Session J22: Focus Session: Fe-based Superconductors - Nodal and Nodeless Superconductivity

Evolution of symmetry and structure of the gap in Fe-based superconductors with doping and interactions

We present a detailed study of the symmetry and structure of the pairing gap in Fe-based superconductors. We treat them as quasi-2D systems, decompose the pairing interaction into $s-$wave and $d-$wave channels and into contributions from scattering between different Fermi surfaces and analyze how each scattering evolves with doping and input parameters. We verify that each interaction is well approximated by the lowest angular harmonics and use this simplification to analyze the interplay between the interaction with and without spin-fluctuation components, the origin of the attraction in the $s\pm$ and $d_{x^2-y^2}$ channels, the competition between them, the nature of angular dependence of the $s\pm$ gaps along the electron Fermi surface, the conditions under which $s\pm$ gap develops nodes, and the origin of superconductivity in heavily electron- or hole-doped systems, when only Fermi surfaces of one type are present. In particular, we find that with increased electron and hole doping, the competition from $d-$wave grows. In the case of strong hole doping, there is some ambiguity over the leading solution, but in the case of strong electron doping, $d-$wave emerges as clear winner.   

Non-Fermi liquid behavior in overdoped iron-pnictides

Electrical transport, magnetic susceptibility and heat capacity data are presented on a series of single-crystal iron-based intermetallic compounds with the ThCr$_2$Si$_2$ structure with transition metal substitution used to heavily over-dope the system. We will present observations of unusual temperature dependences in transport, susceptibility and electronic specific heat that indicate an unexpected deviation from Fermi liquid behavior that persists to milliKelvin temperatures.   

Probing the Superconducting Order Parameter of Co-doped BaFe$_2$As$_2$ by Josephson Interferometry

We probe the superconducting order parameter in Co-doped BaFe$_2$As$_2$ (Ba122) single crystals via measurements of the critical current of Josephson junctions fabricated on polished faces orthogonal to the c-axis. The modulation of the critical current as a function of magnetic flux applied along the c-axis is different for junctions fabricated on different points on a circularly polished face of the Ba122 crystal since each junction probes an effective order parameter of the crystal through an angle in k-space. These modulations map the phase anisotropy and test for the proposed s$\pm$ mode pairing symmetry. We will present preliminary results of these studies and compare to existing theoretical models.   

Nodal structure and quantum critical point beneath the superconducting dome of BaFe$_2$(As$_{1-x}$P$_x$)$_2$

Among BaFe$_2$As$_2$ based materials , the isovalent pnictogen substituted system BaFe$_2$(As$_{1-x}$P$_x$)$_2$ appears to be the most suitable system to discuss many physical properties, because BaFe$_2$(As$_{1-x}$P$_x$)$_2$ can be grown with very clean and homogeneous, as evidenced by the quantum oscillations observed over a wide doping range even in the superconducting dome giving detailed knowledge on the electronic structure. We investigate the structure of the superconducting order parameter in BaFe$_2$(As$_{0.67}$P$_{0.33}$)$_2$ ($T_c=31$\,K) with line nodes by the angle-resolved thermal conductivity measurements in magnetic field. The experimental results are most consistent with the closed nodal loops located at the flat part of the electron Fermi surface with high Fermi velocity. The doping evolution of the penetration depth indicates that nodal loop is robust against P-doping. Moreover, the magnitude of the zero temperature penetration depth exhibits a sharp peak at $x$=0.3, indicating the presence of a quantum phase transition deep inside the superconducting dome.\\[4pt] This work has been done in collaboration with T. Shibauchi, K. Hashimoto, S. Kasahara, M. Yamashita, T. Terashima, H. Ikeda (Kyoto), A. Carrington (Bristol), K. Cho, R. Prozorov, M. Tanatar (Ames), A.B. Vorontsov (Montana) and I.Vekhter (Louisiana).   

London penetration depth in single crystals SrFe$_2$(As$_{0.65}$P$_{0.35}$)$_2$

In a contrast to a fully-gapped charge-doped (Ba,K)Fe$_2$As$_2$ and Ba(Fe,T)$_2$As$_2$ [1], isoelectron - substituted BaFe$_2$(As,P)$_2$ exhibit nodal superconducting gap [2]. To explore possible universality, low-temperature variation of the London penetration depth, $\Delta \lambda (T)$, was measured in optimally - doped SrFe$_2$(As$_{0.65}$P$_{0.35}$)$_2$ with $T_c$=29~K. $\Delta \lambda (T)$ revealed notable deviations from the exponential temperature dependence, expected for a fully-gapped superconductors. Instead the data are best fit with a power-law function, $\Delta \lambda =AT^n$. The analysis of the data below $1/3 T_{c}$ over a variable fitting temperature range produced exponents $n\le2$ which suggests the presence of nodes in the superconducting gap, similar to the P - doped Ba$122$ compounds. \\[4pt] [1] R. Prozorov and V. G. Kogan, Rep. Prog. Phys. {\bf 74}, 124505 (2011). \\[0pt] [2] K. Hashimoto, {\it et. al.} Phys. Rev. B {\bf 81}, 220501(R) (2010).   

