Session Q26: Focus Session: Iron Based Superconductors -- Optics, Heat Capacity, Thermopower

Optical Investigation of the Charge Dynamics in Ba(Co$_x$Fe$_{1-x}$)$_2$As$_2$

We report on a thorough optical investigation over a broad spectral range and as a function of temperature of the charge dynamics in Ba(Co$_x$Fe$_{1-x}$)$_2$As$_2$ compounds for Co-doping ranging between 0 and 18\%. For the parent compound as well as for $x$=0.025 we observe the opening of a pseudogap, due to the spin-density-wave phase transition and inducing a reshuffling of spectral weight from low to high frequencies. For compounds with 0.051$\le x \le$ 0.11 we detect the superconducting gap, while at $x$=0.18 the material stays metallic at all temperatures. We describe the effective metallic contribution to the optical conductivity with two Drude terms, representing the coherent components, and extract the respective scattering rates. Finally through spectral weight arguments, we give clear-cut evidence for moderate electronic correlations for 0$\le x \le$0.061, which then crossover to values appropriate for a regime of weak interacting and nearly-free electron metals for $x\ge$0.11. We also investigate the optical conductivity with light polarized along the in-plane orthorhombic $a$- and $b$-axes of Ba(Co$_x$Fe$_{1-x}$)$_2$As$_2$ for $x$=0 and 2.5$\%$ under uniaxial pressure across their structural and magnetic transitions. The charge dynamics at low frequencies and temperatures on these detwinned, single domain samples reveals an enhancement of both the scattering rate and Drude weight of the charge carriers along the antiferromagnetic $a$-axis with respect to the ferromagnetic $b$-axis. Our findings also allow us to estimate the dichroism, which extends to high frequencies. These results demonstrate the electronic nature of the structural transition found in underdoped Fe-pnictides. Co-authors: A. Dusza, A. Lucarelli, F. Pfuner, J.-H. Chu, I.R. Fischer.   

In-plane and c-axis optical spectroscopy study on 122 Fe-pnictides

I present the in-plane and the c-axis optical spectroscopy investigations on 122 Fe-pnictides. For the parent compound BaFe$_2$As$_2$, the in-plane measurement revealed two different energy gaps in the SDW state, whereas for the c-axis polarized measurement only the energy gap at smaller energy scale could be clearly observed. We suggest different driving mechanisms for the formation of the two energy gaps. The large energy gap is caused by the nesting between disconnected 2D cylinder-like electron and hole Fermi surfaces. It is the main driving force for the SDW instability. The small energy gap is the one formed on the 3D Fermi surface due to the presence of reduced magnetic Brillouin zone which crosses the 3D Fermi surface. It is the consequence of the establishment of the magnetic order. For the doped superconducting 122 samples, the in-plane optical measurement revealed a formation of full superconducting energy gap, whereas the c-axis optical measurement indicated a large residual quasiparticle population down to very low temperature. Those quasiparticles contribute specifically to the c-axis transport. We suggest that there exist horizontal nodes in the superconducting gap in regions of the 3D Fermi surface that contribute dominantly to the c-axis optical conductivity. Work done with Z. G. Chen, W. Z. Hu, B. Cheng, G. Li, J. Dong, T. Dong, R. H. Yuan, P. Zheng, G. F. Chen, J. L. Luo, Z. Fang, X. Dai, C. L. Zhang and P. Dai.   

Optical signature of sub-gap absorption in the superconducting state of Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$

The optical conductivity of Ba(Fe$_{0.92}$Co$_{0.08}$)$_2$As$_2$ shows a clear signature of the superconducting gap, but a simple $s$-wave description fails in accounting for the low frequency response. This task is achieved by introducing an extra Drude peak in the superconducting state representing sub-gap absorption, other than thermally broken pairs. This extra peak and the coexisting $s$-wave response respect the total sum rule indicating a common origin for the carriers. We discuss the possible origins for this absorption as (i) quasiparticles due to pair-breaking from interband impurity scattering in a two band $s_{\pm}$ gap symmetry model, which includes (ii) the possible existence of impurity levels within an isotropic gap model; or (iii) an indication that one of the bands in is highly anisotropic. The results are published in Phys. Rev B vol 82, 100506(R) (2010).   

Femtosecond low-energy dynamics of superconducting and spin-density wave gaps in pnictides

Magnetism and superconductivity (SC) in pnictides as well as a possible link between them are subjects of intense studies. The infrared spectral regime plays a pivotal role en route to a microscopic understanding since it provides direct access to the fundamental low-energy excitations, such as spin-density waves (SDW) and SC-induced energy gaps. We investigate Ba(Fe,Co)2As2 by combining ellipsometry and ultrabroadband terahertz (THz) pump-probe experiments. Following a femtosecond near-infrared excitation, the spectral hallmark of SDW located in the 10 - 30 THz window disappears with a characteristic saturation fluence of $\Phi_{s} \approx$ 50 J/cm$^{2}$ and recovers fast ($\tau <$ 1 ps), while the SC gaps below 3 THz are fully closed at a much smaller fluence $\Phi_{s} \approx$ 3 J/cm$^{2}$ and exhibit a slower relaxation behavior ($\tau >$ 10 ps). The distinct spectral, temporal and saturation behavior provide a unique environment to monitor the interplay of the two order parameters. Furthermore we observe coherent oscillation at 5.5 THz which corresponds to an Arsenic vibration. Our results may add new aspects toward an understanding of interactions between fundamental excitations in pnictides.   

