Synthesis and superconducting properties of FeTe1-xSe Single Crystals under high magnetic fields

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Disorder-dependent superconducting phase-diagram at high magnetic fields inFe1+ySexTe1−x (x ∼ 0.4)

T. Gebre,1 G. Li,1 J. B. Whalen,1, 2 B. S. Conner,1 H. D. Zhou,1 G.

Grissonanche,1 M. K. Kostov,1, 3 A. Gurevich,1, 4 T. Siegrist,1, 2 and L. Balicas1, ∗

1National High Magnetic Field Laboratory, Florida State University, Tallahassee-FL 32310, USA2Department of Chemical and Biomedical Engineering,

Florida State University, Tallahassee-FL 32310, USA3Department of Chemical and Biomedical Engineering,

Florida State University, Tallahassee, Florida 32310, USA4Physics Department, Old Dominion University, Norfolk-VA 23529, USA

(Dated: June 16, 2011)

We compare the superconducting phase-diagram under high magnetic fields (up to H = 45 T)of Fe1+ySe0.4Te0.6 single crystals originally grown by the Bridgman-Stockbarger (BRST) technique,which were annealed to display narrow superconducting transitions and the optimal transition tem-perature Tc & 14 K, with the diagram for samples of similar stoichiometry grown by the traveling-solvent floating-zone technique as well as with the phase-diagram reported for crystals grown bya self-flux method. We find that the so-annealed samples tend to display higher ratios Hc2/Tc,particularly for fields applied along the inter-planar direction, where the upper critical field Hc2(T )exhibits a pronounced downward curvature followed by saturation at lower temperatures T . Thislast observation is consistent with previous studies indicating that this system is Pauli limited.An analysis of our Hc2(T ) data using a multiband theory suggests the emergence of the Farrel-Fulde-Larkin-Ovchnikov state at low temperatures. A detailed structural x-ray analysis, revealsno impurity phases but an appreciable degree of mosaicity in as-grown BRST single-crystals whichremains unaffected by the annealing process. Energy-dispersive x-ray analysis showed that the an-nealed samples have a more homogeneous stoichiometric distribution of both Fe and Se with virtuallythe same content of interstitial Fe as the non-annealed ones. Thus, we conclude that stoichiometricdisorder, in contrast to structural disorder, is detrimental to the superconducting phase diagramof this series under high magnetic fields. Finally, a scaling analysis of the fluctuation conductiv-ity in the superconducting critical regime, suggests that the superconducting fluctuations have atwo-dimensional character in this system.

PACS numbers: 74.70.Xa, 74.25.Dw, 74.62.Dh, 74.25.fc

INTRODUCTION

The Fe1+y(Te,Se) series is a quite unique supercon-ducting system: its end member, FeSe is a supercon-ductor with a superconducting transition temperatureTc ≃ 8 K, [1] which can be increased up to ∼ 14 Kwith the partial substitution of Se for Te, [2, 3] or in-creased all the way up to 36.7 K by the application ofhydrostatic pressure.[4] The other end member of this se-ries Fe1+yTe is not superconducting and instead exhibitsa simultaneous structural and magnetic phase transitionfrom tetragonal to monoclinic lattice accompanied by an-tiferromagnetism (AFM) near TN ≃ 60 to 70 K (Refs.5–7). This AFM structure is distinct from those seen inthe undoped FeAs based compounds.[8–10] The AFM or-der in Fe1+yTe propagates along the diagonal direction ofthe original undistorted Fe square lattice [5, 7], while inFeAs the spin density waves (SDW) are along the nearestneighbor directions of the original Fe square lattice. [8–10] Although this AFM wave-vector in Fe1+yTe changesfrom commensurate to incommensurate when the excessiron y is increased beyond 0.076. [6]

At first glance, these observations would seem to be

surprising given that the density functional theory (DFT)calculations indicate that the Fermi surfaces (FS) of bothFeSe and FeTe are similar to those of the other FeAsbased compounds. Consequently they should also satisfythe nesting condition for the wavevector Qπ,π = (π, π).[11] This apparent lack of universality would seem toquestion the exclusive role of the interband pairing viaQπ,π magnetic fluctuations in the pairing mechanism forall the iron-based superconductors. Although the ob-servation of a spin resonance below Tc together with anenhancement of the spin fluctuations near it, would in-deed suggest a spin-fluctuations mediated superconduct-ing pairing mechanism for this system.[12, 13]

Initial angle resolved photoemission (ARPES) mea-surements in the parent compound Fe1+yTe revealed apair of nearly compensated electron-hole FS pockets,with no evidence of the FS nesting instability associatedwith Qπ,π. [14] This could have suggested the possibil-ity of a distinct mechanism for the superconductivity andfor the magnetic-order in the Fe chalcogenides when com-pared to the Fe arsenides. But a recent ARPES study onsuperconducting Fe1.03Te0.7Se0.3 reveals a holelike andan electronlike FS located at the center and the cornerof the Brillouin zone, respectively. These FSs are nearly

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nested for Qπ,π, indicating a similar pairing scenario forboth families of compounds. [15] Curiously, the samestudy reports an isotropic superconducting gap along theholelike FS with a gap ∆ of ∼ 4 meV (2∆ = kBTc ∼ 7),thus providing evidence for strong-coupling superconduc-tivity. Nevertheless, this contrasts with a recent angle-dependent heat capacity study in Fe1+ySe0.45Te0.55 sin-gle crystals which finds evidence for a significant gapanisotropy but on the electron pockets. [17]

Superconductivity in Fe1+ySe was shown to beextremely sensitive to stoichiometry. [16] In theFe1+y(Te,Se) series, the crystal structure resembles thatof the iron arsenides [1] with the Fe square planar sheetsforming from the edge-sharing iron chalcogen tetrahedralnetwork. But it also allows the partial occupation of ironin the interstitial sites of the (Te, Se) layers, resultingin a nonstoichiometric composition for the Fe1+y(Te,Se)series, where y represents the excess Fe at the intersti-tial sites. [5, 6] To this moment, it remains unclear howthe geometry of the FS evolves with the incorporation ofinterstitial Fe, but it is claimed to suppress superconduc-tivity. [18]

