Point-contact spectroscopy of the phononic mechanism of superconductivity in YB6
P. Szabo, J. Girovsky, Z. Pribulova, J. Kacmarcik, T. Mori, P. Samuely
PPoint-contact spectroscopy of the phononic mechanism of superconductivity in YB P Szab´o, J Girovsk´y, Z. Pribulov´a, J Kaˇcmarˇc´ık, T. Mori, and P. Samuely Centre of Low Temperature Physics @ Institute of Experimental Physics,Slovak Academy of Sciences, Watsonova 47, SK-04001 Koˇsice, Slovakia Advanced Materials Laboratory, National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan
Lortz et al. [Phys. Rev. B , 024512 (2006)] have utilized specific heat and resistivity measure-ments as ”thermal spectroscopies” to deconvolve the spectrum of the electron-phonon interactionin YB assuming a major role of the low frequency phonon mode in mediating superconductivity.Here, we present direct point-contact spectroscopy studies of the superconducting interaction in thissystem. As a result the normalized superconducting gap reveals a strong coupling with 2∆ /k B T c = 4and moreover the spectra contain nonlinearities typical of the electron-phonon interaction at ener-gies around 8 meV. The in-magnetic-field measurements evidence that the phonon features found inthe second derivative of the current-voltage characteristics are due to the energy dependence of thesuperconducting energy gap as their energy position shrinks equally as the gap is closing. This is adirect proof that the superconducting coupling in the system is due to the low energy Einstein-likephonon mode associated with the yttrium ion vibrations in a perfect agreement with determinationsfrom bulk measurements. PACS numbers: 74.45.+c, 74.70.Ad, 74.25.Bt
I. INTRODUCTION
Surprising discovery of superconductivity in MgB atalmost 40 K [1] has re-attracted attention to the super-conductors with an electron-phonon interaction mecha-nism. Due to their eight phonon branches and a high den-sity of scatterers in the form of boron atoms the metal-lic and non-magnetic hexaborides were regarded once aspossible candidates for high-temperature superconduc-tors [2]. These expectations have not been met when YB has the highest transition temperature T c = 8.4 K amongthem [3] and isostructural LaB with a very similar elec-tronic structure is not superconducting at all [4]. It wasbelieved for a long time that a dominant contributionto the electron-phonon interaction (EPI) in hexaboridesleading eventually to superconductivity came from theboron sublattice with a lot of phonon branches stretchedup to 160 meV [5]. But later, Mandrus et al. [6] noticedthat due to a large space of metal atom among the boronoctahedral cages the metal atoms can develop large un-harmonic vibrational amplitudes with strong EPI. Then,LaB or YB can be modeled as a Debye solid of therigid boron framework and metals ions can be treated asindependent harmonic oscillators (Einstein oscillators).The local vibrational modes of the La ions are the mostimportant for explanation of the low temperature resis-itivity and heat capacity in LaB as was also suggestedby the neutron experiments of Smith et al. [7] show-ing rather rapid flattening of the acoustic modes near 13meV due to non-interacting vibrations of La ions. Someof us [8] have measured the EPI function of LaB di-rectly by the point-contact spectroscopy (PCS) detect-ing the whole set of 8 modes starting from the prominentpeak at 13-15 meV up to 160 meV with the resultingelectron-phonon coupling constant λ ≈ .
15 showing veryweak electron-phonon coupling in the system. In case ofYB the rattling motion of Y ion is now supposed to be dominant in the electron-phonon coupling. Based onthis assumption Lortz et al. [9] have exploited the spe-cific heat and resistivity measurements as ”thermal spec-troscopies” to deconvolve the phonon density of statesand the spectrum of the electron-phonon interaction inYB . Their results suggest that the superconductivity ismainly driven by a low lying phonon mode (at ≈ than frequency of La vibrations in LaB has beenattributed to the weaker bond of Y due to smaller radiusin the same boron cage. The electronic specific heat re-vealed that YB is a strong coupling superconductor withthe reduced energy gap 2∆ /k B T c ≈ . λ ≈
1. Three spectroscopy experiments per-formed on YB have been published to our knowledgeso far. Kunii et al. [10] determined from GaAs pointcontacts on YB the superconducting gap ∆ = 1 .
22 meVwhich with the bulk T c = 7 . T c was not mea-sured) yields 2∆ /k B T c ≈ .
8. Also an EPI peak at 11meV was observed with the gap energy subtracted. Thephoto-emission spectroscopy results of Souma et al. [11]indicate similar conclusions. Schneider et al. [12] pre-pared the tunneling sandwich on YB film naturally ox-idized with In top electrode and obtained 2∆ /k B T c ≈ λ ≈ .
