Multiband behavior and non-metallic low-temperature state of KNaFeSe
We report evidence for multiband transport and an insulating low-temperature normal state in superconducting KNaFeSe with K. The temperature-dependent upper critical field, , is well described by a two-band BCS model. The normal-state resistance, accessible at low temperatures only in pulsed magnetic fields, shows an insulating logarithmic temperature dependence as after superconductivity is suppressed. This is similar as for high- copper oxides and granular type-I superconductors, suggesting that the superconductor-insulator transition observed in high magnetic fields is related to intrinsic nanoscale phase separation.
pacs:72.80.Ga, 74.25.F-, 74.81.-g, 74.70.Xa
After the discovery of LaFeAsOF with KKamihara () many efforts have been made to study the temperature dependence of the upper critical field, , of Fe-based superconductors since this provides valuable insight in the coherence length, anisotropy, electronic structure, and the pair-breaking mechanism. Binary -FeSe and Fe(Te,Se) (FeSe-11 type) as well as arsenic-deficient CuZrSiAs structure-type superconductors (FeAs-1111 type) feature a Pauli-limited and are well explained by the single-band Werthamer-Helfand-Hohenberg (WHH) model.LeiH (); LeiH1 (); Fuchs (); Kida () On the other hand, in most FeAs-1111 type, ternary pnictide (FeAs-122 type), and chalcogenide (FeSe-122 type) CuTlSe Fe-based superconductors can only be described by two-band models.Hunte (); Jaroszynski (); Baily (); Mun () Studies of the normal state below in both Cu- and Fe-based high- superconductors are rare since very high magnetic fields are required to suppress the superconductivity. Among the few exceptions are studies of LaSrCuO and BiSrLaCuO, where a logarithmic resistivity and a superconductor-insulator transition (SIT) have been observed in the normal-state region above and below .Ando (); Boebinger (); Ono () Similar studies in FeSe-122-type superconductors have not been available so far due to their air sensitivity and the demanding experimental conditions of pulsed-field experiments.
In this work, we report on results obtained for single-crystalline KNaFeSe with K. is well described by a two-band model. Moreover, when superconductivity is suppressed in high magnetic fields, the in-plane sample resistance follows as , suggesting a SIT, as commonly observed in granular superconductors.
The KNaFeSe single crystals used in this study were synthesized and characterized as described previously with a nominal composition of starting materials K:Na:Fe:Se = 0.6:0.2:2:2.Lei00 () The as-grown crystals were sealed in a Pyrex tube under vacuum (10 Pa), annealed at 400C for 3 hours, and then quenched in air in order to increase the superconducting volume fraction.Lei (); Ryu (); HanF () Powder x-ray diffraction (XRD) spectra were taken with Cu radiation ( nm) by a Rigaku Miniflex X-ray machine. The lattice parameters were obtained by refining XRD spectra using the Rietica software.Hunter () The elemental analysis was done using a scanning electron microscope (SEM). Magnetization measurements were performed in a Quantum Design MPMS-XL5. The ac magnetic susceptibility was measured with an excitation frequency of 100 Hz and field of 1 Oe. Electrical-resistivity measurements were conducted using a standard four-probe method in a PPMS-14. Pulsed-field experiments were performed up to 62 T using a magnet with 150 ms pulse duration and data were obtained via a fast data acquisition system operating with AC current in the kHz range. Contacts were made on freshly cleaved surfaces inside a glove box.
The powder XRD data (Fig. 1(a)) demonstrate the phase purity of our samples without any extrinsic peak present. The pattern is refined in the space groups and with fitted lattice parameters nm, nm and nm, nm, respectively, reflecting phase separation and small sample yield.Lazarevic (); Ryan (); Wang (); Liu (); Ricci (); Li () With Na substitution, the lattice parameter decreases while increases when compared to KFeSe, consistent with lattice parameters of NaFeSe.Guo (); YingTP () The average stoichiometry was determined by EDX, measuring multiple positions on the crystal. The obtained composition KNaFeSe suggests vacancies on both K and Fe sites. FeSe-122 superconductors feature an intrinsic phase separation into magnetic insulating and superconducting regions.Ryan (); Wang (); Liu (); Ricci (); Li () As shown in the SEM image of Fig. 1(b), KNaFeSe also exhibits a similar array of superconducting grains in an insulating matrix. The observed pattern is somewhat inhomogeneous [Fig. 1(b)] with sizes ranging from about several microns to probably several tens of nanometers,WangZ below our resolution limit. It would be of interest to investigate the local structure and electronic properties of KNaFeSe since Na substitution provides chemically induced pressure which might suppress the phase separation similar as for RbFeSe.Bendele ()
The investigated single crystal becomes superconducting at 20 K after and at 28 K before the annealing and quenching procedure [Fig. 2(a) main part and inset, respectively].Lei (); Ryu () For the quenched crystal, the superconducting volume fraction at 1.8 K increases significantly up to 72%, albeit with a reduction of . The post-annealing and quenching process results in a surface oxidation of some crystals which then dominates the magnetization signal. However, FeO is not visible in either of our laboratory or synchrotron X-ray studies.Lei (); Ryu (); HanF () The magnetic hysteresis loops (MHL) of the quenched KNaFeSe single crystal reflects the improvement in crystalline homogeneity since it is much larger and symmetric when compared to an as-grown sample [Fig. 2(b)] due to stronger pinning forces and bulk pinning.Lei () Also similar to KFeSe, there is an enhancement of the in-plane critical-current density calculated from the Bean model:Bean (); Gyorgy () , where , , and are the lengths of a rectangularly shaped crystal (). In view of the improved volume fraction and homogeneity, further investigations of the electronic transport properties were performed on the quenched crystal.