One remarkable feature of these compounds, which hasyet to be fully understood, is their extremely large uppercritical fields Hc2. For instance, according to Ref. 19 fora Fe1.05Te0.89Se0.11 single-crystal with a middle point Tc

of just 11 K, one observes an Hc2(T → 0 K) of ∼ 35 T.Or for a single-crystal of Fe1.11Te0.6Se0.4 with a Tc closeto its optimum value of 14 K one obtains Hc2(T → 0 K)of ∼ 40 to 45 T. [20] Compare these values with thoseof, for instance, MgB2 single crystals: Tc = 39 K withHc

c2(0) = 3.5 T and Habc2 (0) = 17 T, for fields along the

c-axis and along a planar direction, respectively. [21] Infact, to achieve in MgB2 upper-critical fields as large asthose observed in the Fe1+y(Te,Se) series, strong impu-rity scattering should be introduced to optimize the rel-ative strengths of intraband scattering in σ and π bandsof MgB2. [22, 33] The significant differences betweenthese two multi-band superconducting families are at-tributable to the fact that the Fe1+y(Te,Se) superconduc-tors are mostly Pauli limited [19] while the upper-criticalfields in MgB2 are mostly determined by the orbital pair-breaking. However, the shape of the Hc2(T ) curves forFe1+y(Te,Se) series measured in Refs. 20 and 19 are quitedistinct, with the former presenting a nearly linear de-pendence of Hc2(T ) for H‖c while the second displaysa pronounced convex curvature followed by saturation atlower temperatures (as expected for the Pauli limiting ef-fect). Such a curvature has also been reported in Ref. 23although their FeTe0.6Se0.4 single-crystal displays a muchsharper resistive transition and virtually no anisotropyγ = Hab

c2 /Hcc2, in contrast to Ref. 20 which reports an

anisotropy γ = 2 at higher temperatures. Notice thatsome of the Fe arsenide (Nd-1111 and La-1111) systemsexhibit concave-down Hc

c2(T ) consistent with orbitally-limited multi-band superconductivity. [24, 25]

The Pauli-limited behavior of Hc2(T ) for Fe-chalcogenides results from the fact that they are semi-metals with rather low carrier density and low Fermi en-ergies ∼ 20 − 50 meV for different FS pockets [14, 15],unlike the conventional metallic superconductor MgB2.As a result, chalcogenides have very short coherencelengths ξ0 ≃ ~vF /2πTc < 1 nm and thus extremely highorbitally-limited Horb

c2 ∼ φ0/2πξ2 where vF is the Fermi

velocity in the ab plane, and φ0 is the flux quantum.This in turn greatly enhances the Pauli effects quanti-fied by the Maki parameter αM =

√2Horb

c2 /Hp whereHp[T ] = 1.84Tc[K] is the Klogston paramagnetic limit[31]. Chalcogenides typically have αM & 1 above thecritical value at which the FFLO instability develops.Moreover, because of their very short values of ξ0, chalco-genides are naturally in the clean limit ℓ ≫ ξ0 which isone of the conditions of the FFLO instability, where ℓis the mean free path due to elastic impurity scattering[31]. These features of chalcogenides make them goodcandidates to study exotic effects at high magnetic fields,in particular, the interplay of orbital and paramagneticpairbreaking for multiband pairing and the FFLO stateat low temperatures. The small Fermi energies also makesuperconducting properties very sensitive to the dopinglevel, allowing one to tune Hc2 by small shifts of thechemical potential.

In this work we compare the high-field phase-diagramfor the Fe1+y(Te,Se) series, particularly those for the op-timally doping compound Fe1+yTe1−x≈0.6Sex≈0.4 synthe-sized by two methods. The first method is based on atraveling-solvent floating zone growth technique (TSFZ),which leads to crystals of acceptable crystallinity display-ing “non-metallic” resistivity, optimal Tcs, and transi-tion widths ∆Tc ≃ 1 to 3 K. We compare their behav-ior with crystals resulting from a second growth methodbased on the Bridgman-Stockbarger (BRST) techniquewhich in our case leads to crystals of poorer crystallinity(i.e. larger mosaicity), wider transitions and frequentlyto non-optimal Tcs in as grown crystals, as previously re-ported by other groups. [26] These last single-crystalswere subjected an annealing procedure which lead tometallic resistivity, considerably sharper resistive tran-sitions ∆Tc ≃ 1 K, and to superconducting transi-tions comparable to those reported in the literature forhigh quality BRST-grown single crystals as measured bySQUID magnetometry. [27] The annealed crystals hav-ing a clear metallic behavior preceding superconductiv-ity, display considerably higher upper-critical fields whencompared to those showing a poor metallicity, particu-larly for magnetic-fields applied along the inter-layer di-rection. This increase leads to a distinct shape of theHc

c2(T ), i.e. from a approximately linear in T behavior asreported in Ref. 20, to the marked concave-down curva-ture followed by saturation at lower temperatures as seenin Ref. 23.The analysis of our experimental data usinga multiband theory of Hc2(T ) [32] shows that Hc2(T ) is

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indeed strongly Pauli limited αM ≃ 7 − 10, predictingthe FFLO state below ≈ 5 K. A detailed single crystalx-ray analysis reveals that the annealing process does notaffect the crystallinity or the degree of mosaicity of oursingle crystals. Nevertheless, our dispersive x-ray analy-sis indicates that the annealing process leads to a moreuniform distribution of interstitial Fe. Annealing yieldsa considerably more isotropic phase diagram which com-bined with the enhancement in Hc

c2(T ), suggests that thevariations in the content of interstitial Fe contributes tothe suppression of superconductivity. Finally, we show,through a scaling analysis of the fluctuation conductivityin the neighborhood of the superconducting transition,that the superconducting fluctuations in this system aretwo-dimensional in character.

SAMPLE PREPARATION

Single crystals of Fe1+xTe1−ySey, 0.05 ≤ x ≤ 1 and0.1 ≤ y ≤ 0.5 were grown by using the traveling-solvent floating-zone growth technique (TSFZ) and theBridgman-Stockbarger (BRST) techniques. Starting ma-terials with nominal purities of 4N for Fe and 5N for Teand Se were used. These were handled in an argon-filledglove box which kept the oxygen content below 1ppm.Mixtures of Fe, Te, and Se were ground and pelletizedand sealed in quartz ampoules under vacuum and heatedat 400 C for 24 h. The reacted material was regroundand doubly sealed in two quartz ampoules. For samplesgrown through the TSFZ technique, the doubly sealedquartz ampoules were loaded into an optical floating-zonefurnace (NEC Nichiden Machinery 15HD), equipped withtwo 1500 W halogen lamps. The ampoule was rotated at20 rpm, and translated at a rate of 1 to 2 mm/h. Theas-grown samples were annealed by heating to 800 C for48 h, and then cooled at a rate of 100 C/h to 420 C andheld at this temperature for additional 30 h, followed bythe cooling of the furnace to room temperature.A double wall quartz ampoule was also used in the

case of crystals grown by the BRST technique. The innerampoule was narrowly tipped at its bottom and sealedat the top. This Bridgman ampoule was inserting intoa three-zone temperature gradient vertical furnace andlowered at a speed of 4 mm/h. The growth tempera-ture was decreased at a rate of 3 C/h down to 440 Cand subsequently quenched to room temperature. Someof the crystals as well as Se powder were placed intotwo different quartz crucibles, and both placed inside anevacuated quartz ampoule which was sealed under vac-uum and heated slowly to 400 C and then annealed forten days.The so-obtained crystals were checked by both single-

crystal and powder x-ray diffraction (XRD) techniques.From as-grown single crystals, shards were cleaved toobtain suitable samples of approximately 0.3 mm × 0.3

