Abstract In various FeTe1−xSex (x = 0–1), members ofthe 11-iron-pnictide superconductor family, the tempera-ture dependent resistivity ρ can be scaled into a universalcurve. It is found that the ρ(T ) dependences can be repro-duced by the expressions ρ(T ) = ρ0 − (c/T ) exp(− 2Δ
T) and
ρ(T ) = ρ0 + (c/T ) exp(− 2ΔT
) for x = 0–0.3 and 0.4–1.0,respectively. The scaling was performed using the energyscale 2Δ, the parameter c, and the residual resistivity ρ0 asscaling parameters. The compositional variation of the scal-ing parameters 2Δ and ρ0 has been determined. The exis-tence of a universal metallic ρ(T ) curve is interpreted as anindication of a single mechanism which dominates the scat-tering of the charge carriers in FeTe1−xSex (x = 0–1). Thus,the scaling of the normal-state properties seems to be a gen-eral feature not only for high-Tc cuprates but also for theiron-pnictides superconductor family.
Keywords FeTe1−xSex · Pnictides · Transport properties
1 Introduction
Recently, transition-metal oxypnictides composed by an al-ternate stacking of Ln2O2 layers and T2Pn2 layers (Ln: La,Pr, Ce, Sm, Nd; T: Fe, Co, Ni, Ru; Pn: P or As) have been
E. Arushanov · G. Fuchs · S.L. DrechslerLeibniz-Institut für Festkörper- und WerkstoffforschungDresden - IFW Dresden, Helmholtzstr. 20, 01069 Dresden,Germany
E. Arushanov · S. Levcenko (�)Institute of Applied Physics, Academy of Sciences of Moldova,2028, Chisinau, Moldovae-mail: [email protected]
identified as novel high-Tc materials [1–4]. Their supercon-ductivity was discovered 5 years ago with a transition tem-perature Tc of as high as 26 K in LaO1−xFxFeAs [1]. Spir-ited search by the experimentalists has eventually led to anincrease of Tc up to 55 K for another member of this fam-ily of compounds, namely SmFeAsO0.9F0.1 [4]. Shortly af-terward, another family of Fe-based compounds, AFe2As2,(A = Ca, Sr, Ba, or Eu) was also found to be supercon-ducting upon hole doping on the A site with a maximumof Tc = 38 K [5–7].
So far, several tens of superconductors in limited typesof parent materials such as so-called 1111 (LaFeAsO), 122(BaFe2As2), and 111 (LiFeAs) system, have been synthe-sized. The material Fe1+xSe, a member of a simple 11 Fe-based superconductors, was found to be superconductive atapproximately 8 K [8]. The appearance of superconductiv-ity in the FeSe system indicates that Fe2X2 (X = P, As, andSe) layers are essential for the superconductivity in these Fe-based superconductors. Recently, the Fe(Se, Te) system hasbeen intensively investigated, however, the Fe(Se, Te) sys-tem is essentially different from the end member FeSe inthe sense that a magnetically ordered state and a remarkablylarge γ value (∼39 mJ/mol K2) have been found [9]. Underpressure, in the FeTe or FeTe1−xSex system, the transitiontemperature was improved to approximately 37 K [10].
It has been suggested that the 11 phase presents sev-eral peculiarities as compared to the other phases, namely anonparallel orientation of anti-ferromagnetic ordering vec-tor and nesting vector, incommensurate antiferromagneticfluctuations appearing for large Se content and no clear sig-natures in favor of a spin-density-wave (SDW) gap [11].However, a recent theoretical work has suggested that inFe(Te, Se), with increasing Se substitution, the same type ofmagnetic ordering as that of other Fe-based superconductorfamilies develops [12].
The phase diagram of Fe1+δTe1−xSex with a low excess-Fe concentration was established [10]. The tetragonal–orthorhombic structural transition observed in FeSe is sup-pressed with increasing Te concentration. The highest Tc
appears at the tetragonal phase near x = 0.5. With further in-crease of Te content, the Tc decreases and the antiferromag-netic ordering accompanying the tetragonal–monoclinic dis-tortion appears, and the bulk superconductivity disappears.
