Intrinsic charge dynamics in high-Tc AFeAs(O,F) superconductors
A. Charnukha, D. Pröpper, N. D. Zhigadlo, M. Naito, M. Schmidt, Z. Wang, J. Deisenhofer, A. Loidl, B. Keimer, A. V. Boris, D. N. Basov
IIntrinsic charge dynamics in high- T c A FeAs(O,F) superconductors
A. Charnukha,
1, 2, 3, ∗ D. Pr¨opper, N. D. Zhigadlo,
4, 5
M. Naito,
6, 7
M. Schmidt, Z. Wang, J. Deisenhofer, A. Loidl, B. Keimer, A. V. Boris, and D. N. Basov
1, 9 Physics Department, University of California–San Diego, La Jolla, CA 92093, USA Leibniz Institute for Solid State and Materials Research, IFW, 01069 Dresden, Germany Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany Laboratory for Solid State Physics, ETH Zurich, CH-8093 Zurich, Switzerland Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland Department of Applied Physics, Tokyo University of Agriculture and Technology, Koganei, Tokyo 184-8588, Japan TRIP, Japan Science and Technology Agency (JST), Chiyoda, Tokyo 102-0075, Japan Experimental Physics V, Center for Electronic Correlations and Magnetism,Institute of Physics, University of Augsburg, D-86159 Augsburg, Germany Department of Physics, Columbia University, New York, New York 10027, USA
We report the first determination of the in-plane complex optical conductivity of 1111 high- T c superconduct-ing iron oxypnictide single crystals PrFeAsO . F . and thin films SmFeAsO − x F x by means of bulk-sensitive conventional and micro-focused infrared spectroscopy, ellipsometry, and time-domain THz transmission spec-troscopy. A strong itinerant contribution is found to exhibit a dramatic difference in coherence between thecrystal and the film. Using extensive temperature-dependent measurements of THz transmission we identify apreviously undetected 2.5-meV collective mode in the optical conductivity of SmFeAs(O,F), which is stronglysuppressed at T c and experiences an anomalous T -linear softening and narrowing below T ∗ ≈
110 K (cid:29) T c . Thesuppression of the infrared absorption in the superconducting state reveals a large optical superconducting gapwith a similar gap ratio 2 ∆ / k B T c ≈ PACS numbers: 71.20.Be,74.25.Gz,74.25.Jb,74.25.nd,74.70.Xa,78.30.-j,78.40.-q
Almost a decade of intensive research into the phenomenol-ogy of high-transition-temperature (high- T c ) iron-based su-perconductors [1] has revealed that the T c in the vast majorityof these compounds is limited to below about 40 K (Ref. 2).Two notable exceptions to this rule are the oxypnictides ofthe 1111-type A FeAs(O,F) family ( A stands for a rare-earthmetal) with T c ’s up to about 55 K (Ref. 3) and the mono-layer FeSe grown on SrTiO [4–7] with a T c ≈
65 K. It isnow clear, that in the latter case the abnormally high T c isafforded not only by the electronic structure and interactionsinherent in the iron pnictides and chalcogenides [8–12] butalso by additional, extrinsic, interfacial interactions of itiner-ant carriers in FeSe with the SrTiO substrate [13–16]. Inthe absence of the latter, the maximum T c attainable in mono-layer FeSe was found to only reach the aforementioned limitof ∼
40 K [6, 14, 17].These experimental observations emphasize the uniquenessof the superconducting state in the A FeAs(O,F) materials asthey reach the 55-K mark unassisted by extrinsic interactionsand hold the key to our understanding of the mechanism ofhigh- T c superconductivity and further enhancing the super-conducting transition temperatures in iron-based compounds.Unfortunately, high-quality single crystals of these materi-als can only be obtained by a laborious high-pressure growthtechnique [18], which produces microscopic samples. Smalllinear dimensions and mass effectively bar a large number ofbulk-sensitive experimental techniques from contributing toour knowledge base of iron-oxypnictide phenomenology. Af-ter several pioneering optical works on polycrystalline 1111-type samples at the dawn of the iron-pnictide research [19–21], few further attempts have been