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FIG. 1: (color online) Top panel: Resistivity as a function oftemperature for a Fe1.13Se0.45Te0.55 single crystal synthesizedby the traveling floating zone method under zero magneticfield. Inset: Resistive superconducting transition under zero-field in a limited temperature range.

mm × 0.03 mm. An Oxford-Diffraction Xcalibur-2 CCDdiffractometer with Mo K source was used to collectreflections. CrysAlis Pro 171.33.55 software (OxfordDiffraction) was used for the unit cell refinement andanalytical absorption correction. Final structure refine-ments were conducted using SHELXTL. For the powderdiffraction runs, the single-crystals were ground by handfor approximately 1 minute using an agate mortar andpestle. Patterns were detected by a Huber-Guinier 620camera with a Rigaku Ultrax Cu Kα direct drive rotat-ing anode source. WinPow software was used for unit cellparameter least-squares calculations and peak fitting.

Scanning electron-microscope energy-dispersive x-rayanalysis (SEM-EDX) was performed by using a JEOL5900 scanning electron microscope (30 kV acceleratingvoltage) equipped with IXRF energy dispersion spec-troscopy software (IXRF Systems, Inc.) in order to de-termine the elemental compositions of the single crystals.We found that this EDX set-up would show a tendencyto underestimate by nearly 3 % the overall fraction of Fewhen comparing with detailed single-crystal x-ray refine-ments.

Longitudinal resistivity was measured using a conven-tional four-contact method in continuous magnetic fieldsup to 45 T by using either a PPMS or the hybrid mag-net of the National High Magnetic Field Laboratory inTallahassee.

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FIG. 2: (color online) Top panel: Resistivity as a functionof temperature for an as-grown Fe1.11Se0.4Te0.6 single crys-tal, synthesized through the Bridgman-Stockbarger method(red curve) and under zero magnetic field. After annealing,the sample no longer displays the weak-localization like tem-perature dependence. Instead it displays a metallic character(black trace). Inset: Superconducting resistive transition forthe annealed crystal under zero field and in a limited tem-perature range. Bottom panel: Magnetic susceptibility as afunction of T for the same annealed single-crystal and respec-tively, for magnetic field-cooled (red markers) and zero-fieldcooled conditions (black markers).

SAMPLE CHARACTERIZATION

Figure 1 shows a typical trace of resistivity ρ as a func-tion of the temperature for a single crystal grown by thetraveling-solvent floating-zone method described above,whose stoichiometry was extracted by a detailed singlecrystal x-ray analysis refinement. Although the width∆Tc ∼ 1 K of the superconducting transition (see inset)is relatively narrow when compared with the width ofthe transitions shown for instance in Ref. [19], the be-havior of the metallic state shows the typical negativeslope ∂ρ/∂T < 0 or logarithmic divergence of the resis-tivity, which was attributed to the high content of inter-stitial Fe and which leads to weak localization. [18] Thesame characteristic temperature dependent resistive be-havior is observed also in as-grown samples synthesizedby the Bridgman-Stockbarger method (red line), as seenin the top panel of Fig. 2. As seen, the as-grown samplestend to exhibit lower superconducting transition temper-

atures and broader transitions. The annealing proceduredescribed above leads to a slightly smaller resistivity atroom temperature (black line) but most importantly to aquite distinct temperature dependence for the resistivity,which below T ∼ 175 K exhibits a clear metallic depen-dence with ∂ρ/∂T > 0. The magnetic susceptibility onthe other hand, shows a very clear diamagnetic signal(black markers) below the onset of Tc at T = 14 K, asseen in the lower panel of Fig. 2. At higher tempera-tures, the magnetic susceptibility is virtually tempera-ture independent, as reported in Ref. 28 , and only atlow temperatures one observes a very mild upturn in thesusceptibility suggesting the presence of a small amountof localized magnetic moments. Although none of thesusceptibility traces in Ref. 28 show a clear diamagneticsignal below Tc ≃ 14 K but below ∼ 10 K.

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FIG. 3: (color online) Powder x-ray diffraction pattern fortwo Fe1.11Se0.4Te0.6 single crystals grown through the Bridg-man technique, collected by using the Mo-Kα line. Black linecorresponds to the spectrum of an as-grown crystal, while thered line is the spectrum obtained from a subsequently an-nealed single-crystal. In both cases well-defined Bragg peaksare observed and indexed within the space-group P4/nmm.We find no evidence for impurity phases or a change in struc-ture/stoichiometry induced by the annealing process.

We also characterized our single crystals throughsingle-crystal and powder x-ray diffraction measure-ments. Figure 3 shows two typical powder x-ray spec-trum for one as-grown BRST crystal (black line) witha nominal stoichiometry Fe1.11Se0.4Te0.6, and for oneannealed BRST single crystal (red line) from the samebatch. These “powder” patterns were produced from in-tegrating the intensities from single-crystal x-ray diffrac-tion measurements. This powder like pattern was ob-tained on the same single crystals used for the mag-netic and transport measurements shown throughout thismanuscript, by superimposing several of the θ to 2θscans along the different crystallographic orientations.

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FIG. 4: (color online) (a) X-ray intensity for an as-grown BSsingle-crystal as a function of 2θ for an angular scan aroundthe Bragg-peak observed along the real-space direction [abc]= (200). Red line is a fit to a Gaussian function which yieldsa full-width at half-maximum of ∼ 0.5. (b) X-ray rockingcurve around the Bragg peak at (200) as a function of theangle Ω, which corresponds to an arc along a direction nearlyperpendicular to θ. One observes a very broad feature whichcan be adjusted to three Gaussian distributions (blue lines)of crystallite orientations. (b) Same as in (a) but for a Braggpeak centered at the (002) position. Red line is a fit to aGaussian having a full-width at half-maximum of ∼ 0.25.(d) Same as in (b) but for the peak around the (002) position,although in this case two Gaussian distributions are neededto adjust the observed broad peak.