Optical properties of BaFe$_{\mathbf{1.85}}$Co$_{\mathbf{0.15}}$As$_{\mathbf 2}$

The detailed in-plane optical properties of the electron-doped iron-arsenic superconductor BaFe$_{1.85}$Co$_{0.15}$As$_2$ have been determined over a wide frequency range above and below $T_c = 25$~K. Despite being a multiband system, the normal state reveals that a single (electron) band dominates the low-frequency conductivity, which can be modeled by a single Drude component with plasma frequency $\omega_{p,D} \simeq 7840$~cm$^{-1}$ and scattering rate $1/\tau_D \simeq 126$~cm$^{-1}$, determined just above $T_c$. For $T \ll T_c$ the superconducting plasma frequency is $\omega_{p,S} \simeq 5200$~cm$^{-1}$ ($\lambda_{\it eff} \simeq 3000$~\AA ), indicating that less than half the free carriers in the normal state have collapsed into the condensate, suggesting that this material is not in the clean limit. There are two energy scales for the superconductivity, $\Delta_1(0) = 3.1\pm 0.2$~meV and $\Delta_2(0) = 7.4\pm 0.3$~meV. This corresponds to either the gapping of the electron and hole pockets, respectively, or an anisitropic {\em s}-wave gap on the electron pocket; both views are consistent with the $s^\pm$ model.\footnote{J. J. Tu {\em et al.}, Phys. Rev. B {\bf 82}, 174509 (2010).}   

Raman investigation of the magneto-structural transition in electron doped Ba(FeAs)$_2$

We report a doping dependent Raman scattering study of the magneto-structural transition in Co doped Ba(FeAs)2. Several zone centered phonons display significant anomalies at the tetragonal to orthorhombic transition. In particular, the doubly degenerate in-plane Eg phonon shows an enhanced splitting in the ortho phase. The splitting weakens considerably with doping and gives evidence for strong spin-phonon coupling in iron-pnictides. The electronic Raman continuum displays a systematic upturn at low energy around the magneto-structural transition. This quasi-elastic scattering is similar to magnetic energy fluctuations usually observed in magnetic insulators. Interestingly significant fluctuations are observed at low temperature even for x=0.065 doping, where the Neel temperature goes to zero and optimal Tc is reached. At high energy and low doping, the electronic Raman continuum displays clear signatures Fermi surface reconstruction due to the opening of the spin density wave gap at the magnetic transition.   

Effect of annealing on the gap structure of Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$: low temperature specific heat studies

We report on the effect of annealing on the temperature and field dependencies of the low temperature specific heat of the electron-doped Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ for under- (x = 0.045), optimal- (x = 0.08) and over-doped (x = 0.105 and 0.14) regimes. We observed that annealing significantly improves some superconducting characteristics in Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$. It considerably increases $T_{c}$, decreases $\gamma_{0}$ in the superconducting state and suppresses the Schottky-like contribution at very low temperatures. The improved sample quality allows for a better identification of the superconducting gap structure of these materials. We examine the effects of doping and annealing within a self-consistent framework for an extended s-wave pairing scenario. At optimal doping our data indicates the sample is fully gapped, while for both under- and over-doped samples significant low-energy excitations remain, possibly consistent with a nodal structure. The difference of sample quality offers a natural explanation for the variation in low temperature power laws observed by many techniques.   

The low-temperature specific heat of Co-doped BaFe$_{2}$As$_{2}$

We have measured the low-temperature specific heat of Ba(Fe$_{1- x}$Co$_{x}$)$_{2}$As$_{2}$ ($x$=0,0.08,0.2) single crystals. The electronic specific heat of Ba(Fe$_{0.92}$Co$_{0.08}$)$_{2} $As$_{2}$ in the superconductiong state with $T_{c}$=21 K is revealed. A $T^{2}$ term was observed at low temperatures, providing the evidence of nodes in the gap. Furthermore, the data suggest a multi-gap feature for Ba(Fe$_{0.92}$Co$_{0.08}$) $_{2}$As$_{2}$. The mixed state data will also be reported.   