made at determining the intrinsic optical itinerant response of iron oxypnictides withinthe superconducting FeAs-layers and its modification in thesuperconducting state [22, 23]. Another major complicationis the polar character of the cleaved crystal planes, which leadsto excess charge on the sample surface and makes the interpre-tation of angle-resolved photoemission spectroscopy as wellas scanning-tunneling spectroscopy measurements far fromtrivial [24–27]. Currently no consensus exists regarding thebulk electronic structure of iron oxypnictides. It is, therefore,imperative to investigate the charge dynamics of these mate-rials and its modification in the superconducting state using S m F e A s ( O , F ) t h i n f i l m T c = 5 5 KT e m p e r a t u r e ( K ) Resistivity (m W cm) b ) C a F s u b s t r a t eS m F e A s O 1 7 0 n mS m F P r F e A s O F m i c r o c r y s t a l a ) F CZ F C
H = 1 0 O eT e m p e r a t u r e ( K )
Magnetic susceptibility c T o n s e tc = 2 3 . 8 Km = 1 6 0 m g2 0 0 m m FIG. 1: (a) Temperature dependence of the ac magnetic suscepti-bility of PrFeAsO . F . cooled in a zero (blue line) and a 10 Oe(black line) magnetic field, subsequently measured in a 10 Oe fieldin both cases. The deviation from perfect diamagnetism χ = − a r X i v : . [ c ond - m a t . s up r- c on ] A p r g = 5 m e V a ) : P r F e A s O F m i c r o c r y s t a l E = 2 8 m e V 1 0 0 K 2 0 0 K 3 0 0 K 8 K 1 6 K 2 4 K 3 2 K 5 0 K P h o t o n e n e r g y ( m e V ) Reflectance a ) (cid:1) w t o tp l = g = 4 0 m e V 1 1 0 1 0 0 1 0 0 0051 01 5 b ) t h r o u g h d ) : S m F e A s ( O , F ) t h i n f i l m (cid:1) w t o tp l = g = g = 1 5 0 m e V 7 0 K 1 0 0 K 2 0 0 K 3 0 0 K P r , 3 0 0 K 1 0 K 2 0 K 3 0 K 4 0 K 5 0 K 6 0 KP h o t o n e n e r g y ( m e V ) s W -1cm-1) b ) ... e c ) T c c T e m p e r a t u r e ( K ) s W -1cm-1) d ) FIG. 2: (a) Temperature dependence of the infrared reflectance of PrFeAsO . F . . Vertical dashed line indicates the energy E atwhich reflectance reaches unity. (b) Temperature dependence of the optical conductivity of SmFeAs(O,F) (solid lines) compared to that ofPrFeAsO . F . (dotted line). (c) Temperature dependence of the real part of the dielectric function at various photon energies as indicated inthe panel. Vertical dashed line indicates the T c determined from the dc resistivity in Fig 1b. (d) Temperature dependence of the real part of theoptical conductivity at the same photon energies as in panel (c). Additional thermal anomaly is visible at T = T ∗ . a bulk-sensitive probe of the electronic structure and interac-tions.In this Letter, we report the results of a bulk-sensitivebroadband optical-spectroscopy study that overcomes theaforementioned materials-related challenges. We use twocomplementary approaches to shed first direct light ontothe bulk charge-carrier response of iron oxypnictides andits modification in the superconducting state. The firstapproach employs conventional and micro-focused Fourier-transform infrared reflectance spectroscopy as well as micro-focused CCD-based spectroscopic ellipsometry to investigatethe intrinsic electrodynamics of microscopic high-pressure–grown [18] single crystals of PrFeAsO . F . (see Fig. 1a)in a wide spectral range from 15 meV to 6 eV. The sec-ond approach makes use of a unique fluorine-diffusion dop-ing process by means of in situ annealing after growth ofnon-superconducting parent SmFeAsO single-crystalline thinfilms synthesized by state-of-the-art molecular beam epitaxyon a CaF substrate and capped by a SmF layer [28] (seeFig. 1b). This approach has been shown to result in high-quality optimally doped iron-oxypnictide SmFeAs(O,F) thinfilms with a maximum T c =
55 K. We have carried outextensive synchrotron– and thermal-source–based variable-angle-of-incidence spectroscopic ellipsometry as well as time-domain THz transmission spectroscopy measurements onthese films in the range from 1 meV to 6 . . F . microcrystal (Fig. 2a), indicative of a strongitinerant response. By means of a Drude-Lorentz fit [29]we extract the total plasma frequency of 1 . γ of about 5 meV) — a property of materials with lowlevels of crystalline disorder. Below T c =