The resistance of an inhomogeneous sample contains contributions from both metallic () and nonmetallic () regions. At , due to superconductivity () the insulating part of the sample is short-circuited. The insulating regions have a several orders of magnitude higher resistivity than the metallic part;Shoemaker () hence, around and when in the high-field normal state . This is similar to the resistance of a polycrystalline sample in the presence of grain boundaries and in agreement with the observation that insulating regions do not contribute to the spectral weight in angular resolved photoemission data in the energy range near .YiM () In what follows below, we focus on the temperature-dependent sample resistance, .
The superconducting transition in is rather wide and shifts to lower temperatures in applied magnetic fields [Figs. 3(a-d). The shift is more pronounced for , which implies an anisotropic . The temperature-dependent upper critical fields shown in Fig. 3(c) were determined from the resistivity drops to 90%, 50%, and 10% of the normal-state value. It is clear that all experimental data feature a similar temperature dependence irrespective of the criteria used. All data for are above the expected values for the single band Werthamer-Helfand-Hohenberg (WHH) model (dotted lines). We proceed our further analysis using the 10% values, similar as done for LaFeAsOF.Hunte () The curves are linear for near and show an upturn at low T for [Fig. 3(e)]. The initial slope near for is much larger than for [Fig. 3(f) and Table I]. These slopes are similar to values for as-grown and quenched KFeSe.Mun (); Lei1 ()
There are two basics mechanisms of Cooper-pair breaking by magnetic field in a superconductor. Orbital pair breaking imposes an orbital limit due to the induced screening currents, whereas the Zeeman effect contributes to the Pauli paramagnetic limit of . In the single-band WHH approach, the orbital critical field is given by = -0.693.WHH () For KNaFeSe, this leads to 42(3) T for and 10(2) T for [Fig. 3(f)]. On the other hand, the Pauli-limiting field is given by , where is the electron-phonon coupling parameter.Orlando () Assuming = 0.5, which is a typical value for a weak-coupling BCS superconductor,Allen () is 32(1) T. This is larger than the orbital pair-breaking field for estimated above, yet smaller than the value for , which possibly implies that electron-phonon coupling is much stronger than for typical weak-coupling BCS superconductors.
The experimental data for lie above the expected values from WHH theory [Fig. 3(f)], suggesting that multiband effects are not negligible. In the dirty limit, the upper critical field found for the two-band BCS model with orbital pair breaking and negligible interband scattering is:Gurevich ()
where , is the digamma function, , and are diffusivities in band 1 and band 2, , and Wb is the magnetic flux quantum. , , and , where, , , and . and are pairing (intraband coupling) constants in band 1 and 2, and and quantify interband couplings between band 1 and 2. For , Eq. (1) simplifies to the one-band model (WHH) in the dirty limit.WHH () When describing our data by use of the two-band BCS model fitting, we consider two different cases, and , which imply either dominant intraband or dominant interband coupling, respectively. The solid lines in Fig. 3(f) are fits using Eq. (1) for and which indicates strong intraband coupling.Jaroszynski (); LeiH2 () The extrapolated is 38 T for and 150 T for . Further, the dashed lines in Fig. 3(f) show fits with and for strong interband couplingJaroszynski (); LeiH2 () that give 48 T for and 160 T for .