As clearly seen, for both crystals we observe the sameset of well-defined Bragg peaks, where all peaks can beindexed within the tetragonal unit cell having the spacegroup symmetry P4/nmm. Most importantly, we do notdetect the presence of any impurity phase in either crys-tal, concluding that the annealing process preserves theoriginal crystallographic structure and therefore the sto-ichiometry of the crystals. From this first analysis itwould seem that both crystals are equivalent in struc-tural quality despite their marked differences in physicalbehavior as seen in the top panel of Fig. 2.

To clarify if disorder and mosaicity is at the origin ofthese differences in physical behavior, we performed adetailed x-ray rocking curve analysis in both single crys-tals around specific Bragg peaks. Figure 4 (a) shows the(200) Bragg reflection. By fitting the intensity as a func-tion of 2θ to a Gaussian distribution, one obtains a fullwidth at half maximum (FWHM) of ∼ 0.5, suggestingat first glance a modest but sizeable mosaic spread amongcrystallites. However, an exploration of the width of thispeak along an arc Ω whose orientation is nearly perpen-dicular to 2θ reveals a very broad feature as seen in Fig.4 (b). This broad maximum can be adjusted (red line) to3 Gaussian distributions (blue lines), with one of themshowing a FWHM as large as & 2.5. Each Gaussianwould represent an ensemble or distribution of crystal-

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FIG. 5: (color online) (a) X-ray intensity for an annealed

BRST single-crystal of Fe1+yTe0.6Se0.4 as a function of 2θ foran angular scan around the Bragg-peak observed along thereal-space position [abc] = [200]. Red line is a fit to a Gaussianfunction which yields a width at half maximum of ∼ 0.4. (b)X-ray rocking curve around the Bragg peak at (200) as afunction of the angle Ω. One observes a very broad featurewhich can be adjusted to at least two Gaussian distributions(blue lines) of crystallite orientations. (b) Same as in (a) butfor a Bragg peak observed along (002) position. Red line is afit to a Gaussian which yields a full width at half-maximumof ∼ 0.3. (d) Same as in (b) but for the peak around the(002) position.

lites having a similar relative orientation. The observa-tion of several distributions with varying widths indicatesa large degree of mosaicity around the (200) position, orwithin the planes. A similar study around the (002) po-sition shown respectively in Figs. 4 (c) and 4 (d), revealsseemingly a smaller degree of mosaicity among crystal-lites within distinct planes.To clarify if the annealing process affects the structural

degrees of freedom, for instance, by releasing strain in-duced in the single-crystals by the synthesis process, wehave attempted a similar detailed structural analysis inan annealed single crystal of Fe1+yTe0.6Se0.4. Figure 5(a) shows the intensity of the Bragg peak located alongthe (200) direction as a function of the angle 2θ, whileFig. 5 (b) shows the intensity of the same peak as func-tion of the angle Ω. The first measurement leads to aGaussian peak (red line) having a FWHM of ≃ 0.4 whilethe second one can be adjusted to two Gaussian distri-butions (blue lines) with the widest distribution havinga FWHM of ≃ 1.6. Fig. 5 (c) shows the intensity of theBragg peak observed as the angle 2θ is scanned aroundthe (200) direction. One extracts a FWHM of ≃ 0.3

by fitting its intensity to a Gaussian distribution (redline). Finally, Fig. 5 (d) shows the intensity of the Braggpeak observed at the (200) position as a function of theangle Ω. As shown in the figure, to reproduce the ob-served broad feature one would need to fit it to at leastthree Gaussian distributions with the widest one having

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a FWHM of & 2.1.From this detailed comparison between the as-grown

and the annealed BRST Fe1+yTe0.6Se0.4 single crystals,we can firmly conclude that the annealing process has noor perhaps just a marginal effect on the degree of crys-tallinity of the BRST grown samples. Although as seenin Fig. 2 (a), the behavior of the metallic state, and eventhe width of the superconducting transition is affectedby this treatment and as we shall see below, it also af-fectsHc2(T ). Therefore, from our study we can state thatthe degree crystallinity, or the relative orientation amongcrystallites in a single-crystal, has virtually no effect onthe superconducting properties of the 11 series.Nevertheless, by comparing the EDX data taken on

several annealed and non-annealed BRST-grown single-crystals, on approximately a dozen of collection sites ineach crystal, one notices marked differences between an-nealed and non-annealed crystals: in average the non-annealed crystals displayed a variability ∆y of ∼ 7.7 %in the fraction y of interstitial Fe and a ∆x ≃ 8.8 % in thefraction x of Se, when compared respectively to ∆y = 1.8% and ∆x = 6.1 % for the annealed samples. EDX indi-cates that the annealing process has virtually no effect onthe average value of either x or y, so it just homogenizesboth values (specially y) throughout the sample.However, this observation does not address the ori-

gin of for instance, the “non-metallic” like resistivity ob-served in the TFZ-grown crystals when compared to themetallic response seen in annealed BRST-grown crys-tals. For the first ones, we were able to observe clearBragg peaks and proceed with single-crystal x-ray refine-ments in shards taken from them, indicating relativelylarge values for y ranging from 0.07 to 0.12. Remark-ably, for the second ones and despite the physical charac-terization shown above suggesting relatively high-qualitysingle-crystals, we were unable to extract well-definedintegrated intensities for single crystal refinements, andthus proceed with single-crystal x-ray refinements in or-der to determine the precise values of x and y. Forthese crystals, EDX indicates nearly stoichiometric val-ues for y, i.e. y ∼ 0 although, as previously mentioned,it tends to underestimate the content of Fe when com-pared to single-crystal x-ray refinements. These observa-tions indicate that the physical properties of the 11 Fe-chalcogenides are oblivious to their degree of crystallinitybut depend on the amount of interstitial Fe and on howevenly distributed it is throughout the sample.

SUPERCONDUCTING PHASE DIAGRAM AT

HIGH FIELDS

In this section we compare the high-field supercon-ducting phase-diagrams of several crystals grown respec-tively by the floating zone the Bridgman-Stockbargertechniques. In either case, only the crystals display-

ing the sharpest superconducting transitions ∆Tc =T (ρ(0.9Tc) − T (ρ(0.1Tc)) . 1.0 K (where ρ(0.9Tc) andρ(0.1Tc) are the values of the resistivity at respectively,the onset of the resistive transition or 90 % of ρ, and thefoot or 10 % of ρ at the transition) were chosen for theelectrical transport measurements under high fields. Asindicated by Fig. 2, for the crystals grown by BRST themethod, only the annealed samples showed the optimumTc and the sharpest superconducting transitions amongall of the measured samples.