24 K the infraredreflectance approaches unity below the characteristic energy E =
28 meV indicative of the opening of a nodeless super-conducting gap [30, 31]. Such a high gapping energy is re-markable for a superconductor with k B T c ≈ − x F x thin film, analogous Drude-Lorentzdecomposition of the optical conductivity (shaded areas inFig. 2b) reveals an equally strong itinerant response but signif-icantly less coherent (as can also be seen from the direct com-parison with the optical conductivity of the PrFeAsO . F . microscrystal shown as a dotted line in Fig. 2b). The quasi-particle scattering rate is found to be 150 meV at 300 K andremains unchanged down to lowest temperatures, thus exceed-ing its PrFeAsO . F . counterpart by almost two orders ofmagnitude.By virtue of the large surface area of our SmFeAsO − x F x thin film we were able to investigate its optical response deepin the infrared regime extending to sub-THz frequencies. Thisunprecedented for the 1111-type iron oxypnictides spectro-scopic access uncovered the existence of a low-energy col-lective mode, manifested as a broad peak in the optical con-ductivity centered at 2 . Ω − cm − at its maximum — an order ofmagnitude larger than the normal-state dc resistivity values ofup to 2 m Ω − cm − . It then rapidly decreases at lower photonenergies to values consistent with the dc transport. The detec-tion of this collective mode requires robust optical access toenergies below 3 meV and has not been observed previouslyin any iron pnictide or chalcogenide.In the superconducting state, we find a strong signature of acoherent superconducting condensate, manifested in the dras- S m F e A s ( O , F ) t h i n f i l m s ( m W - 1 c m - 1 ) a ) (cid:1) w ( m e V )0 1 0 0 2 0 0 3 0 051 01 52 02 5 T e m p e r a t u r e ( K )1 0 f ( e V ) T c T * 2345 b ) (cid:1) G ( m e V ) FIG. 3: (a) THz conductivity at three different temperatures reveal-ing the thermal evolution of the collective mode. Open circles — ex-perimental data, solid lines — fit using two asymmetric Lorentzianson a linear background. (b) Temperature dependence of the collectivemode oscillator strength f (black symbols and line), energy ¯ h ω (redsymbols and line), and width ¯ h Γ (blue symbols and line) extractedfrom the fit in panel (a). Dashed blue line indicates the linear tem-perature dependence of ¯ h Γ between T c (black dashed line) and T ∗ (red arrow). tic suppression of the real part of the dielectric function inthe THz spectral range (Fig. 2c). The real part of the opti-cal conductivity in Fig. 2d is likewise sensitive to the onsetof superconductivity and allows us to extract the supercon-ducting energy gap in what follows. Finally, we discover adistinct temperature scale of T ∗ =
110 K (cid:29) T c (black arrowin Fig. 2d), at which the real part of the optical conductivitydisplays an additional thermal anomaly.The low-energy collective mode shows dramatic sensitivityto both T c and T ∗ . To demonstrate it, we fit the energy depen-dence of the real part of the THz conductivity σ ( ¯ h ω ) usingtwo asymmetric Lorentzians on a linear background. The re-sults of such a fit are shown in Fig. 3a for three representa-tive temperatures. The excellent quality of the fit allows us toextract the Loretzian parameters for all investigated temper-atures with low uncertainty. The temperature dependence ofthe oscillator strength f , center energy of the mode ¯ h ω , andthe mode width ¯ h Γ is plotted in Fig. 3b and clearly revealsthe two characteristic temperatures present in this compound: T c and T ∗ . The oscillator strength f shows a dramatic sup-pression upon entering the superconducting state below 55 Kbut reveals no strong anomalies near T ∗ . The mode energy¯ h ω shows the opposite