London penetration depth in heavily over-doped Ba(Fe$_{1-x}$Co$_x$)$_{2}$As$_{2}$

The low-temperature variation of London penetration depth, $\Delta\lambda(T)$, has been previously studied in heavily over-doped Ba(Fe$_{1-x}$Ni$_{x}$)$_{2}$As$_{2}$ [1] and the authors suggested the development of line nodes. Similar conclusion was made from thermal conductivity measurements in Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ [2]. However, $\Delta\lambda(T)$ in this system has only been measured for $x \leq x=0.102$ [3], which is not far enough from optimal doping. Here we report tunnel - diode resonator (TDR) measurements in heavily overdoped single crystals of Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ with Co content of $x=0.108$ ($T_{c}$=14.8~K) and $x=0.127$ ($T_{c}$=9~K. We found a robust power-law behavior of $\Delta \lambda = A T^n$ with $n=2.5$ and $n=2.11$ respectively. To test whether the nodes are symmetry imposed or accidental, samples were irradiated with heavy ions. The produced disorder, leads to a decrease in $T_c$ and of the exponent $n$. These results effects will be discussed in a context of unconventional pairing in Fe-based superconductors. \\[4pt] [1] C. Martin {\it et. al.}, Phys. Rev. B {\bf 81}, 060505 (2010).\\[0pt] [2] J.-Ph. Reid {\it et. al.}, Phys. Rev. B {\bf 82}, 064501 (2010).\\ [0pt] [3] R.T. Gordon et.al. Phys. Rev. B {\bf 82}, 054507 (2010).   

Specific Heat To H$_{c2}$: Evidence for Nodes or Deep Minima in the Superconducting Gap of Under- and Overdoped BaFe$_{2-x}$Co$_{x}$As$_{2}$

Low temperature specific heat, C, in magnetic fields up to H$_{c2}$ is reported for BaFe$_{1.91}$Co$_{0.09}$As$_{2}$ (underdoped, H$_{c2}\approx $16 T, T$_{c}$=8 K), BaFe$_{1.79}$Co$_{0.21}$As$_{2}$ (overdoped, H$_{c2}\approx $27 T, T$_{c}$=17 K), and - for comparison - BaFe$_{1.95}$Ni$_{0.05}$As$_{2}$, which should have properties similar to the underdoped Co-sample. Previous measurements of thermal conductivity (as a function of temperature and field) and penetration depth on comparable composition samples gave some disagreement as to whether there was fully gapped/nodal behavior in the under-/overdoped materials respectively. The present work shows that the measured behavior of the specific heat $\gamma $ ($\propto $ C/T as T$\to $0, i. e. a measure of the electronic density of states at the Fermi energy) as a function of field obeys $\gamma \approx $H$^{0.6\pm 0.1}$, similar to the Volovik effect for nodal superconductors, over the entire field range for both under- and overdoped Co samples as well as for the underdoped Ni sample. By comparison to theory, the possibility of two bands, one with line nodes and one fully gapped, being present in these materials is discussed.   

Nodal versus nodeless order parameters in LiFeP and LiFeAs superconductors

There is growing evidence that the superconducting gap structure is not universal in the iron-based superconductors. It is essential to determine experimentally what causes nodal and nodeless states. The 111 materials, LiFeAs and LiFeP provide a unique route to study this problem as both materials are superconducting, nonmagnetic, and importantly very clean, with long electronic mean-free paths. Here we report on high-precision measurements of magnetic penetration depth $\lambda$ in clean single crystals of LiFeAs and LiFeP superconductors, which reveal contrasting low-energy excitations of quasiparticles. In LiFeAs the low-temperature $\lambda(T)$ shows a flat dependence indicative of a fully gapped state, which is consistent with previous studies. In contrast, LiFeP exhibits a $T$-linear dependence of superfluid density $\propto \lambda^{-2}$, indicating a nodal superconducting order parameter. A systematic comparison of quasiparticle excitations in the 1111, 122, and 111 families of iron-pnictide superconductors implies that the nodal state is induced when the pnictogen height from the iron plane decreases below a threshold value of $\sim 1.33$\,\AA.   

