Session A22: Focus Session: Fe-based Superconductors - Gap Structure

Anisotropic Energy-Gaps of Iron-based Superconductivity from Intra-band Quasiparticle Interference in LiFeAs

Cooper pairing in the iron-based high-$T_C$ superconductors is thought to occur due to the projection of the antiferromagnetic interactions between neighboring iron atoms onto the complex momentum-space electronic structure. A key consequence is that distinct anisotropic energy gaps $\Delta_i(k)$ with specific relative orientations should occur on the different electronic bands $i$. However, the high-precision spectroscopy required to demonstrate anisotropy of the energy gaps, and to determine the relationship between the $\Delta_i(k)$ on different bands, has not been achieved. Here we introduce intra-band Bogoliubov quasiparticle scattering interference (QPI) to iron-based superconductor studies, focusing specifically on LiFeAs. This approach provides direct spectroscopic confirmation of multiple anisotropic energy gaps on different bands. We identify the QPI signatures of the three hole-like bands assigned by photoemission studies to be $\gamma$, $\alpha_2$ and $\alpha_1$. Then, by introducing a new QPI technique, we determine the magnitude and relative orientations of the anisotropic $\Delta_i(k)$. Intra-band Bogoliubov QPI therefore yields the spectroscopic information required to identify the mechanism of superconductivity in iron-based superconductors.   

Low temperature specific heat of the codoped iron-arsenic superconductor Ba$_{0.55}$K$_{0.45}$Fe$_{1.95}$Co$_{0.05}$As$_{2}$

Despite large experimental and theoretical efforts the structure of the superconducting gap and the origin of the pairing mechanism in iron-based superconductors in still unresolved. Measurements of the low temperature specific heat and its magnetic response inside the superconducting state give important information about the symmetry of the gap. Here, we present results of our studies of codoped Ba$_{0.55}$K$_{0.45}$Fe$_{1.95}$Co$_{0.05}$As$_{2}$ with a $T_{c}$ of 32.5 K. The high quality of the material is marked by a pronounced peak at $T_{c}$ as well as by a low residual specific heat $\gamma_{0}$ = 2.4 mJ/mol K$^{2}$. We will discuss the implications of the new specific heat results on the symmetry of the order parameter in this system.   

Gap structure of the iron-based superconductor KFe$_2$As$_2$ via thermal conductivity

The thermal conductivity of the iron-based superconductor KFe$_2$As$_2$ was measured at temperatures down to 50 mK in magnetic fields up to 15 T, as a way to probe the superconducting gap structure. A large residual linear term in the $T=0$ limit is observed in zero field, showing that the gap structure contains nodes, consistent with a previous report [J.K. Dong et al., PRL 104, 087005 (2010)]. We discuss the possible interpretations for the nature of these nodes, in light of three different theoretical proposals: accidental line nodes in an extended $s$-wave state which are either horizontal [K. Suzuki et al., arXiv:1108.0657] or vertical [S. Maiti et al., arXiv:1111.0306], or symmetry-imposed vertical line nodes in a $d$-wave state [R. Thomale et al., PRL 107, 117001 (2011)].   

Gap structure of iron-based superconductors via directional thermal conductivity

Because the structure of the superconducting gap as a function of direction reflects the pairing interaction, it can shed light on the nature of the pairing mechanism. In the iron pnictides, the experimental situation in this respect remains unclear and so far suggests the lack of a universal picture. Here I present a systematic study of the superconducting gap structure through directional thermal conductivity measurements [1] on hole-doped K-Ba122 [2,3], electron-doped Co-Ba122 [4,5], self-doped LiFeAs [6] and the chalcogenide FeTeSe. We observe a general trend for the evolution of the superconducting gap with doping. At optimal doping, the gap structure is nodeless and isotropic (3D). Away from optimal doping, nodes appear on the Fermi surface at the edges of the superconducting dome, as seen for K-Ba122 and Co-Ba122. This strongly suggests that the presence of these nodes is accidental and therefore not imposed by symmetry. It would instead depend on the competition between intra- and inter-band interactions controlled by the evolving band structure and Fermi surface, and by the onset of antiferromagnetic order.\\[4pt] Work done in collaboration with M. A. Tanatar, X. G. Luo, H. Shakeripour, R. Gordon, A. Juneau-Fecteau, N. Doiron-Leyraud, S. Ren\'e de Cotret, F. Lalibert\'e, E. Hassinger, J. Chang, N. Ni, S. L. Bud'ko, P. C. Canfield, H. Kim, R. Prozorov, B. Shen, H. Luo, Z. Wang, H.-H. Wen, K. Cho, Y. J. Song, Y. S. Kwon, and Louis Taillefer.\\[4pt] [1] H. Shakeripour et {\it al}., New Journal of Physics {\bf 11}, 055065 (2009).\\[0pt] [2] X. G. Luo et {\it al}., Physical Review B {\bf 80}, 140503 (2009).\\[0pt] [3] J.-Ph. Reid et {\it al}., arXiv:1105:2232.\\[0pt] [4] M. A. Tanatar et {\it al}., Physical Review Letters {\bf 104}, 067002 (2010).\\[0pt] [5] J.-Ph. Reid et {\it al}., Physical Review B {\bf 82}, 064501 (2010).\\[0pt] [6] M. A. Tanatar et {\it al}., Physical Review B {\bf 84}, 054507 (2011).   

