing. Furthermore, we show the presence of the bosonic mode with the energy identical to that of the neutron resonance and a simple linear relation $\Omega $/k$_{\mathrm{B}}$T$_{\mathrm{c\thinspace }}\approx $ 4.3, being explained a consequence of the S\textpm pairing. The STS spectrum in Li$_{\mathrm{1-}}_{x}$Fe$_{x}$OHFeSe clearly indicates the presence of double superconducting gaps with $\Delta_{\mathrm{1}} \quad \approx $ 14.3 meV and $\Delta_{\mathrm{2}} \quad \approx $ 8.6 meV. Further analysis based on QPI allows us to assign the larger (smaller) gap to the outer (inner) hybridized electron pockets[4]. The huge value 2$\Delta _{\mathrm{1}}$/$k_{\mathrm{B}}T_{\mathrm{c\thinspace }}=$ 8.7 discovered here undoubtedly proves the strong coupling mechanism. [1] H. Yang et al., Nature Communications \textbf{4}, 2947 (2013). [2] Z. Y. Wang, et al., Nature Physics \textbf{9}, 42(2013). [3] D. L. Fang, X. Shi et al., arXiv: Condmat.1412.0945. Phys. Rev. B 2015. [4] Z. Y. Du et al., arXiv: Condmat. 1506.04645.   

Specific Heat in High Magnetic Fields of BaFe$_{\mathrm{2}}$(As$_{\mathrm{1-x}}$P$_{\mathrm{x}})_{\mathrm{2}}$

We measure the magnetic field dependence of the specific heat in BaFe$_{\mathrm{2}}$(As$_{\mathrm{1-x}}$P$_{\mathrm{x}})_{\mathrm{2}}$ with x ranging from x$=$0.31 to x$=$0.6 in fields up to 34.5T. We report three important observations: $\surd $H behavior indicating a nodal superconducting gap with a linear energy dispersion, saturation of the heat capacity at the magnetic field that corresponds to the resistive onset [1], and a calculated quasiparticle mass using the increase in the electronic specific heat coefficient when entering the normal state, $\Delta \gamma $ $= \quad \gamma $(34.5T) -- $\gamma $(0T), as a measure of the normal state specific heat. [1] James G. Analytis, H-H. Kuo, Ross D. McDonald, Mark Wartenbe, P. M. C. Rourke, N. E. Hussey {\&} I. R. Fisher. \textit{Nature Phys}. 10, 194--197 (2014)   

Direct evidence for a pressure induced nodal superconducting gap in the Ba$_{0.65}$Rb$_{0.35}$Fe$_{2}$As$_{2}$ superconductor

In contrast to other unconventional superconductors, in the Fe-based superconductors (Fe-HTSs) both $d$-wave and extended $s$-wave pairing symmetries are close in energy. Probing the proximity between these different superconducting (SC) states and identifying experimental parameters that can tune them is of central interest. We report high-pressure muon spin rotation experiments on the temperature-dependent magnetic penetration depth in the optimally doped nodeless $s$-wave Fe-HTS Ba$_{0.65}$Rb$_{0.35}$Fe$_{2}$As$_{2}$. Upon pressure, a strong decrease of the penetration depth is observed, while the SC transition temperature remains nearly constant. More importantly, the low-temperature behavior of the inverse squared magnetic penetration depth, which is a direct measure of the superfluid density, changes qualitatively from an exponential saturation at zero pressure to a linear-in-$T$ behavior at higher pressures, indicating that hydrostatic pressure promotes the appearance of nodes in the SC gap.   

Thermoelectric signatures of time-reversal symmetry breaking states in multiband superconductors

We demonstrate that superconductors which break time-reversal symmetry can exhibit thermoelectric properties, which are entirely different from the Ginzburg mechanism. As an example, we show that in the s$+$is superconducting state there is a reversible contribution to thermally induced supercurrent, whose direction is not invariant under time-reversal operation. Moreover in contrast to Ginzburg mechanism it has a singular behavior near the time-reversal symmetry breaking phase transition. A local hot spot in such superconductors is surrounded by a multipolar magnetic field, sensitive to the presence of domain walls and crystalline anisotropy of superconducting states. A non-stationary heating process produces an electric field and a charge imbalance in different bands. These effect can be measured and used to distinguish s$+$is and s$+$id superconducting states in the candidate materials such as Ba$_{\mathrm{1-x}}$K$_{\mathrm{x}}$Fe$_{\mathrm{2}}$As$_{\mathrm{2}}$.   

Raman resonance due to magnetic fluctuations in iron-based superconductors

We perform theoretical analysis of polarization-sensitive Raman spectroscopy on NaFe$_{1-x}$Co$_x$As and Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$, focusing on two features seen in the $B_{1g}$ symmetry channel (in one Fe unit cell notation): the strong temperature dependence of the static, uniform Raman response in the normal state and the existence of a collective mode in the superconducting state. We show that both features can be explained by the coupling of fermions to pairs of magnetic fluctuations via the Aslamazov-Larkin process. We argue that the singular temperature dependence in the normal state comes from the Aslamazov-Larkin vertex, while the resonance is due to the interaction between two propagating spin fluctuations in an $s^{+-}$ superconductor.   