The Electronic Specific Heat of Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ from 2K to 380K

Using a unique differential technique, we have measured the specific heat capacity of polycrystalline Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ with x = 0, 0.1, 0.2, 0.3, 0.5 0.9 and 1.0, between 2K and 380K and in magnetic fields (H) from 0 -- 13T. We determine the electronic specific heat coefficient $\gamma $ ($\equiv $ C$_{el}$/T) over the entire range of T, H and x and compare it with the magnetic susceptibility of the seven samples. We show that our results are consistent with single crystal studies but give further interesting information. For x $<$ 0.3, $\gamma $ is progressively reduced at low T by a SDW gap, but is only weakly doping and T-dependent above the structural/magnetic transition. For x = 0.3 the normal state $\gamma _{n}$ is constant up to 380K, but as x increases from 0.3 to 1.0, $\gamma _{n}$ becomes increasingly T-dependent, increasing by a factor two at low-T and decreasing by a factor 1.5 at 380K for x = 1. We consider possible explanations for this striking T-dependence in terms of a sharp peak in the electronic density of states, a strongly x- and T-dependent effective mass enhancement, or low energy magnetic excitations. The H-dependent measurements allow us to extract the critical fields, superfluid density and coherence length as functions of doping and temperature.   

Specific Heat to 35 T in P-doped and Co-doped BaFe$_{2}$As$_{2}$: Evidence for Nodes or Not?

We have measured the low temperature specific heat of annealed single crystal Ba(Fe$_{0.955}$Co$_{0.045})_{2}$As$_{2}$, unannealed single crystal BaFe$_{2}$(As$_{0.7}$P$_{0.3})_{2}$, and other BaFe$_{2}$As$_{2}$ derivatives in fields to 35 T. We report contrasting behavior, with the underdoped Co sample exhibiting behavior (specific heat $\gamma \quad \sim $ H$^{0.7})$ essentially up to H$_{c2}$ similar to the Volovik effect prediction ($\gamma \quad \sim $ H**0.5) for nodal behavior for fields H $<$ 0.1H$_{c2}$. In contrast, $\gamma $ up to 35 T (2/3 of H$_{c2})$ in BaFe$_{2}$(As$_{0.7}$P$_{0.3})_{2}$ exhibits linear with field dependence, consistent with fully gapped behavior but inconsistent with indications of nodal behavior from other measurements. Possible explanations, and up-to-date measurements will be presented.   

Thermoelectric power of Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$ and Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$: possible changes in Fermi surface with and without changes in electorn count

Temperature-dependent, in-plane, thermoelectric power (TEP) data are presented for Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$ ($0\le x \le 0.36$) single crystals. The previously outlined by resistivity and susceptibility $x - T$ phase diagram for this system is confirmed. The analysis of TEP evolution with Ru-doping suggests two concentrations, $ x\sim 7\%$ and $x\sim 30\%$ of Ru-doping levels, near which significant changes in the electronic structure, correlations and/or scattering occur. These results are compared with an extended set of TEP data for the electron doped Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ ($0.13\le x \le 0.42$) single crystals. An analysis of TEP data for Co-doping in the overdoped region suggests two more concentrations, $x\sim 11\%$ and $x\sim 22\%$, in addition to x$\sim 2\%$ previously reported, where Lifshitz transition might occur. These data for Co-doping were recently confirmed by ARPES measurements.   

Nernst and Seebeck coefficients of the iron-pncitide superconductor Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$

The Nernst and Seebeck coefficients of the iron-pnictide superconductor Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ were measured in single crystals for K concentrations ranging from the parent compound at x=0 to the optimally-doped superconductor at x=0.40, where Tc=38 K. Both coefficients show sharp anomalies at T$_{N}$, the onset temperature for antiferromagnetic order. This allows us to track the doping dependence of T$_{N}$ and hence to map out the T-x phase diagram of Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_ {2}$. The reconstruction of the Fermi surface by the antiferromagnetic order causes a huge enhancement of the quasiparticle Nernst signal, suggesting that carrier density and Fermi temperature are dramatically reduced in the magnetic phase. The Nernst signal due to superconducting fluctuations is small by comparison, and it remains detectable up to a temperature approximately 15{\%} above T$_{c}$, in the optimally-doped sample.   

Coherence peak and pair-breaking effects in the ac conductivity of BaFe$_{2-2x}$Co$_{2x}$As$_2$ epitaxial thin films

We report a study of high quality pnictide superconductor BaFe$_{1.84}$Co$_{0.16}$As$_2$ epitaxial thin films using time-domain THz spectroscopy. Near T$_c$ we find evidence for a coherence peak and qualitative agreement with the weak-coupling Mattis-Bardeen form of the conductivity. At low temperature, we find that the real part of the THz conductivity is not fully suppressed and $\sigma_2$ is significantly smaller than the Matthis-Bardeen expectation. The temperature dependence of the penetration depth $\lambda$ follows a power law with an unusually high exponent of 3.1. We interpret these results as consistent with impurity scattering induced pair-breaking. Taken together our results are strong support for an extended s$\pm$ symmetry order parameter.