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H (T)

FIG. 6: (color online) Left panel: Resistance as a function oftemperature T across the superconducting transition for anannealed Fe1.11Se0.4Te0.6 single crystal (nominal stoichiom-etry) synthesized by the Bridgeman technique, and respec-tively for fields along an in-plane direction (a) and the inter-plane c-axis (b). Right panel: Resistance as a function offield H for the same single-crystal and for different temper-atures, and respectively for an in-plane direction (c) and theinter-plane c-axis (d).

Figures 6 (a) and (b) show the resistance as a func-tion of temperature for an annealed Fe1+yTe0.6Se0.4 sin-gle crystal for different fieldsH‖ab and H‖c, respectively.Clearly, fields along the c-axis produce broader transi-tions as a function of temperature. Figures 6 (c) and (d)show the resistance as a function of magnetic fields H‖aband H‖c (up to H = 45 T) for the same single crystal fordifferent temperatures. The transitions become progres-sively sharper in field as the temperature decreases, con-sistent with the reduction of vortex fluctuations at lowerT . We have also collected similar data-sets for severalsingle-crystals grown by the TSFZ-method with differ-ent Se and Fe contents but the corresponding raw data isnot shown here. The stoichiometric fractions of Fe and Sewere determined through a detailed single-crystal x-raydiffraction refinement of small shards cleaved off fromeach single-crystal. For these TSFZ samples the mea-sured superconducting transition temperatures rangedfrom Tc ∼ 12 K (y = 0.26, x or fraction of Se = 0.16) tothe optimal Tc value & 14 K (y = 0.06 and x = 0.44).In Fig. 7 (a) we compare the superconducting

7

0.0 0.2 0.4 0.6 0.8 1.0

0

1

2

3

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

(b)

FeTe0.9

Se0.1

H // abH // c

FeTe0.8

Se0.2

H // abH // c

FeTe0.7

Se0.3

H // abH // c

FeTe0.5

Se0.5

H // abH // c

FeTe0.65

Se0.35

H // ab H // c

Hc2

/Tc (T

/K)

t

Floating zone:

Fe1.11Te0.6Se0.4

(Self-flux) H // ab H // c

Hc2

/Tc (T

/K)

t

AnnealedFe1.11Te0.6Se0.4

(Bridgman) H // ab H // c

(a)

FIG. 7: (color online) (a) Comparative superconductingphase-diagram under high magnetic fields where the uppercritical field Hc2 normalized by the superconducting transi-tion temperature Tc, is plotted as a function of the reducedtemperature t = T/Tc for two single crystals: respectively forthe Fe1+δSe0.4Te0.6 single crystal in Ref. 20 and for our an-nealed Fe1.11Se0.4Te0.6 (nominal stoichiometry) BRST single-crystal. (b) Superconducting phase-diagram for several TSFZgrown single-crystals, where the phase-diagram for our an-nealed Fe1.11Se0.4Te0.6 BRST single-crystal is also included.Open and solid markers depict the phase-boundary betweenmetallic and superconducting states for fields along the c-axisand along a planar direction, respectively. All points in bothgraphs were extracted from the middle point of the resistivetransition.

phase-diagram at high-fields for our annealed BRSTFe1+yTe0.6Se0.4 single-crystal (circles) with the resultsof Ref. 20 (squares), and in Fig. 7 (b) with the phase-diagram obtained for several TSFZ single-crystals (vari-ous markers excluding circles). In either graph, both thefield- and the temperature-axis are rescaled with the zero-field Tc of each sample (corresponding to the middle pointof its resistive transition). Here, we use this scaling forcomparative purposes only, and not to indicate that thesecompounds are placed within the dirty limit. The plotin Fig. 7 (a) leads to a similar scaling quality when com-pared with aHc2(T )/T

2c as a function of T/Tc plot, previ-

ously observed in some of the Fe arsenide compounds [25]and wich was deemed to be consistent with an effectiveclean limit scenario due to the small superconducting co-herence lengths of the Fe-pnictide compounds. As clearlyseen in both figures, the annealed BRST-grown crystalhas considerably larger upper-critical fields than all theother crystals, particularly for fields along the c-axis andat intermediary reduced temperatures, i.e. from ∼ 35 to∼ 60 % larger Hc2s for T/Tc ≃ 0.5. For T/Tc ≃ 0.2, theupper-critical field still is ∼ 5 % larger than the valuereported in Ref. 20. On the other hand, the anisotropyparameter γ ≃ 1.8 for T → Tc is slightly smaller than thevalues reported in Ref. 20 (γ ≃ 2 for T → Tc), Ref. 23

0.01 0.1 1

1

10

H // ab-plane H // c-axis

Hc2

(T)

1- (T / T

c )

FIG. 8: (color online) Upper critical fields Hc2 as a functionof 1− t where t = T/Tc is the reduced temperature. Red linesare fits to Eq. 1.

(γ ≃ 3 for T → Tc), and Ref. 29 (γ ≃ 3.5−4 for T → Tc).Given that the level of structural disorder (i.e. mosaicity)seen in crystals showing quite broad transitions and lowerTcs (as-grown BRST crystals) is very similar to the levelof mosaicity seen in the annealed crystals which displayrelatively sharp transitions, optimum Tc, and higherHc2,one is lead to conclude that the superconducting phasediagram of the Fe1+yTe1−xSex series for a given valueof x is mostly controlled by ∆y and ∆x respectively theoverall fluctuation on the value of y the fraction of inter-stitial Fe and in the value of x the fraction of Se.Another intriguing observation is that the supercon-

ducting phase-diagram for the more Fe stoichiometricsamples shows a pronounced downward curvature as Tis lowered which was attributed by several authors to thePauli limiting effect [19, 29], in contrast with for example,the linear dependence seen in Ref. 20) for Hc

c2. Indeed,all Hc2/Tc ≃ 3 ratios shown in Fig. 7 are above the BCSparamagnetic limit, Hc2/Tc = 1.84, indicating that thePauli pairbreaking is indeed very essential.

