Multi-band Superconductivity in the Chevrel Phases SnMo6S8 and PbMo6S8
A.P. Petrović, R. Lortz, G. Santi, C. Berthod, C. Dubois, M. Decroux, A. Demuer, A.B. Antunes, A. Paré, D. Salloum, P. Gougeon, M. Potel, Ø. Fischer
MMulti-band Superconductivity in the Chevrel Phases SnMo S and PbMo S A.P. Petrovi´c , R. Lortz , G. Santi , C. Berthod , C. Dubois , M. Decroux , A. Demuer ,A.B. Antunes , A. Par´e , D. Salloum , P. Gougeon , M. Potel , and Ø. Fischer DPMC-MaNEP, Universit´e de Gen`eve,Quai Ernest-Ansermet 24, 1211 Gen`eve 4, Switzerland Department of Physics,The Hong Kong University of Science & Technology,Clear Water Bay, Kowloon, Hong Kong Laboratoire des Champs Magn´etiques Intenses CNRS,25 rue des Martyrs, B.P. 166,38042 Grenoble cedex 9, France Sciences Chimiques, CSM UMR CNRS 6226,Universit´e de Rennes 1, Avenue du G´en´eral Leclerc,35042 Rennes Cedex, France (Dated: November 8, 2018)Sub-Kelvin scanning tunnelling spectroscopy in the Chevrel Phases SnMo S and PbMo S re-veals two distinct superconducting gaps with ∆ = 3 meV, ∆ ∼ = 3.1 meV,∆ ∼ predominantlyseen when scanning across unit-cell steps on the (001) sample surface. The spectra are well-fittedby an anisotropic two-band BCS s -wave gap function. Our spectroscopic data are confirmed byelectronic heat capacity measurements which also provide evidence for a twin-gap scenario. PACS numbers:
Among the vast zoo of poorly-understood supercon-ductors, Chevrel Phases (CP) stand out for their highupper critical fields H c , many of which exceed thePauli limit [1]. These materials were first synthesisedin 1971 [2] and enjoyed a wealth of attention in the early1980s. Unfortunately, the discovery of the cuprate super-conductors largely swept CP under the laboratory carpet,despite a lack of detailed understanding of their large H c values. A multi-band scenario (incorporating strong-coupling effects and enhanced spin-orbit scattering) wassuggested as a possible explanation [3], but until now thishypothesis has remained experimentally unexplored.Multi-band superconductivity was first proposed 50years ago as a potential avenue for increasing criticaltemperatures [4]. Interband scattering between non-degenerate bands at the Fermi level E F enables supercon-ductivity to be induced in bands which may not directlyparticipate in the pairing mechanism, thus increasing theeffective density of states (DoS) and hence the transi-tion temperature T c . However, with the exception ofsome transition metal calorimetric data [5] and tunnellingin doped SrTiO [6], multi-band superconductivity re-mained a largely theoretical concept until the discovery ofMgB in 2001 revived interest in the field [7]. In this ma-terial, superconductivity in the quasi-2D σ -band inducescoherence in the quasi-3D π -band with an unexpectedlyhigh T c of 39 K. The two gaps have been imaged by a va-riety of techniques, including local spectroscopic [8] andbulk thermodynamic approaches [9]. Recently, evidencehas been found for multi-band superconductivity in boro-carbides [10], sesquicarbides [11], skutterudites [12] and, perhaps most interestingly, pnictides [13]. CP and pnic-tides share similar anomalously large values of H c and donot follow standard Werthamer-Helfand-Hohenberg the-ory. However, in contrast with the pnictides, the Mo X ( X = S, Se) Chevrel cluster does not exhibit any intrin-sic magnetism or competing order. This greatly simpli-fies the analysis and interpretation of its low-temperatureproperties, particularly any multi-band effects. Band-structure calculations have indicated the presence of twoMo d bands at E F in CP [14]: in this Letter we presentlocal spectroscopic evidence for two distinct supercon-ducting gaps in SnMo S and PbMo S . These data aresupported by specific heat measurements displaying clearsignatures of a second gap.We have chosen to focus on SnMo S and PbMo S since these two materials have the highest values for T c and H c within the CP family: 14.2 K, ∼
40 T and14.9 K, >
80 T respectively [15]. Single crystals of eachcompound with typical volume 1 mm were grown at1600 ◦ C by a chemical flux transport method using sealedmolybdenum crucibles. Their high purity was confirmedby AC susceptibility (ACS) yielding ∆ T c = 0.1 K forSnMo S and 0.3 K for PbMo S . Local spectroscopy(STS) was performed on room-temperature-cleaved sam-ples with a home-built helium-3 scanning tunnelling mi-croscope in high-vacuum ( < − mbar), using a lock-inamplifier technique. Heat capacity measurements werecarried out at the Grenoble High Magnetic Field Labo-ratory with a high-resolution microcalorimeter using the“long relaxation” technique [16] and in Geneva using aQuantum Design TM PPMS. a r X i v : . [ c ond - m a t . s up r- c on ] J un The first hint of a two-band order parameter arisesfrom fast spectroscopic traces over several tens ofnanometers in the (001) plane of each material (Fig. 