behavior, dropping at T ∗ with no dis-cernible thermal anomaly at the superconducting transitiontemperature. The mode width ¯ h Γ is sensitive to both T c and T ∗ .We hypothesize that the observed collective mode couldoriginate in the quantum critical fluctuations of incommen-surate density-wave order. Density-wave fluctuations/orderhave been found in both the spin [33, 34] and, possibly,charge [35] channel in proximity to the optimally doped iron-oxypnictide superconductors. The hydrodynamic descriptionof these fluctuations indicates that they should manifest them-selves as a low-energy collective mode in the optical conduc-tivity of strongly correlated bad metals [36], such as iron- based superconductors [10]. Both the mode energy ¯ h ω andwidth ¯ h Γ are predicted to exhibit a conspicuous linear temper-ature dependence, ¯ h ω ∼ ¯ h Γ ∼ k B T , analogous to the T -lineardc resistivity observed in many unconventional superconduc-tors [37, 38]. Fig. 3b shows that both ¯ h ω and ¯ h Γ of the collec-tive mode in the SmFeAs(O,F) thin film display a clear lineartemperature dependence below T ∗ , consistent with the afore-mentioned interpretation.In both the PrFeAsO . F . microcrystal and the Sm-FeAs(O,F) thin film the onset of superconducting coherenceis manifested in the transfer of a portion of the infrared spec-tral weight (hatched areas in Figs. 4a,c) to the dissipationlessresponse at zero frequency according to the Ferrell-Glover-Tinkham sum rule [39]. This spectral weight corresponds di-rectly to the London penetration depth of a superconductorand in our analysis amounts to λ PrL = ±
100 nm in the mi-crocrystal and a significantly larger λ SmL = ±
50 nm in thethin film.The signatures of the superconducting optical gap are best
P r F e A s O F m i c r o c r y s t a l g D , c o h2 4 K = 5 m e V a )
P h o t o n e n e r g y ( m e V ) s W -1cm-1) b ) P h o t o n e n e r g y ( m e V ) s w ,T)/ s w ,24K) E = 2 8 m e V » D D = 7 k B T c D = 3 3 m e V = 7 . 2 k B T c P h o t o n e n e r g y ( m e V ) s SC 1( w ,T)/ s NS 1( w ,60K) d ) S m F e A s ( O , F ) t h i n f i l m g D6 0 K = 1 5 0 m e V s W -1cm-1) c ) FIG. 4: (a,c) Temperature dependence of the infrared optical con-ductivity of PrFeAsO . F . and optimally doped SmFeAs(O,F)thin film, respectively. Hatched area indicates the missing spec-tral weight in the superconducting state that is transferred intothe coherent response of the Cooper-pair condensate at zero en-ergy. (b) Photon-energy dependence of the far-infrared conductiv-ity of PrFeAsO . F . above (32 K, cyan circles) and below (8 K,black circles) T c =
24 K normalized to that in the normal state at24 K. Black arrow indicates the photon energy E at which op-tical absorption is completely suppressed (equivalently, reflectancereaches unity) in the superconducting state. (d) Photon-energy de-pendence of the far-infrared conductivity of the SmFeAs(O,F) thinfilm at several temperatures in the superconducting state normalizedto that in the normal state at 60 K. Vertical dashed line indicatesthe largest energy of the maximum suppression of the infrared con-ductivity (consistent with the optical superconducting gap 2 ∆ in animpure superconductor). Grey line is a fit to the 10 K data using theMattis-Bardeen expression for the normalized optical conductivity ofan impure superconductor in the superconducting state [32]. revealed in the ratio of the optical conductivity below T c to thatin the normal state just above T c : ˜ σ ( ω ) = σ SC1 ( ω ) / σ NS1 ( ω ) .We examine these ratios for the case of the PrFeAsO . F . microcrystal and SmFeAs(O,F) thin film in Figs. 4b,d, respec-tively. Corresponding to the near-unity reflectance below E in the superconducting state of PrFeAsO . F . in Fig. 2a,˜ σ ( ω ) for this material vanishes below the same energy. Ina conventional superconductor with a high impurity concen-tration, the onset of absorption in the superconducting stateoccurs when the photon energy is