From these fits we obtain values of 0.063 and 0.021 for dominant intraband ( 0) and interband ( 0) coupling, respectively, i.e., largely different and implying different electron mobilities in the two bands. The upward curvature of is governed by ; it is more pronounced for . The large difference in the intraband diffusivities could be due to pronounced differences in effective masses, scattering, or strong magnetic excitations.Gurevich (); Jaroszynski () The fit results are not very sensitive to the choice of the coupling constants, yet they mostly depend on . This indicates either similar interband and intraband coupling strengths or that their difference is beyond our resolution limit. Our results are consistent with the data obtained on pure crystals, i.e., the large difference of electronic diffusivities for different Fermi surface sheets is maintained in the doped crystal.Gasparov () This is in agreement with the band-structure calculations that showed negligible contribution of K to the Fermi surface and density of states at the Fermi level.Kreisel (); Yan () On the other hand, we find no enhancement of the superconducting with Na substitution in KFeSe ( 30 K). This is somewhat surprising because NaFeSe and NaFeSe that crystallize in I4/mmm space group have ’s of 45 and 46 K.YingTP () The Na substitution might affect the magnetic order in phase separated KFeSe since the existence of a large magnetic moment in the antiferromagnetic phase was proposed to be important for the relatively high ’s.HuangMS ()
Due to the limited data points, it is difficult to unambiguously estimate for . Based on results reported for similar Fe-based superconductors, NdFeAsOF,Jaroszynski () (Ba,K)FeAs,Yuan () and KFeSe,Mun () shows a pronounced upward curvature for while it tends to saturate for . The real for might be smaller than we estimated. The calculated coherence lengths, using and based on the two-band BCS fit results, are similar to values obtained for as-grown and quenched KFeSe and are shown in Table I.Mun (); Lei1 ()
Superconductivity in KNaFeSe is completely suppressed above about 60 T for , allowing for a clear insight into the low-temperature electronic transport in the normal state (Fig. 4). Interestingly, we do not observe metallic transport below about 40 K implying that a superconductor-to-insulator transition (SIT) is induced in high magnetic fields. Kondo-type magnetic scattering is not very likely since a field of 62 T should suppress spin-flip scattering.Ando () A thermally activated semiconductor-like transport or variable range hopping (VRH) as occurring for Anderson localization is unlikely since the resistance in 62 T cannot be fit by , , with = 1/2, 1/3, 1/4, and .Mott (); Abrahams (); Gorkov () Instead, the resistance increases logarithmically with decreasing temperature in the normal state at 62 T as shown with the dashed line in Fig. 4. Hence, the SIT might originate from the granular nature of KNaFeSe. In a bosonic SIT scenario, Cooper pairs are localized in granules.Gantmakher (); BeloborodovRMP () When , virtual Cooper pairs form, yet they cannot hop to other granules when which induces the increase in resistivity as temperature decreases. The grain size can be estimated from , where is the average grain radius and nm is the average in-plane coherence length. The obtained nm is in agreement with the phase-separation distance. The bosonic SIT mechanism in granular superconductors predicts (‘inverse Arrhenius law’) in the superconducting region near the SIT when due to the destruction of quasi-localized Cooper pairs by superconducting fluctuations. Our data in 14, 20, and 30 T might be fitted with this formula (solid lines in Fig. 4). We note that near is non-monotonic, similar as for granular Al and LaSrCuO.Ando (); BeloborodovRMP (); Gerber ()
In summary, we reported the multiband nature of superconductivity in KNaFeSe as evidenced in the temperature dependence of the upper critical field and a SIT in high magnetic fields. Granular type-I but also copper-oxide superconductors are also intrinsically phase separated on the nanoscale.Strongin (); Imry (); Lang (); Zeljkovic () Hence, a SIT in high magnetic fields seems to be connected with the intrinsic materials’ granularity in inhomogeneous superconductors. This suggests that the insulating states found in cuprates as a function of magnetic fieldAndo (); Boebinger () or dopingFukuzumi () might involve Josephson coupling of nanoscale grains as opposed to quasi-one-dimensional metallic stripes bridged by Mott-insulating regions in the spin-charge separated picture.Emery ()
Acknowledgements.Work at Brookhaven is supported by the U.S. DOE under Contract No. DE-AC02-98CH10886 and in part by the Center for Emergent Superconductivity, an Energy Frontier Research Center funded by the U.S. DOE, Office for Basic Energy Science (C.P.). We acknowledge the support of the HLD at HZDR, member of the European Magnet Field Laboratory (EMFL). CP acknowledges support by the Alexander von Humboldt Foundation.
‡ hryu@bnlgov and email@example.com †Present address: European XFEL GmbH, Notkestrasse 85, 22607 Hamburg, Germany
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