Electron pairing in the presence of incipient bands in iron-based superconductors

Recent experiments on certain Fe-based superconductors (SC) have hinted at a role for paired electrons in “incipient” bands that are close to, but do not cross the Fermi level. Within a simple multiband weak-coupling BCS approximation, we categorize the problem into two cases: case(I) where SC arises from the incipient band pairing alone, and case(II) where it is induced on an incipient band by pairing due to Fermi-surface based interactions. Negative conclusions regarding the importance of incipient bands are largely based on case(I). However, we show explicitly that models under case(II) can explain the mild suppression of Tc, as well as robust large gaps on an incipient band. We also model the interplay between phonon and spin fluctuation (SF) driven SC and describe the bootstrap of electron-phonon SC by SF coupling the incipient and the regular bands. We argue that pairing on incipient bands may be important in several Fe-based materials, including LiFeAs, FeSe intercalates and FeSe monolayers on SrTiO$_3$, and indeed may contribute to high Tc in some cases. In addition, we address the question whether this conclusion holds if the SF interaction is derived explicitly in the incipient band scenario and retardation effects are included on the level of the Eliashberg equations.   

Smearing of the Lifshitz transition by superconductivity

We consider a multiband metal with deep primary bands and a shallow secondary one [1]. In the normal state the system undergoes Lifshitz transition when the bottom of the shallow band crosses the Fermi level. In the superconducting state Cooper pairing in the shallow band is induced by the deep ones. As a result, the density of electrons in the shallow band remains finite even when the bottom of the band is above the Fermi level. We study the density of states in the system and find qualitatively different behaviors on the two sides of the Lifshitz transition. On one side of the transition the density of states diverges at the energy equal to the induced gap, whereas on the other side it vanishes. We argue that this physical picture describes the recently measured gap structure in shallow bands of iron pnictides and selenides.\newline [1] A. E. Koshelev and K. A. Matveev Phys. Rev. B \textbf{90}, 140505(R) (2014)   

Microscopic theory of superconductivity near a Lifshitz transition

Observation of robust superconductivity in some of the iron based superconductors in the vicinity of a Lifshitz point has attracted many theoretical and experimental studies. The majority of these studies have been phenomenological. Here we discuss a microscopic treatment of the pairing mechanism for a bilayer Hubbard model, which goes through a Lifshitz transition. We study pairing driven by spin-fluctuations by solving the strong coupling Eliashberg equations and make a systematic comparison of the results with non-perturbative dynamical cluster quantum Monte Carlo calculations. Our findings are quite general and we will discuss their application to some of the iron based superconductors.   

Topological Phase Transitions in Line-nodal Superconductors

Fathoming interplay between symmetry and topology of many-electron wave-functions deepens our understanding in quantum nature of many particle systems. Topology often protects zero-energy excitation, and in a certain class, symmetry is intrinsically tied to the topological protection. Namely, unless symmetry is broken, topological nature is intact. We study one specific case of such class, symmetry-protected line-nodal superconductors in three spatial dimensions (3d). Mismatch between phase spaces of order parameter fluctuation and line-nodal fermion excitation induces an exotic universality class in a drastic contrast to one of the conventional $\phi^4$ theory in 3d. {\it Hyper-scaling violation} and {\it relativistic dynamic scaling} with unusually large quantum critical region are main characteristics, and their implication in experiments is discussed. For example, continuous phase transition out of line-nodal superconductors has a {\it linear} phase boundary in a temperature-tuning parameter phase-diagram.   

Orbital-selective pairing: a $\tau $3 B1g pairing candidate state for the alkaline iron selenides.

The iron-based unconventional superconductors are inherently multi-orbital systems and show remarkable variation in the Fermi-surfaces and pairing symmetries. In the alkaline iron selenides cases, ARPES experiments indicate fully gapped superconducting states, which suggests s-wave pairing, while neutron-scattering studies show resonances in the spin-spectrum with wave vectors across the electron Fermi pockets, suggesting d-wave pairing. We propose a novel superconducting state composed of a direct product of an s-wave form factor and a rotational symmetry-breaking orbital matrix in the $d_{xz/yz\thinspace }$sectors [1]. It belongs to the $B_{1g}$ representation of the D$_{\mathrm{4h}}$ point group, allowing for the overall change in sign between the pairing field at the electron pockets close to the 1-Fe BZ edge. While it supports a spin resonance, it also produces a fully gapped quasiparticle spectrum, making it a candidate pairing state for the alkaline iron selenide compounds. Our results also show how such a state can become energetically competitive in the regime of quasi-degeneracy between the s and d-wave pairing states. In a broader context, this pairing provides an alternative to the $s+$\textit{id }to reconstruct the degenerate pairing states, while preserving the time-reversal symmetry. We discuss possible analogs in other multi-band strong-coupling superconductors such as the heavy fermions. [1] ''Emergent superconducting state from quasi-degenerate s$-$ and d$-$wave pairing channels in iron-based superconductors,'' E. M. Nica, R. Yu, and Q. Si, arXiv:1505.04170v1 (2015).   

Searching for the Genes of Unconventional High Temperature Superconductors

In the past, both curates and iron-based superconductors were discovered accidentally. Lacking of successful predictions on new high Tc materials is one of major obstacles to reach a consensus on the high Tc mechanism. In this talk, we discuss two emergent principles, which are called as the correspondence principle and the selective magnetic pairing rule, to unify the understanding of both cuprates and iron-based superconductors. These two principles provide an unified explanation why the d-wave pairing symmetry and the s-wave pairing symmetry are robust respectively in cuprates and iron-based superconductors. In the meanwhile, the above two principles explain the rareness of unconventional high Tc superconductivity, identify necessary electronic environments required for high Tc superconductivity and finally serve as direct guiding rules to search new high Tc materials. We predict that the third family of unconventional high Tc superconductors exist in the compounds which carry two dimensional hexagonal lattices formed by cation-anion trigonal bipyramidal complexes with a d_ filling configuration on the cation ions. Their superconducting states are expected to be dominated by the d+id pairing symmetry and their maximum Tc should be higher than those of iron-based superconductors. Verifying the prediction can convincingly establish the high Tc superconducting mechanism and pave a way to design new high Tc superconductors