1).The corresponding topography in SnMo S shows atom-ically flat terraces separated by steps of size 12 ± S are of rather lower quality with an RMS rough-ness of ∼ ∼ ± E F .This confirms the presence of states within the large gap.Such a dramatic spectral variation as a function of thelocal topography has not previously been observed in anyother superconductor. It may therefore be natural to sug-gest that the isolated appearance of these multi-gap sig-natures at unit cell steps could be due to a surface boundstate or defect. However, a localised state would not dis-play the particle-hole symmetry of the peaks we observe.We have imaged a large number of separate unit cell stepsand a second gap is consistently observed upon scanningacross them. Another explanation for the double-gapbehaviour could be the proximity effect inducing weaksuperconductivity in a metallic surface layer [17]. How-ever, the small gap induced would vary strongly with thethickness of the surface metallic layer. Apart from thefact that measurements are performed on freshly-cleavedsamples, thus rendering any surface layer deposition im-plausible, a layer of metallic impurities would not be ex-pected to have a uniform thickness. This would causesubstantial variation in the size of the induced gap andan extremely high zero-bias conductance (ZBC), both ofwhich are incompatible with our data.In Figure 2 we display a range of spectra with fits us-ing a multi-band model. The Bardeen-Cooper-Schrieffer(BCS) quasiparticle density of states for an anisotropic s -wave n -band superconductor may be written as N ( ω ) = n (cid:88) j =1 N j π (cid:90) π Re ( ω + i Γ j )sign( ω ) dθ (cid:113) ( ω + i Γ j ) − ∆ j F j ( θ ) (1)where N j is the contribution of band j to the DoS at E F , Γ j the scattering rate due to lifetime effects, ∆ j the magnitude of the gap within band j and F j ( θ ) = a j + (1 − a j ) cos θ measures the anisotropy of the corre-sponding gap with 0.5 < a j <
1. We include the temper-ature and the experimental smearing (0.3 meV) before
FIG. 1: (a) Zero-field 35nm trace on SnMo S taken at T = 0.4K, junction resistance R T = 0.03 GΩ. (i) Topographyshowing double unit-cell steps; (ii) spectroscopic trace; (iii,iv)individual spectra taken on a flat terrace (1) and above a unit-cell step (2). (b) Zero-field 40nm trace on PbMo S taken at T = 0.5K, R T = 0.015 GΩ. (i) Spectroscopic trace; (ii) averagespectrum from entire trace; (iii) topographic variation. Alldata are raw and unaveraged. performing least-squares fits to our data with N j , ∆ j , F j and Γ j as free parameters. Note that the spectral back-grounds between ± S produce homoge-neous spectra (Fig 2(a)) which may be fitted using onlya single band (i.e. n =1 in (1)). There is a slight deterio-ration in the fit quality at low energy, which is attributedto a very small contribution from the second band. Incontrast, Fig. 2(b) shows the average of around 50 spec-tra acquired above a unit cell step. There is clearly a FIG. 2: (a-c) SnMo S spectra and fits taken at 0.4 K, R T = 0.03 GΩ. (d-e) PbMo S spectra and fits taken at 0.5 K, R T = 0.015 GΩ. (f) PbMo S spectrum taken at 1.9 K, R T = 0.025 GΩ from [18]. See text for details and table I for fitparameters. significant contribution from the smaller gap, necessi-tating a two-band fit. Similar fits are carried out onspectra from a flat zone and a broad step in PbMo S and the parameters obtained listed in Table I. We find2∆ /k B T c ∼ is 30-40 %larger in PbMo S than SnMo S . In both materials thegap anisotropies are similar: a small anisotropy in H c ( (cid:15) = 0.67) has been observed in PbMo S [3], but withthe present data we are unable to judge whether this isdue to the anisotropy in ∆ or ∆ . We believe it unwiseto draw quantitative conclusions on the symmetry of ∆ ,since our experiment has a finite resolution imposed bya 0.3 meV broadening from the lock-in. However, anyinterband scattering will preclude a pure d -wave orderparameter in ∆ due to the dominant isotropic s -wavecomponent in ∆ .Previous STS experiments on PbMo S provided ev-idence for low-energy excitations within the supercon-ducting gap, but lacked sufficient resolution to distin-guish two separate gaps. This is due to three factors:sample age, temperature and environment. In [18], mea-surements were performed on old crystals at 1.9 K in anexchange gas, compared with freshly-grown samples at0.4-0.5 K and high vacuum in the present work. The in-creased thermal broadening at 1.9 K blurs the two gaps,though this should not be sufficient to render the smallergap invisible. The major factor here is a deteriorationin the sample surface due to the exchange gas environ-ment. It is well-known that in a two-band superconduc-tor, interband scattering due to impurities mixes the twogaps and reduces T c , resulting in an effective single-bandanisotropic superconductor in the dirty limit. This wasfirst predicted for MgB [19, 20] and later observed in TABLE I: Superconducting gap parameters and relative DoScontributions from tunnelling (STS), heat capacity (HC) andAC susceptibility (ACS) data. Both gaps ∆ , are measuredin meV. Γ , ≤ SnMo S PbMo S technique bulk bulk T c ACS 14.2 ± ± H c HC 42 ± ± γ HC 6.4 ± − K − ± − K − ∆ HC 3.06 ± ± HC 0.86 ± ± N HC 96 ±