The temperature dependence of the resistivity, thermo-electric power, susceptibility, and heat capacity data havebeen reported for FeTe1−xSex (x = 0.0–0.5 [11, 13–15] andx = 0.5 [16, 17]). Also, scanning tunnelling spectroscopymeasurements have been reported for these compounds [18].Angle-resolved photoemission spectroscopy of the iron-chalcogenide superconductor Fe1.03Te0.7Se0.3 has been per-formed to investigate the electronic structure relevant tosuperconductivity. A hole-like Fermi surface (FS) and anelectron-like FS at the Brillouin zone center and corner, re-spectively, was observed as well as similarity of low-energyelectronic excitations between iron-chalcogenides and iron-arsenides [19].
More attention has been paid to end-point compounds,especially to FeSe [9, 20–24]. Density functional calcula-tions of the electronic structure, Fermi surface, phonon spec-trum, magnetism, and electron-phonon coupling for the su-perconducting phase FeSe, as well as the related compoundsFeS and FeTe was reported [20]. It was found that the Fermi-surface structure of these compounds is very similar to thatof the Fe-As based superconductors, with cylindrical elec-tron sections at the zone corner, cylindrical hole surface sec-tions, and depending on the compound, other small holesections at the zone center. Both FeSe and FeTe show spin-density wave (SDW) ground states. The normal state of theiron chalcogenide superconductors shows a range of inex-plicable features. Both a bad metallic resistivity, characteris-tic pseudogap features and the proximity to insulating statemark these systems as correlated non-Fermi liquid metals[21, 22].
An insight into the normal state might be in principlehelpful also for the understanding of the superconductivitymechanism itself [25]. The evolution of the normal transportproperties of the high-Tc superconductor cuprates (HTSCs)and that of other unconventional superconductors with tem-perature and doping still retain some features that are notyet understood. Clues which might help to solve some ofthe remaining questions can be obtained from the tempera-ture dependent scaling of the normal state transport proper-ties [26]. The scaling analysis of experimental data in HTSCis a simple but powerful tool in elucidating the underly-ing physics without invoking a specific model. In the nor-mal state, if the pseudogap is a predominant energy scalecontrolling low energy excitations, then the low-temperaturebehavior of any measurement physical quantity should sat-isfy a doping independent scaling law [27]. It has been
shown that the temperature-dependent resistivity ρ(T ) andthe Hall coefficient RH (T ) of YBa2Cu3Ox , SmBa2Cu3Ox ,and La2−xSrxCuO4 can be scaled [26–33]. A scaling be-havior on the basis of certain physical models was reportedby Levin and Quader [34] for Y1−xPrxBa2Cu3O7−δ . Fur-thermore, it has been shown that the superlinear ρ(T ) de-pendence observed in underdoped cuprates between Tc andT ∗ (with T ∗ as the crossover temperature from the super-linear to a linear ρ(T ) dependence) can be described byan exponential expression for ρ(T ) derived for quantumtransport in a 1D striped material [29]. Recently, the ρ(T )
dependence for LaO1−xFxFeAs, SmO1−xFxFeAs [35–37],SrFe2−xNixAs2 [38], and Ba(Fe1−xCox)2As2 [39–42] wasdescribed by a power-law fit ρ(T ) = a + bT n [35–37] andby the exponential fit [35, 38–43].
In this work, we report the scaling of the normal-statetransport properties of FeTe1−xSex (x = 0.0–1.0) supercon-ductors in a broad temperature range from Tc up to 300 K byusing the exponential fit [35, 38–40] which works in a widertemperature interval than the above mentioned power-law fit[35, 41].
This new scaling approach was earlier successfully ap-plied to 1111 [35] and 122 iron oxypnictides [38–40] andmight provide some important guidelines for theoreticalmodels proposed to describe beside the superconductivityin future also the normal-state properties of the new high-Tc
superconductors.