Proximity fingerprint of $s_{\pm}$ superconductivity

We suggest a straightforward and unambiguous test to identify possible opposite signs of superconducting order parameter in different bands proposed for iron-based superconductors ($s_{\pm}$-state). We consider proximity effect in a weakly coupled sandwich composed of a $s_{\pm} $-superconductor and thin layer of $s$-wave superconductor. In such system the $s$-wave order parameter is coupled differently with different $s_{\pm} $-gaps and it typically aligns with one of these gaps. This forces the other $s_{\pm}$-gap to be anti-aligned with the $s$-wave gap. In such situation the aligned band induces a peak in the $s$-wave density of states (DoS), while the anti-aligned band induces a dip. Observation of such contact-induced negative feature in the $s$-wave DoS would provide a definite proof for $s_{\pm}$-superconductivity.   

Doping dependence of the specific heat of single crystal BaFe$_{2}$(As$_{1-x}$P$_{x})_{2}$

We present a systematic study of the specific heat transitions on a series of BaFe$_{2}$(As$_{1-x}$P$_{x})_{2}$ single crystals with phosphorous doping ranging from near optimum doped x = 0.3 to strongly over doped x = 0.55. Our results reveal that BaFe$_{2}$(As$_{1-x}$P$_{x})_{2}$ follows the scaling \textit{$\Delta $C/T}$_{c }\sim \quad T_{c}^{2}$ remarkably well.\footnote{S. L. Bud'ko, N. Ni, P. C. Canfield, Phys. Rev. B \textbf{79}, 220516 (2009).} The clean-limit nature of this material imposes new restraints on theories aimed at explaining the scaling. We find that the Ginzburg-Landau parameter decreases significantly with doping whereas the superconducting anisotropy is $\Gamma \sim $2.6, independent of doping.   

Gap Symmetry in KFe$_2$As$_2$

We revisit the issue of the gap symmetry in K$Fe_2$As$_2$, which is an Fe-pnictide superconductor with only hole pockets. Previous theoretical studies mostly argued for a $d-$wave gap in K$Fe_2$As$_2$ since transport and thermodynamic measurements point to the presence of the gap nodes. However, a $d-$wave gap is inconsistent with recent laser-based angle-resolved photoemission measurements. We propose the scenario for a nodal $s-$wave superconductivity induced by a non-magnetic intra-band and inter-band interactions between fermions near the two hole pockets at $\Gamma$ point. The superconducting gap that we find changes sign between the two hole pockets at $\Gamma$ point and has $\cos {4\theta}$ angular dependence and can have accidental nodes on one or several hole pockets. We argue that strong angle dependence is the consequence of near-degeneracy between inter-pocket and intra-pocket interaction on the hole pockets. We also provide a connection between the the relative phase of 4$\theta$ oscillations and the shapes of the Fermi surface and discuss the implications in the light of photoemission and tunneling experiments.   

Disorder induced transition between $s_{\pm}$ and $s_{++}$ states Fe-based superconductors

The symmetry and structure of the superconducting gap in recently discovered Fe-based materials is one of the main challenges in this exciting new field (see, e.g. P.J. Hirschfeld, M.M. Korshunov, and I.I. Mazin, Rep. Progr. Phys. 2011). We have reexamined the problem of disorder in 2-band superconductors, and shown within the framework of the $T$-matrix approximation that the suppression of $T_c$ can be described by a single parameter depending on the intra- and interband impurity scattering rates. $T_c$ is shown to be more robust against nonmagnetic impurities than would be predicted in the trivial extension of Abrikosov-Gor'kov theory. We find disorder-induced transition from the $s_{\pm}$ state to a gapless and then to a fully gapped $s_{++}$ state, controlled by the sign of the average coupling constant.   

Doping - dependent anisotropic superconducting gap in Na$_{1-\delta}$FeAs and NaFe$_{1-x}$Co$_x$As pnictides

London penetration depth, $\lambda$ (T), was measured in single crystals of self electron-doped Na$_{1-\delta}$FeAs and chemically electron-doped NaFe$_{1-x}$Co$_{x}$As superconductors. Doping level $\delta$ in self-doped ones was controlled by the deintercalation of Na$^+$ ions, stimulated by ultrasonic treatment. Use of the two doping techniques allowed us to cover the whole doping phase diagram from underdoped parent NaFeAs to heavily Co-overdoped compositions, with the optimal doping, $T_c \sim$ 25 K, achieved for $x = $ 0.025. Use of two protocols also allowed us to monitor the effect of disorder, introduced by chemical substitution in Fe sublattice. The low-temperature variation of $\lambda$ (T), measured as a function of doping, was analyzed using a power-law fit, $\Delta \lambda$ = A T$^n$. The exponent, $n$, changes from $n \sim$ 1.85 at the optimal doping to much lower values in the underdoped, $n \sim$ 1.1, and heavily overdoped, $n \sim$ 1.3, samples. This doping-evolution of $\lambda$ (T) cannot be explained by isotropic gap with scattering and suggests that while the superconducting gaps are isotropic at the optimal doping, at least one of them develops strong anisotropy at the dome edges. This scenario appears to be common for many other Fe-based superconductors.   