Two-band analysis of the Hc2 data

In order to evaluate the contributions of both orbitaland Pauli pairbreaking effects for either field orientation,and to compare the results with those extracted fromheat capacity measurements, we first analyze our Hc2(T )data at temperatures close to Tc where the Ginzburg-Landau theory yields Ref. [29, 32]:

(

H

Hp

)2

+H

Ho

= 1− T

Tc(1)

Very close to the critical temperature, (Tc − T )/Tc ≪(Hp/Ho)

2, the first paramagnetic term in the left hand

8

side is negligible and Eq. (1) yields the orbital linear GLtemperature dependence, Hc2 = Ho(1− T/Tc). At lowertemperatures, (Tc − T )/Tc > (Hp/Ho)

2, the Pauli limit-ing field Hp dominates the shape of Hc2(T ) ∝ (1− t)1/2

even in the GL domain if Hp < Ho. The latter in-equality is equivalent to the condition that the Makiparameter αM ∼ Ho/Hp > 1 is large enough, assur-ing that the paramagnetic effects are essential. Shownin Fig. 8 are the log-log plot of our Hc2(T ) as a func-tion of 1 − T/Tc where the red lines are fits to Eq.(1). These fits are excellent for the high-field region(excluding the highest fields), but less so very close toTc, probably due to the relatively large errors in deter-mining temperatures (∆T ∼ 25 mK) which are inherentto transport measurements, or perhaps due to broad-ening of the resistive transition due to local Tc inho-

mogeneities. The fit yields H‖cp = (72.3 ± 3.5) T and

H‖abp = (62.6± 2.4) T for the Pauli limiting field, respec-

tively for fields along the c-axis and along the ab-plane,

and H‖co = (160.1±17.3) T and H

‖abo = (439±136) T for

the orbital limiting fields which are in very good agree-ment with those reported in Ref. 29. Defining the effec-tive GL coherence lengths, ξab(T ) = ξab(1 − T/Tc)

−1/2

and ξc(T ) = ξc(1 − T/Tc)−1/2, we obtain a rather small

in-plane value of ξab = (φ0/2πH‖co )1/2 = 14±4 A and an

even smaller c-axis value of ξc = ξabH‖co /H

‖abo ∼ 5.1 A,

which is shorter than the inter-planar distance c ∼ 6 A.[30]

0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Hc 2

/Tc (T

/K)

t

H // ab-plane H // c-axis Fit

Q / Q0

= 2.3 = 0.9

FIG. 9: (color online) High-field superconducting phase-diagram or upper critical-field normalized by the super-conducting transition temperature at zero field as functionof the reduced temperature, for an annealed BRST-grownFe1+δSe0.4Te0.6 single crystal, where the red line is a fit to themodel described in the text. Blue line depicts the tempera-ture dependence of the modulation wave-vector for a FFLOstate, which would explain the shape of the phase-boundaryat lower temperatures.

The phenomenological Eq. (1) only describes the rangeT ≈ Tc, but does not take into account the possibility ofthe FFLO state which occurs if αM > αc is large enough(αc ≈ 1.8 for a single parabolic band [31]). To analyzeour Hc2(T ) data at all temperatures and to reveal themicroscopic meaning of the scaling fields Hp and Ho, weuse a two-band generalization of the WHH theory [32]in the clean limit, taking into account both orbital andparamagnetic pair-breaking, and the possibility of theFFLO with the wave vector Q(T,H). In this case theequation for Hc2 is given by

a1G1 + a2G2 +G1G2 = 0, (2)

G1 = ln t+ 2eq2

Re

∞∑

n=0

∫ ∞

q

due−u2×[

u

n+ 1/2− t√

btan−1

(

u√b

t(n+ 1/2) + iαb

)]

G2 =

ln t+ 2esq2

Re

∞∑

n=0

∫ ∞

q√s

due−u2×[

u

n+ 1/2− t√

bηtan−1

(

u√bη

t(n+ 1/2) + iαb

)]

(3)

The FFLO wave vector Q(T,H) is determined self-consistently by the condition that the solution Hc2(T,Q)of Eq. (2) is maximum, a1 = (λ0 + λ−)/2w, a2 =(λ0 − λ−)/2w, λ− = λ11 − λ22, λ0 = (λ2

− + 4λ12λ21)1/2,

w = λ11λ22 − λ12λ21, t = T/Tc, and

b =~2v21H

8πφ0k2BT2c g

21

, α =4µφ0g1kBTc

~2v21=

πkBTcm

EFm0

,

(4)

q2 = Q2zφ0ǫ1/2πH, η = v22/v

21 , s = ǫ2/ǫ1. (5)

Here vl is the in-plane Fermi velocity in band l = 1, 2,ǫl = mab

l /mcl is the mass anisotropy ratio, µ is the mag-

netic moment of a quasiparticle, λ11 and λ22 are the in-traband pairing constants, and λ12 and λ21 are the in-terband pairing constants, and α ≈ 0.56αM . The factorsg1 = 1 + λ11 + |λ12| and g2 = 1 + λ22 + |λ21| describethe strong coupling Eliashberg corrections. For the sakeof simplicity, we consider here the case of ǫ1 = ǫ2 = ǫ forwhich s = 1, and Hab is defined by Eqs. (2) and (3)with g1 = g2 and rescaled q → qǫ−3/4, α → αǫ−1/2 and√b → ǫ1/4

√b in G1 and

√ηb → ǫ1/4

√ηb in G2 [32].

Equation (2), which describes Hc2(T ) at all tempera-tures, simplifies close to Tc where it reduces to Eq. (1)with

Ho =48πφ0k

2BT

2c

7ζ(3)~2[v21 + v22 + (v21 − v22)λ−/w](6)

Hp =2πkBTc

µ√

7ζ(3)(7)

9

where ζ(3) ≈ 1.202. The slope H ′c2 = |dHc2/dT | is max-

imum at Tc where Eqs. (2) and (6) yield

H ′c2 =

24πφ0k2BTc

7ζ(3)~2(c+v21 + c−v22)(8)

For identical bands, (v1 = v2 = v, λ11 = λ22, c+ = c− =1/2), Eq. (8) reduces to the single-band GL expression,H ′

c2 = φ0/2πTcξ20 , where ξ0 = (~v/πkBTc)[7ζ(3)/48]

1/2

is the GL coherence length in the clean limit [32]. Forthe s± pairing (c+ → c− → 1/2), the dependence of H ′

c2

on the materials parameters resembles the behavior ofHc2(T ) in the s++ dirty limit: for strong band asymme-try (η ≪ 1 or η ≫ 1), Hc2 in Eq. (8) is limited by theband with larger Fermi velocity, similar to Hc2 mostlylimited by the band with larger diffusivity for the s++

case [33]. Paramagnetic effects decrease the slope of H ′c2

and reduce the effect of band asymmetry.Figure 9 shows the fit of the measured Hc2(T ) to

Eq. (2) for H‖ab. For this field orientation, the resis-tive transitions in Fig. 6c are considerably sharper thanfor H‖c. This allowed us to clearly define the middlepoint of the resistive transition for the traces taken atlower temperatures, increasing the number of the Hc2

data points. For the sake of simplicity, we consider herethe case of ǫ1 = ǫ2 = ǫ for which γ = ǫ−1/2, and Hab isdefined by Eqs. (2) and (3) with rescaled q → qǫ−3/4,α → αǫ−1/2 and