2 Results and discussions
A commonly adopted approach in the scaling analysis is toassume that by normalizing both the measurement quantityF(T ) and the temperature by the corresponding values at asample dependent characteristic temperature T ∗, then all theexperimental data should fall onto a single curve describedby the scaling function [27]. In fact, the ρ(T ) and RH (T )
data of YBa2Cu3Ox , SmBa2Cu3Ox , and La2−xSrxCuO4
have been successfully scaled [26, 28–33]. The temperaturewas rescaled with a temperature T ∗ defined as the tempera-ture above which ρ(T ) shows a linear dependence [28], orwith Δ where Δ is estimated on the basis of an analysis ofthe nonlinear part of ρ(T ) [26, 29, 30], or with the tem-perature TH , temperature at which RH (T ) changes from anessentially temperature-independent (T > TH ) to a rapidlyincreasing behavior (T < TH ) [31, 32] or with TR , deter-mined from the analysis of the RH exponential temperaturedependence [33]. The latter is correlated to an activation en-ergy ER that can be interpreted as the difference betweenthe Fermi level and the saddle-point position observed in theelectronic band structure of a CuO2 plane.
Gor’kov and Teitel’baum [44] presented the Hall effectdata for a number of carriers in La2−xSrxCuO4 as the sum
J Supercond Nov Magn (2012) 25:1753–1759 1755
of two components: a temperature independent term, whichis due to external doping, and the thermally activated contri-bution. The activation energy for thermally excited carrierswas found to equals the energy between the Fermi surface“arc” and the band bottom, as seen in angle-resolved pho-toemission spectroscopy experiments.
We analyzed the scaling behavior of the resistivity forFeTe1−xSex (x = 0.00–0.50; 1.00). We apply the scalingmethods reported in [26, 29, 30, 35], and [38–40]. Our anal-ysis is based on the data recently presented in [11, 14],and [24].
In Figs. 1(a) and 1(b), the temperature dependence of theresistivity for FeTe1−xSex both for polycrystalline samples(x = 0.00–0.50) and single crystals (x = 0.1, 0.4, 0.5 and1.0) are shown. For the latter, the in-plane resistivity is pre-sented. Superconductivity appears in these samples exceptfor x = 0 − 0.075. The values of Tc for single- and poly-crystalline samples are comparable. As for 0 ≤ x ≤ 0.1, theresistivity shows a semiconductor-like behavior at high tem-peratures, drops at T0 of about 75, 65, 55, and 50 K forx = 0, 0.025, 0.05, and 0.075, respectively, and then exhibitsa metallic behavior at low temperatures. The discontinuouschange in resistivity probably is due to the structural phasetransition accompanied by the magnetic transition both forx = 0 [14] and x = 0.025, 0.05, and 0.075.
Samples with x = 0.10–0.30 show semiconducting-likebehavior at temperatures above Tc. Samples with x = 0.4,0.5, and 1.0 show an increasing resistivity at temperaturesabove Tc with a tendency to saturation at high temperatures.
We have found that the ρ(T ) dependences for FeTe1−x
Sex can be reproduced by
ρ(T ) = ρ0 − (c/T ) exp
(−2Δ
T
), (1)
and
ρ(T ) = ρ0 + (c/T ) exp
(−2Δ
T
)(1a)
for samples with x = 0–0.3 and 0.4, 0.5, 1.0, respectively,as shown in Figs. 1(a) and 1(b). Whereas for the compoundswith 0.1 ≤ x ≤ 1.0, the ρ(T ) data can be fitted by Eq. (1)or (1a) in the whole temperature range between Tc and300 K; this fit is restricted for the underdoped compounds(0 ≤ x ≤ 0.1) to the temperature range between T0 and300 K. It should be mentioned that Eq. (1a) was also appliedfor the analysis of resistivity data of Ba1−xKxFe2As2 [40].