Inter-Layer Superconducting Pairing Induced c-axis Nodal Lines in Iron-based Superconductors

A layered superconductor with a full pairing energy gap can be driven into a nodal superconducting (SC) state by inter-layer pairing when the SC state becomes more quasi-3D. We propose that this mechanism is responsible for the observed nodal behavior in a class of iron-based SCs. We show that the intra- and inter-layer pairings generally compete and the gap nodes develop on one of the hole Fermi surface pockets as they become larger in the iron-pnictides. Our results provide an explanation of the c-axis gap modulations and gap nodes observed by angle resolved photo emission spectroscopy. In addition, we predict that an anti-correlated c-axis gap modulations on the hole and electron pockets should be observable in the $s\pm$-wave pairing state.   

Thermal-transport measurement of the nodal superconductor KFe$_2$As$_2$

Hole-doped Fe-based superconductors, (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$, possess two different superconducting gap structures; a fully-gapped state near the optimally dope (x$\sim$0.5) and a nodal gap state at the hole-dope end (x = 1). To investigate the detail gap structure, we performed thermal-transport measurements of KFe$_2$As$_2$ with very high purity (RRR$\sim$ 1,600) down to 80 mK. From the temperature dependence of thermal conductivity at zero field, we find a finite residual of $\kappa / T$ in the zero-temperature limit. This residual increases by magnetic field as $\propto \sqrt{H}$ in low fields, followed by a rapid increase near $H_{c2}$. Thermal conductivity measurements of different dopes (x = 0.88, 0.93) will be reported.   

Microwave Surface Impedance Measurements of SrFe$_2$(As,P)$_2$ Single Crystals

Various pairing symmetries have been proposed concerning Fe-based superconductors both theoretically and experimentally. It was reported that LaFePO[1] and BaFe$_2$(As,P)$_2$[2] have line nodes in their superconducting gap. It is in sharp contrast to other Fe-based compounds such as LiFeAs[3] and Fe(Se,Te)[4]. To confirm whether line nodes in gap function is a common feature among P doped systems, we measured the microwave surface impedances of SrFe$_2$(As,P)$_2$ single crystals ($T_c\sim30K$). \\ Single crystals were grown by self-flux method. The surface impedances were measured using a cavity perturbation technique. The imaginary part of surface impedance, which is proportional to London penetration depth in the superconducting state, shows a power law, $\lambda(T)-\lambda(0)\propto T^n$. The power law indicates low-energy quasiparticle excitation, and an exponent slightly smaller than 2 does not exclude the possibility of the existence of line nodes. \\ $\left[ 1 \right]$ J. D. Fletcher {\it et al.}, Phys. Rev. Lett. 102 (2009) 147001.\\ $\left[ 2 \right]$ K. Hashimoto {\it et al.}, Phys. Rev. B 81 (2010) 220501(R).\\ $\left[ 3 \right]$ Y. Imai {\it et al.}, J. Phys. Soc. Jpn. 80 (2011) 013704.\\ $\left[ 4 \right]$ H. Takahashi {\it et al.}, Phys. Rev. B 84. (2011) 132503.   

Doping-induced line nodes in the superconducting gap of the iron arsenide Ba$_{1-x}$K$_x$Fe$_2$As$_2$ from thermal conductivity

The thermal conductivity $\kappa$ of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ was measured down to 50 mK in magnetic fields up to 15 T, for heat current both parallel and perpendicular to the tetragonal c axis, across a range of K concentrations from optimal doping (T$_c$=38 K) down to T$_c$=7 K, deep into the region of coexistence with antiferromagnetic order. From optimal doping down to T$_c\simeq$15 K, well into the coexistence region, there is no residual linear term in $\kappa$(T) as T$\to$0, showing that there are no nodes in the superconducting gap anywhere on the Fermi surface. For concentrations in a narrow range such that 9 K$<$T$_c<$13 K, a large residual linear term appears, signaling the onset of nodes in the superconducting gap, most likely vertical line nodes running along the c axis. For T$_c<$9 K, the gap is again nodeless. We propose that these changes in the superconducting gap structure are triggered by changes in the Fermi surface as it is reconstructed by the growing antiferromagnetic order.   

Evidence for line nodes in the energy gap of overdoped Ba(Fe$_{1-x}$Co$_{x})_{2}$As$_{2}$: A low-temperature specific heat study

We report the low-temperature specific heat (SH) study on Ba(Fe$_{1-x}$Co$_{x})_{2}$As$_{2}$ single crystals in a wide doping region under different fields. For the overdoped sample, we find the clear evidence for the presence of T$^{2}$ term in the electronic SH data, suggesting the presence of line nodes in the energy gap. This term is absent both for the underdoped and optimal doped samples. Moreover, the field induced electronic SH coefficient $\Delta \gamma $(H) increases more quickly with the field for the overdoped sample than the underdoped and optimal doped ones, showing a large anisotropy of the gap for the overdoped sample. Our results suggest that the energy gap(s) in the present system may have different structures strongly depending on the doping regions.