√b → ǫ1/4

√b in G1 and

√ηb → ǫ1/4

√ηb

in G2 [32]. The fit in Fig. 9 was done for s± pairingwith λ11 = λ22 = 0, λ12λ21 = 0.25, η = 0.9, H‖ab,α = 2.3. Equation (2) describes Hc

c2(T ), Habc2 (T ) and

γH(T ) = b‖(T )/√ǫb⊥(T ) where b‖(T ) is the solutions of

Eq. (2) for H‖c very well.To see if the observed values ofH ′

c2 are at least qualita-tively consistent with Eq. (8) and the materials param-eters of chalcogenides, we use the ARPES data [40–42]which give EF ≃ 20 − 50 meV. Taking EF = 30 meVin Eq. (8) yields H ′ab

c2 [T/K] ≃ 0.64γ(m/m0), so the ob-served H ′ab

c2 = Habo /Tc = 31.4 T/K and γ = Hab

o /Hco ≈

2.75 corresponds to the value of m ≃ 15m0 consistentwith the ARPES data of m/m0 = 3-20 for different FSpockets [40]. These estimates show that the paramag-netic effects for Fe-11 chalcogenides are indeed essential,and the parameter αab = γα defined by Eq. (4) is greaterthan 1. For EF = 30 meV and Tc = 14 K, we ob-tain αab ≃ 0.13γm/m0, giving αab ∼ 5. The values ofα > 1 indicate that paramagnetic pair-breaking becomesso strong that it can trigger the FFLO instability at lowertemperatures.As follows from the results shown in Fig. 9, the

anisotropy parameter γH(T ) decreases as T decreases.This behavior reflects the significant role of the Zeemanpair-breaking in FeSeTe given that α‖ = α/

√ǫ = 2.3

for H⊥c is well above the single-band FFLO instabil-ity threshold, α ≈ 1 [32]. In this case γH(T ) near Tc

is determined by the orbital pairbreaking and the massanisotropy ǫ, but as T decreases, the contribution of the

isotropic Zeeman pairbreaking increases, resulting in thedecrease of γH(T ).The fit to our experimental data based on the solution

of Eq. (2) predicts the FFLO transition for H ||ab. Inthis case Fig. 9 shows that the FFLO wave vector Q(T )appears spontaneously at T < TF ≈ 0.35Tc ≈ 5K. HereQ(T ) increases from zero at T = TF to the maximum Q0

at T = 0, where Q0 = 4πTcb(0)1/2/~v1. In addition to

the strong Pauli pairbreaking α > 1, the FFLO transitionrequires weak impurity scattering in the clean limit ℓ ≫ ξwhere ℓ is the mean free path due to elastic scattering onimpurities [31]. The latter condition is likely satisfied inthe crystals studied in this work, given the very shortcoherence lengths ξab ∼ 14A and ξc ∼ 5A extractedfrom the fit described above. Thus, the chalcogenidesare very good candidates to study the FFLO transitionby magneto-transport, specific heat, magnetic torque orNMR measurements.

ANALYSIS OF THE CRITICAL REGION

In the critical region of the metal to superconduct-ing transition, and in the limit of strong magnetic fields,one expects a scaling form for the thermodynamic func-tions. At very high fields if the quasiparticles are confinedwithin the lowest Landau level, the transport of chargecarriers becomes nearly one-dimensional along the direc-tion of the applied field. Fluctuation effects close to thesuperconducting transition are expected to be enhancedby the lower effective dimensionality of the system. Inthe critical regime the fluctuation conductivity was cal-culated in Ref. 34 by including a quartic term in thefree energy within the Hartree approximation, and ob-tained a scaling law for the fluctuation conductivity ∆σin magnetic fields, in terms of unspecified scaling func-tions F2D and F3D, valid for two-dimensional and three-dimensional superconductors, [34] respectively:

∆σ(H)2D =

(

T

H

)1/2

F2D

(

αT − Tc(H)√

TH

)

, (9)

∆σ(H)3D =

(

T 2

H

)1/3

F3D

(

βT − Tc(H)

(TH)2/3

)

, (10)

Where α and β are characteristic constants of a specificmaterial. Presumably, these functionals remain valideven if the quasiparticles are not confined to just thelowest Landau level, but are placed in a few higher Lan-dau levels, as long as the interaction between quasi-particles in distinct Landau levels remains negligible.[35, 36] In the cuprates, either type of scaling has beenobserved in materials having distinct degrees of elec-tronic/superconducting anisotropies. [37]We define the contribution of the fluctuations to the

conductivity ∆σ as the difference between the normal

10

state conductivity σn = 1/ρn (ρn is the normal stateresistivity) and the measured conductivity σ = 1/ρ. Hereσn is obtained from a polynomial fit of the resistivityin a temperature interval ∆T ∼ 2Tc above Tc, wherethe contribution of the fluctuations to σ should becomenegligible.

100

101

102

103

104

105

H = 1 T

H // abH = 9 T

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4

100

101

102

103

104

105

H = 9 T

H = 1 T

(1/

- 1/

n ) (H

/T2 )1/

3 ()

(T - TC(H))/(TH)2/3 (K1/3T-2/3)

H // c

100

101

102

103

104

105

H = 9 T

H // ab

H = 1 T

-0.2 0.0 0.2 0.4 0.6 0.810-1

100

101

102

103

104

105

H = 9 T

H = 1 T

(T - TC (H))/(TH)1/2 (K1/2T -1/2)

(1/

- 1/

n ) (

H/T

)1/2 (

-1T1/

2 K-1

/2)

H // c

FIG. 10: (color online) Left panel: ∆σ(H/T )1/2 versus [T −

Tc(H)]/(TH)1/2 for the annealed BRST single-crystal and forboth field orientations, as expected for the two-dimensionalscaling relation of Eq. (2). Right Panel: ∆σH1/3/T 2/3 versus

[T − Tc(H)]/(TH)2/3 as expected for the three-dimensionalscaling relation in Eq. (3).

In the left panel of Fig. 10, we plot ∆σ(H/T )1/2 ver-sus [T − Tc(H)]/(TH)1/2 for the annealed BRST single-crystal for both field orientations, as expected for thetwo-dimensional scaling relation in Eq. (9). For fieldsabove a relatively small value of just 4 T, and for bothorientations, this two-dimensional scaling clearly suc-ceeds in collapsing all the curves over an extended tem-perature range particularly above Tc. Given that thehigh field resistive transitions shown in Fig. 6 are re-markably broad, it is not possible to unambiguously de-fine the functional form of ρn(H) in order to also col-lapse those curves in Fig. 10. To compare this two-dimensional scaling relation with the three-dimensionalone, in the right panel of Fig. 10, we plot ∆σH1/3/T 2/3

versus [T − Tc(H)]/(TH)2/3 as expected for the three-dimensional case described by Eq. (10). Clearly, thetwo-dimensional relationship provides a better scaling ofthe data both above and below Tc. Indeed, in the three-dimensional case, the curves at different fields open likea fan above Tc and also tend to separate from each otherbelow this critical temperature. On the other hand, inthe 2D case, the curves above 4 T basically overlap overthe entire range. The 2D behavior of fluctuation con-ductivity, already observed in the Fe arsenides, [38, 39]implies that the inter-plane coherence length ξc is smalleror in the order of the inter-plane spacing, or, equivalently,that the Josephson coupling between adjacent supercon-ducting planes is smaller than the intra-plane condensa-tion energy. Two-dimensional scaling also suggests that

such fluctuations can contribute to the broad transitionsseen in Fig. 6, which become considerably sharper atlower temperatures.