We also analyzed the scaling behavior of the resistivityfor Fe1+δTe0.7Se0.3 with different values of δ. It was foundthat in Fe1+δ Te0.7Se0.3 the resistivity value at 300 K in-creases almost linearly with δ, demonstrating that the nom-inal Fe content is a good parameter to represent the ac-tual Fe content [11]. For δ = −0.10 and −0.05, the neg-ative temperature slope at room temperature turns into a
Fig. 1 Temperature dependence of the resistivity for (a) polycrys-talline FeTe1−xSex ; (b) FeTe1−xSex single crystals and (c) Fe1+δTe0.7Se0.3. The solid line represents a fit using Eq. (1) or (1a) as mentionedin the text
metallic dependence in a temperature range above Tc, whilefor δ = 0,+0.05, and +0.10, a resistivity upturn is ob-served, roughly described by a Kondo-like − ln(T ) depen-dence [11]. We have found that the ρ(T ) dependence forFe1+δTe0.7Se0.3 with δ = 0,0.05,0.10, and −0.05,−0.10can be reproduced by Eq. (1) or (1a) (see Fig. 1(c)).
The obtained values of the fitting parameters ρ0 and 2Δ
are presented in Table 1. The characteristic energy 2Δ showsa minimum value at x = 0.5 which corresponds to the high-est Tc value and an increase (up to about 3 times) for de-creasing x down to 0. We found that the characteristic en-
1756 J Supercond Nov Magn (2012) 25:1753–1759
Fig. 2 (a) 2Δ vs. Se content x and (b) 2Δ vs. Fe content δ
ergy 2Δ drops roughly linearly with doping (see Fig. 2(a)).A similar variation of 2Δ and/or the characteristic tempera-ture is observed in SrFe2−xNixAs2 [38], YBa2Cu3Ox [29]and La2−xSrxCuO4 [32] as well as in 12 different membersof the cuprate family (see Fig. 11 in [27]) and consistentwith the doping dependence of their pseudogap observed byARPES, tunneling, and other measurements [27].
The variation of the characteristic energy 2Δ with theiron content δ in Fe1+δTe0.7Se0.3 is shown in Fig. 2(b). Forexcess Fe content, 2Δ decreases up to about 1.5 times forincreasing δ up to 0.1. An even stronger suppression of 2Δ
by about a factor of three is found for samples with Fe deficit(δ ∼ −0.05, . . . ,−0.1).
In Figs. 3(a) and 3(b), the scaled ρ(T ) curve is plottedfor the FeTe1−xSex samples with 0 ≤ x ≤ 1.0 and for theFe1+δTe0.7Se0.3 samples with δ from −0.1 to +0.1, respec-tively. According to [40], the temperature is rescaled withthe characteristic energy 2Δ and the resistivity is plotted as
ρ0−ρρ0−ρ2Δ
or ρ−ρ0ρ2Δ−ρ0
for samples with x = 0–0.3, δ = 0–0.1,and x = 0.4–1.0, δ = −0.5 ÷ −0.1, respectively, where ρ2Δ
is the resistivity at T = 2Δ. All the ρ(T ) curves collapseonto one universal curve.
The residual resistivity ρ0 has been also extracted as afitting parameter. The zero-field data show that the sam-ples studied are rather poor conductors having relatively lowresidual resistivity ratios ρ290/ρ0 (0.7 to 3.6 for FeTe1−xSex ,
Fig. 3 Scaling analysis on the temperature dependence of the resistiv-ity of various (a) FeTe1−xSex , 0 ≤ x ≤ 1.0 and (b) Fe1+δTe0.7Se0.3,δ = −0.1 ÷ +0.1 The temperature is rescaled with 2Δ (an energyscale) and the resistivity is given by ρ0−ρ
ρ0−ρ2Δor ρ−ρ0
ρ2Δ−ρ0(as mentioned
in text) in which the extrapolated residual resistivity ρ0 has been sub-tracted and ρ2Δ is the resistivity at T = 2Δ
0 ≤ x ≤ 1.0) compared to pure normal metals whereρ290/ρ0 ∼ 1000 (Table 1). This agrees with previous find-ings on all superconducting high-Tc cuprates and indicatestheir relative impure state [29].