Proximity effect of iron-based superconductor in conventional $s$-wave superconducting thin films

The proximity effect has been proposed as a mechanism to unambiguously identify the possible $s_{\pm}$-state in iron-based superconductors.\footnote{A. E. Koshelev, V. Stanev, Europhysics Letters, Vol. 96, 27014 (2011)} With a thin $s$-wave superconductor atop a $s_{\pm}$-superconductor it is suggested that the $s$-wave order parameter will couple to the $s_{\pm}$-gaps differently, inducing a correction to the $s$-wave density of states that can be probed using electron tunneling spectroscopy. In this talk, we will present recent results of the superconducting proximity effect in s-wave MoGe thin films sputtered on top of bulk superconducting Ba$_{0.6}$K$_{0.4}$Fe$_{2}$As$_{2}$ (T$_{c}$=35K) pnictide. Electron tunneling spectroscopy measurements were performed for several MoGe film thicknesses using a homemade point contact setup. Finally, results will also be presented for similar measurements using two conventional $s$-wave superconductors.   

Volovik effect in the s$\pm$ state of Ba$_{0.67}$K$_{0.33}$Fe$_{2}$As$_{2}$ from high field NMR

he spatially averaged density of states of an unconventional $d$-wave superconductor is magnetic field dependent, proportional to $H^{1/2}$, owing to the Doppler shift of quasiparticle excitations in a background of vortex supercurrents.~[1, 2] This phenomenon, called the Volovik effect, is absent in an $s$-wave state; however, it has been predicted~[3] to exist for a sign changing $s\pm$ state with a characteristic field dependence, proportional to $H$. We have observed this behavior in the $^{75}$As NMR spin-lattice relaxation rate of a single crystal of Ba$_{0.67}$K$_{0.33}$Fe$_{2}$As$_{2}$ studied over a wide range of fields up to 28 T. Our spatially resolved measurements show that Doppler contributions to the rate increase toward the vortex core, consistent with the superconducting state having unconventional $s\pm$ symmetry.\\ {[1]} G. E. Volovik, J. Phys. C. {\bf 21}, L221 (1988)\\ {[2]} G. E. Volovik, JETP Lett. {\bf 58}, L221 (1988)\\ {[3]} Y. Bang, Phys. Rev. Lett. {\bf 104}, 217001 (2010)   

Origin of the variety of superconducting gap structure in iron-based superconductors: competition between orbital and spin fluctuations

To understand the pairing mechanism in iron-based superconductors, we study the three-dimensional gap structure based on the orbital fluctuation theory. We focus on the fully-gapped state in (i) heavily electron-doped KFe$_2$Se$_2$ [1], nodal gap structure in (ii) isovalent-doped BaFe$_2$(As,P)$_2$, and strongly band-dependent gap structure in (iii) hole-doped (Ba,K)Fe$_2$As$_2$. Based on the three-dimensional ten orbital model for (i), we obtain orbital-fluctuation-mediated fully-gapped $s_{++}$ wave state without sign reversal. For (ii), we reproduce the loop-shaped nodal structure on the electron-Fermi surface, due to the competition between orbital and spin fluctuations. For (iii), we obtain a drastic change in the gap structure by hole-doping, reflecting the variation of orbital fluctuations due to the topological change of electron-pockets. These results indicate the significant role of orbital fluctuations in iron-based superconductors. [1] Saito et al., PRB 83, 140512(R) (2011)   

Microscopic Mechanism for a Pairing State with Time-Reversal Symmetry Breaking in Iron-Based Superconductors

The multipocket Fermi surfaces of iron-based superconductors promote pairing states with both s$\pm$ -wave and dx2-y2 -wave symmetry. We argue that the competition between these two order parameters could lead to a time-reversal-symmetry breaking state with s + id-pairing symmetry in the iron-based superconductors, and propose serveral scenarios in which this phase may be found. To understand the emergence of such a pairing state on a more rigorous footing, we start from a microscopic 5-orbital description representative for the pnictides. Using a combined approach of functional renormalization group and mean-field analysis, we identify the microscopic parameters of the s + id-pairing state. There, we find the most promising region for s + id-pairing in the electron doped regime with an enhanced pnictogen height.\\[4pt] [1] arXiv:1106.5964v1