2% 90 ± N HC 4 ±
2% 10 ± STS 2.92 ± ± ± ± STS – 1.05 ± ± ± a STS 0.85 ± ± ± ± a STS – 0.91 ± ± ± N STS – 62 ±
4% 90 ±
4% 66 ± N STS – 38 ±
4% 10 ±
4% 34 ± irradiated samples [21]. However, due to extremely weakscattering between σ and π bands, the single band limitis never reached in MgB . This may not be the casefor CP: Fig. 2(c) displays a SnMo S spectrum from aterrace after 3 months of measurements comprising nu-merous thermal and magnetic cycles. It is qualitativelysimilar to the results of [18] (shown in Fig. 2(f)), provid-ing good evidence for low-energy states within the largegap, but does not display a distinct smaller gap. Thisis consistent with the presence of strong interband sur-face scattering. The ZBC is also rather high in both (c)and (f), which we attribute to a decrease in the super-fluid density due to enhanced pair-breaking from inelasticscattering.Upon increasing the temperature the large gap is grad-ually reduced and closes at the bulk T c determined byACS. No pseudogap is visible above T c , confirming thatsuperconductivity arises from a metallic ground state andhence justifying the use of a BCS model to fit the spec-tra. In Fig. 3 we have plotted the variation of the largegap ∆ with temperature for each compound, with thetheoretical BCS weak-coupling s -wave curve for compar-ison. A small kink is visible within each curve (shaded FIG. 3: Variation of ∆ ( T ) in (a) SnMo S and (b) PbMo S .The gap was determined by fitting with a BCS single-bandanisotropic s -wave model for simplicity and all spectra wereacquired on a flat terrace. areas). Similar features have been observed for the π -band (smaller) superconducting gap in MgB and origi-nate from interband scattering “stretching” the effective T c of the weakly-coupled π band to the bulk T c . Wesuggest that in CP a small contribution from a weakly-coupled band “stretches” the intrinsic T c of a strongly-coupled band (which provides the majority of the DoS)to the measured bulk T c . The position of the kink athigher energy and lower temperature in PbMo S com-pared with SnMo S is consistent with our observationthat band 2 is more strongly-coupled in PbMo S . Wehypothesise that this may be the key to PbMo S hav-ing a significantly higher H c than SnMo S , althoughfurther experiments will be required for confirmation.It is instructive to complement our STS measurementswith bulk thermodynamic (HC) data, in order to con-clusively rule out any spurious surface effects being re-sponsible for ∆ . Figure 4 (a) and (b) display the elec-tronic heat capacity C elec in SnMo S and PbMo S : thisis measured by subtracting the HC in an applied field H = 28 T from the zero-field data C . To eliminatethe effect of fluctuations above T c in high field, we limitour data to T > . T c (28T), where T c (28T) = 4.4 Kand 9.3 K in SnMo S and PbMo S respectively. InCP there is a large contribution to the lattice HC C latt from a low-energy Einstein phonon due to vibrations ofthe cation between the Mo X clusters: it is thereforenot possible to calculate C latt and hence extract C elec using the conventional Σ nj =1 B j +1 T j +1 model. How-ever, the Sommerfeld constant γ may still be calculatedusing entropy considerations (see Table I). We find that γ / T c = 0.45 mJgat − K − in each compound, suggestingthat T c scales with the DoS at E F . Using a two-band α -model [22] we have performed fits to C elec and sum-marise our results in Table I. For both gaps, the valuesof 2∆/ k B T c from our STS data agree perfectly with thosefrom HC experiments. While it is not possible to quan-titatively compare our STS-measured N j (which also de-pends on the tunnelling matrix element) with the bulk N j , the trends observed by each technique ( N >N ) arequalitatively in agreement.The final signature of 2-band superconductivity is pro-vided by the low-temperature variation of C elec ( H ) ineach material. In a single-band BCS s -wave supercon-ductor γ ( H ) should be linear. However, at T = 0.35 Kwe observe bends in C elec ( H ) at H x = 2.8 ± ± S and PbMo S respectively, remi-niscent of the low-field behaviour of MgB . Extrapolat-ing the high-field linear fits to the normal-state value for γ , we obtain H c = 42 ± ± H x corresponds to the crossover between filling ∆ in band 2 followed by ∆ in band 1 and hence estimate N =93 ± N =7 ± N =96 ± N =4 ± S and PbMo S . These figures FIG. 4: (a),(b) C elec /γT with two-band α -model fits [22].Insets: C/T at 0 T and 28 T. 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