Following [29, 30, 35], and [38], we point out that thescaling behavior of ρ(T ) observed in FeTe1−xSex , (x =0–1.0) and Fe1+δTe0.7Se0.3 (δ = −0.1 + 0.1) suggests thatthe transport properties in the studied samples in the abovementioned interval of x are dominated by the same scatter-ing mechanisms. Taking into account some similarity of theobserved scaling behavior with that reported for cuprate su-perconductors [29, 30] as well as for 1111 [35] and 122 Fe-based pnictide superconductors [38–40], we could assumethat the dominant scattering mechanisms are probably alsoof magnetic origin.
It should be mentioned that the observed negative tem-perature slope of resistivity of FeTe1−xSex is likely due toKondo scattering by the localized magnetic moments of ex-cess Fe ions [11]. The scatterer introduced by the excess Fe,which is responsible for the increase of ρ(300 K), act asmagnetic scatterer for the Kondo effect as well [11].
In the normal state, if the pseudogap is a predominantenergy scale controlling low energy excitations, then the
J Supercond Nov Magn (2012) 25:1753–1759 1757
Table 1 Residual resistivity ρ0, the ratio ρ290/ρ0 and the scaling pa-rameters 2Δ
SamplesFeTe1−xSex
ρ0 (m� cm) ρ290/ρ0 2Δ (K) T ac (K)
x = 0.00 1.479 0.77 450 –
x = 0.025 1.801 0.75 424 –
x = 0.05 1.374 0.81 394 10.6
x = 0.075 1.559 0.82 396 10.7
x = 0.1 1.446 0.83 360 11.6
x = 0.1b 0.93 0.47 301 11.3
x = 0.15 1.869 0.80 402 12.1
x = 0.20 1.910 0.85 454 13.7
x = 0.30 1.819 0.77 301 14.1
x = 0.40b 0.269 1.25 250 14.2
x = 0.50 0.973 1.42 160 14.9
x = 0.50b 0.54 1.19 200 14.0
x = 1.0b 0.943 3.61 394 8.1
a The Tc values were taken from [11, 14], and [24] for FeTe1−xSex ,0 ≤ x ≤ 0.5, and x = 1.0, respectivelyb Single crystals [14, 24]
low-temperature behavior of any measured physical quan-tity should satisfy a doping independent scaling law [27].Our observation of a doping independent scaling law inthe normal state of pnictide superconductors studied hereis similar to that observed in cuprates [27], and recentlyin 1111 [35] and 122-iron-pnictide superconductor [38–40]could be probably used as indication that a gap-like featureis the reason for a predominant energy scale which controlsthe low energy excitations.
The possible existence of a pseudogap in LaO1−xFxFeAsand SmFeAsO1−xFx 1111 pnictide compounds has been re-ported by Liu et al. [45], Jia et al. [46], and Ou et al. [47]on the base of high resolution photoemission measurements.Two superconducting gaps (of about 12 meV on the twosmall hole-like and electron-like Fermi surface (FS) sheets,and 6 meV on the large hole-like FS) were observed byDing et al. [48] in the hole doped Ba0.6K0.4Fe2As2 using ahigh-resolution angle-resolved photoelectron spectroscopystudy. Both gaps, closing simultaneously at the bulk tran-sition temperature (Tc), are nodeless and nearly isotropicaround their respective FS sheets. In the electron dopedBa(Fe1−xCox )2As2, the most of the experiments includ-ing point contact measurements reveal in a quite broadenedspectra only a single gap with a strong coupling strength.The high precision ARPES measurements on this systemidentified two gaps but very close to each other, both point-ing to a strong coupling regime with 2Δ/kTc ≈ 5 and 6,respectively [49] or to the vicinity of a peak in the electronicdensity of states in the presence of antiferromagnetic spinfluctuations.