sufficient to dissociate aCooper pair with the binding energy of 2 ∆ [32, 40]. However,we have demonstrated earlier (see Fig. 2a and the correspond-ing discussion in the text), that PrFeAsO . F . microcrys-tals exhibit a high degree of coherence at low temperatures.In such a clean superconductor, the direct dissociation of aCooper pair by an incident photon in a two-body process isforbidden by the conservation of energy and momentum. Foroptical absorption to occur at low temperatures, a quantum ofthe field mediating the pairing interaction must be excited inaddition. If the excitation spectrum of the mediating boson isgapped up to the energy E g then absorption becomes allowedabove 2 ∆ + E g (Ref. 41). In iron-based superconductors themediating interaction is believed to be of spin-fluctuation ori-gin and indeed has a gapped excitation spectrum in the su-perconducting state [2], with the spin-gap energy E g reaching2 ∆ [42, 43]. The combination of multiple Andreev reflec-tion spectroscopy [44] and powder inelastic neutron scatter-ing [45] clearly demonstrate that the gap energy in the familyof 1111-type materials is E g ≈ ∆ . Therefore, optical absorp-tion in the superconducting state is expected to occur at anenergy of 2 ∆ + E g ≈ ∆ , which in the present case results in ∆ ≈ ∆ / k B T c ≈
7, in a good agree-ment with the largest values found in the pnictides in gen-eral [2] and, more importantly, in the materials of the samefamily via ARPES [26]. Signatures of mediating-boson–assisted absorption in the infrared conductivity have been pre-viously identified in Ba . K . Fe As , BaFe ( As . P . ) ,and NaFe . Co . As in Refs. 29, 43, 46, respectively.Similarly to the case of PrFeAsO . F . , ˜ σ ( ω ) below T c inthe optimally doped SmFeAs(O,F) thin film reveals a plateaubelow an energy of about 33 meV (see Fig. 4c), albeit theabsorption does not vanish completely at any photon energyand a sizable residual optical conductivity is present (this ob-servation is consistent with the previous steady-state and ul-trafast spectroscopy measurements on 1111-type single crys-tals and thin films [22, 23]). In this case, the significantlyless coherent itinerant response than in the PrFeAsO . F . microcrystal allows for a direct dissociation of the Cooperpairs without the assistance of the mediating boson, as the ex-cess momentum is taken up by the lattice via defects. Onemay thus expect that the standard Mattis-Bardeen expres-sion for the anomalous skin effect in an impure supercon-ductor with a nodeless gap [32] should apply. Indeed, wefind that our experimental data are very well reproduced bythis theory (grey line in Fig. 4d). The nodeless characterof the superconducting gap is consistent with previous stud- ies of 1111-type compounds [23, 26, 27, 44, 47]. The ob-served agreement between experiment and theory allows usto assign the energy of 33 meV directly to the binding en-ergy of the Cooper pair, 2 ∆ , which results in a gap ratio2 ∆ / k B T c ≈ .
2. This value is remarkably similar to that inPrFeAsO . F . and, furthermore, to the largest gap ratioidentified via ARPES in NdFeAsO − x F x (Ref. 26) and op-timally doped Ba . K . Fe As (Refs. 48, 49). This com-monality suggests a single pairing mechanism in all of thesecompounds and a strong coupling between electrons and thepairing boson. Our work paves the way to future systematicspectroscopic studies of the in-plane infrared charge responseof the high-Tc 1111-type iron oxypnictides. Such investiga-tions will enable the extraction of the spectral function of thepairing boson [29, 43, 50] and its evolution across the phasediagram, shedding light onto the microscopic origin of thehighest bulk superconducting transition temperature amongthe iron-based superconductors.We would like to thank J. Hilfiker and T. Tiwald atJ. A. Woollam Co for their help with conventional and mi-crofocused ellipsometry measurements and R. K. 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