DISCUSSION

There are several puzzling aspects in theFe1+yTe1−xSex family that have yet to be understoodand/or conciliated. For instance, optical spectroscopymeasurements in Fe1.06Te0.88S0.14 indicates the absenceof a Drude peak in optical conductivity, suggesting theabsence of well-defined coherent quasi-particles in thismaterial [43]. Although, for FeSe0.42Te0.58 the in-planeoptical conductivity is found to be indeed describablewithin a Drude-Lorentz model with a marked increasein the scattering rate among quasiparticles as T islowered [44] but with an incoherent response along theinter-planar direction [45]. Therefore, one could evenask if the concept of Fermi surface would be applicableto these compounds. In sharp contrast, a recent angleresolved photoemission study on FeSe0.42Te0.58 [46]reveals a Fermi surface which is in relative good qualita-tive agreement with the generic Fermi surface proposedfor the family of Fe pnictide superconductors. Namely,composed by two concentric hole-like cylindrical surfacesat the Γ point and two electron-like cylinders at theM point of the Brillouin zone, which in this case arecharacterized by a large FS-sheet dependent effective-mass enhancement ranging from 6 to 20 respect to theband mass. This clearly indicates that correlations areparticularly relevant for these materials and is consistentwith the size of the anomaly observed in the heatcapacity at the superconducting transition [47] or thelarge Hc2 reported here and by other groups [20, 23, 29].This geometry would be consistent with the observationof a resonance mode for a characteristic wave-vectorconnecting both types of cylindrical Fermi surfaces [12]pointing towards an itinerant, nesting-like mechanismfor the origin of the spin-fluctuations observed in thesesystems. Nevertheless, this scenario seems somewhatdifficult to conciliate with the rather large magneticmoment of 1.6 to 1.8 µB for the non-interstitial Fe(I)ion extracted from careful magnetic susceptibility mea-surements in superconducting samples [48], and does notexplain the observation of short-range magnetic-orderin (superconducting samples) for the same wave-vectoras the one extracted for the magnetically ordered stateof Fe1+yTe which is rotated by 45 with respect tothe aforementioned nesting-vector [6]. Presumably, theinterstitial Fe(II) is characterized by an even larger mo-ment of ∼ 2.5 µB [6, 48] and from the superconductingperspective it should act as a magnetic impurity.A recent DFT + DMFT study suggests that a com-

bination of Hund’s rule and structural degrees of free-dom, such as the pnictogen height and the bond angle

11

between Fe and the pnictide element, are the key pa-rameters defining the role of correlations, i.e. the degreeof localization and therefore the concomitant size of themagnetic moment of Fe in iron pnictide compounds [49].For instance, the larger the size of the pnictogen atom orequivalently the larger the distance between Fe and thiselement, or the greater the deviation with respect to theideal tetrahedral angle of 109.5, the larger the degree oflocalization in the Fe site. Or equivalently, the strongerthe correlations on those Fermi surface sheets having amarked t2g character which would favor the developmentof a magnetic instability. It is therefore easy to speculateon the role played by the interstitial Fe(II): it should favorlocal lattice distortions that are likely to further distortthe Fe-pnictogen angle away from 109.5 favoring localmagnetism in detriment of superconductivity. The largerthe content in Fe(II) the stronger this detrimental ef-fect, while larger fluctuations in y could create randomlydistributed nearly magnetic patches having a strongerFe(II) content which could lead to pair-breaking effects.This rather simple scenario would explain why the an-nealed BRST-grown samples display clearer and sharpersuperconducting transitions when compared to the non-annealed ones despite a similarly poor crystallinity.As for the presence of the FFLO state [31], it is sen-

sitive to impurities so it would be difficult to conciliateunambiguously if the FFLO state would survive the pres-ence of magnetic Fe(II) atoms. But our results suggestthat our BRST-grown samples (annealed as well as non-annealed) are closer to having a nearly stoichiometric Fecontent. Moreover, the low-T upturn in Hc

c2(T ) indica-tive of the FFLO instability observed in this work, wasalso observed by other groups, see, for example, Ref. 23.Finally, the interplay between magnetism and a potentialFFLO-state is still poorly understood [50], so its exis-tence in the Fe1+yTe1−xSex will hopefully be clarified byfuture calorimetric, magnetic torque or NMR measure-ments at high fields.

CONCLUSION

A relatively weak disorder in the distribution of in-terstitial Fe is found to be detrimental to the supercon-ducting properties of the Fe1+yTe1−xSex series, broad-ening the width of the superconducting transition andsuppressing the diamagnetic response. We attribute thisto local lattice distortions associated with the intersti-tial Fe(II) which are likely to locally increase the elec-tronic correlations leading to a higher degree of carrierlocalization favoring magnetism in detriment of super-conductivity. On the other hand, superconductivity ap-pears to be not very sensitive to the structural disorderor mosaicity. In samples displaying the sharpest super-conducting transitions and a very clear diamagnetic sig-nal, we observe a mild upturn in the upper critical field

at lower temperatures consistent with the Farrel-Fulde-Larkin-Ovchinnikov instability. These samples displaymetallic resistivity suggesting also the formation of co-herent quasi-particles at lower temperatures in contrastto previous reports [43], and implying that a relativelymild excess of randomly distributed Fe(II) atoms may beenough to suppress the phase coherence. Finally, our es-timates of the inter-plane coherence length ξc ∼ 5.1 < 6A where c ≃ 6 A is the inter-planar lattice constant, isconsistent with the quasi-two-dimensional superconduct-ing fluctuations in the critical region (also observed byother groups[38, 39]), indicating that the superconduct-ing atomic Fe planes in this system may be Josephson-coupled.

ACKNOWLEDGEMENTS

The NHMFL is supported by NSF through NSF-DMR-0084173 and the State of Florida. L. B. is supported byDOE-BES through award de-sc0002613. JW, TG andTS acknowledge support from FSU.

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