Recently, the resistivity data of 11 [11] and 1111 [11, 35]families of Fe-based superconductors were analyzed in apseudogap framework. Two characteristic temperatures Tflex
and T ∗ have been identified [10]. These temperatures corre-spond to those at which abrupt changes in the temperaturebehavior of Hall resistance and of Seebeck coefficient oc-cur, suggesting that they are signatures of pseudogaps open-ing in the density of states. The direct correlation betweenthese characteristic temperatures and the superconductingtransition temperatures suggests that the pseudogap and thesuperconducting state originate from the same mechanism.Scaling procedures of resistivity curves confirm such pro-portionality [11].
Scanning tunneling microscopy measurements on Fe(Te,Se) crystals have shown a kink at 300 meV, possiblyattributed to a pseudogap [50]. Incoherent pseudo-gaplike low-energy features in angle-integrated photoemission(PES) was reported for FeSe [9, 19]. Susceptibility andPES data show up the normal state pseudogap (PG) inFeSe1−xTex [21]. Theoretical papers [21] and [51] reportthat FeSe displays a pseudogap in the LDA density of states.An inflection point near 110 K observed at temperature de-pendence of the resistivity is possibly due to excitations ofthe pseudogap ground state [23].
Anyhow, the origin of the large gap values needs furtherexperimental and theoretical studies [47]. Whether it can becaused by (i) local SDW fluctuation or (ii) CDW (chargedensity wave)/BOW (bond order wave) fluctuations sup-ported by a strong enough electron-boson coupling and spe-cial intersite Coulomb interactions. Fluctuations of a meso-scopically heterogenous phase separation state like the well-known stripe state in cuprates might involve features of allcomponents mentioned above.
3 Conclusions
We have demonstrated that the zero-field normal-state re-sistivity of FeTe1−xSex (0 ≤ x ≤ 1.0), a member of the11-iron-pnictide superconductor family, can be scaled ontoa single universal curve for various levels of doping. It isworth mentioning that in the case of cuprates the resistivityscales only in the underdoped regime [27–31]. In 11 pnic-tides studied, the scaling of the resistivity is observed bothin the undoped, underdoped, and optimally doped regimes.
The scaling method used here is based on the assump-tion that the ρ(T ) dependence of FeTe1−xSex and of Fe1+δ
Te0.7Se0.3 can be reproduced by the expressions ρ(T ) =ρ0 − (c/T ) exp(− 2Δ
T) and ρ(T ) = ρ0 + (c/T ) exp(− 2Δ
T)
for the compositions 0 ≤ x ≤ 0.3 (δ = 0–0.1) and x =0.4–1.0 (δ = −0.05 ÷ −0.1), respectively.
Furthermore, the energy scale 2Δ and the residual resis-tivity ρ0 are suitable scaling parameters. An excellent scal-ing of the normal-state resistivity for material studied has
1758 J Supercond Nov Magn (2012) 25:1753–1759
been observed. The existence of a universal metallic ρ(T )
curve is interpreted as an indication of a single mechanismwhich dominates the scattering of the charge carriers inFeTe1−xSex , 0 ≤ x ≤ 1.0. The results obtained are in goodagreement with respect to the presence of a characteristic en-ergy 2Δ which resembles the pseudogap feature in cuprates.
The physical nature of this gap like feature remains un-clear at present. Among other possibilities, at least three sce-narios are worth to be studied theoretically in more detail.(i) A long-range Coulomb interaction disorder related fea-ture. (ii) A pairing mechanism related pseudo-gap as dis-cussed for the cuprates and (iii) a band structure relatedfeature from a band slightly below the Fermi energy. Also,a corresponding study of other less two-dimensional ironpnictides of the 111 families is of considerable interest andmight be helpful to discriminate between the proposed sce-narios.
A comparison with recent observation in cuprates, 1111-and 122-iron-pnictide superconductors indicates that scal-ing of the normal-state properties is a general feature notonly for high Tc cuprates, but also for the iron-pnictides su-perconductor family in both undoped, under and overdopedregimes.
Acknowledgements One of us (E.A.) would like to thank the DFGfor financial support and the IFW Dresden for hospitality. S.L.D.thanks the “Pakt for Forschung” for funding.
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