9. No significant contribution to EPI wasdetected above 16 meV.We present a detailed experimental study on YB single crystal with T c of 7.5 K via point-contact (PC)spectroscopy. Single s -wave superconducting energy gapwith a reduced value of 2∆ /k B T c close to 4 togetherwith its classical temperature and magnetic-field depen-dence have been found. Moreover, an electron-phonon-interaction peak has been directly observed in the secondderivative of the current-voltage characteristics in the su-perconducting state. Upon application of magnetic field a r X i v : . [ c ond - m a t . s up r- c on ] M a r the energy position of this peak shifts to lower energies.From data analysis the magnetic field dependence of thesuperconducting energy gap has been inferred. Impor-tantly, the energy position of the EPI feature shifts inincreasing magnetic field to lower energy exactly likewisethe superconducting gap is closing. This has been a di-rect proof that the low energy phonon mode near 7.6meV is mediating superconducting pairing, in agreementwith the conclusions of Lortz et al. II. POINT-CONTACT SPECTROSCOPY OFSTRONG COUPLING SUPERCONDUCTORS
A micro-constriction between two metals with the con-tact diameter d much smaller than the mean free path ofelectrons l can serve as a device for quaisparticles’ spec-troscopy since applied voltage V is directly related tothe quasiparticle energy excess ∆ E = eV , where e is theelectron’s charge.In case of two normal metals forming the junctionthe PC current I comprises beside the major term V /R N , where R N is the PC resistance also a smallnegative inelastic contribution δI Nph ( V ) on the order of ∼ = d/l in , where l in is the electronic inelastic mean freepath, yielding nonlinearities in I − V curve at char-acteristic EPI energies/voltages. Small nonlinearitiesare better pronounced as peaks in the second deriva-tive d V /dI ( V ) which is directly related to the point-contact form of the electron-phonon interaction function g P C = α P C ( ω ) F ( ω ) [13, 14]. Here, the matrix element α P C ( ω ) describes the strength of electron-phonon inter-action in the PC geometry and F ( ω ) is the phonon den-sity of states.When one of the PC-forming electrode is a supercon-ductor, below T c a phase coherent state of Cooper pairsis formed in it. For a bias energy | eV | < ∆, a directtransfer of the quasi-particles is not possible due to ex-istence of the energy gap ∆ in the spectrum of the su-perconductor. The transport of the charge carriers isrealized through Andreev reflection with an excess cur-rent I exc ( V ) which makes the PC current inside the gapvoltage twice bigger than in the normal state. For biaseslarger than the gap voltage the excess current becomesconstant and equals to I exc ∝ ∆ /R N . The PC conduc-tance σ = dI/dV shows a double increase below the gapvoltage | V | < ∆ /e compared to the normal state or towhat is observed at very large bias where the couplingvia the gap is inefficient. If a barrier is formed at thepoint-contact junction a Giaever-like tunneling compo-nent contributes to the charge transfer as well. Evolutionof the dI/dV vs. V curves for different interfaces charac-terized by arbitrary transmission probability T has beenmodeled by Blonder, Klapwijk and Tinkham (BTK) the-ory [15]. In case of a PC interface with an intermediatetransmission probability 0 < T < eV = 0, but also two peaks are visible at eV ∼ ± ∆ /e . The experimentally measured PC con- ductance data can be compared with this model usingas input parameters the energy gap ∆, the parameter Z (measure of the interface barrier strength with trans-mission coefficient T = 1 / (1 + Z )), and a parameterΓ for the quasi-particle lifetime broadening of the spec-trum [16]. The fitting procedure is described for examplein Ref.[17].When a point-contact micro-constriction is formed be-tween a normal metal and a strongly coupled supercon-ductor, due to significant energy dependence of the su-perconducting gap ∆( eV ) a small negative correction tothe elastic excess current δI exc ( V ) caused by the Andreevreflection will make a measurable effect [14]. Generally,the PC current will read as I ( V ) = VR N + δI Nph ( V ) + I exc ( V ) + δI exc ( V ) , (1)where the first three terms are described above and thelast term is given as δI exc ( V ) ∼ = (∆( V ) /hω ) [18], where ω is a characteristic frequency of phonons mediating thesuperconducting pairing. This term exceeds the inelasticcomponent of the PC current and the electron-phononinteraction modes mediating superconductivity can bevisible in the second derivative d V /dI ( V ) as peaks notexactly at characteristic EPI energies, but, importantly,shifted to higher energies by the value of the supercon-ducting energy gap ∆, in the same way as in the tun-neling spectroscopy. When the gap is closed for exampleby increasing temperature or in applied magnetic field,the EPI peaks should move to lower energies followingthe gap and decrease their intensity. This would be asmoking gun for the coupling mode which mediates thesuperconductivity in the system. III. EXPERIMENT
The measurements presented in this paper were per-formed on high-quality single-crystalline YB samplesprepared by the traveling solvent floating zone method[19]. All measurements were performed on crystals fromthe same batch. The crystals had a cubic form with theedge of about 0.5 mm. The values of the critical tem-perature T c have been determined by the point-contact-spectroscopy, resistivity and ac-calorimetry specific-heatmeasurements [20]. The first two techniques give T c =7 . ÷ . T c = 7.32 K, a reason-ably close value.The point-contact micro-constrictions were formed in-situ by pressing a Pt tip on the YB surface using adifferential screw mechanism allowing for a positioningof the tip on different spots on the sample. The PC tipshave been cut off from 50 µ m Pt wires. Spectra withthe best resolution have been obtained on the shiny blueYB surfaces prepared by cleaving before cooling downin the cryostat. PC spectroscopy measurements (the firstand second derivatives of I − V characteristics) have beenrealized by the standard lock-in modulation technique [8]. IV. RESULTS AND DISCUSSION
PC resistances were typically in the range R N ∼ =3Ω ÷ dI/dV obtained at T = 4 . T c orabove the upper-critical-field value H c . The open sym-bols represent the fits by the BTK model. Although ourexperiments have been performed on freshly cleaved YB surfaces, the finite Z parameter has always been found.Its size scattered as Z ≈ . − .
8. It means that thereis always an effective interface barrier between the Pt tipand the sample. In some cases we were able to form pointcontacts with a high spectral resolution, as witnessed bya small value of the smearing parameter Γ obtained fromthe fits. For the three spectra shown in Fig. 1 from topdownwards the values of Γ achieved 5, 13 and 37 % ofthe gap values, respectively. The values of the supercon-ducting gap obtained at 4.2 K on many junctions havebeen scattered between 1.18 to 1.22 meV.Point-contact spectroscopy explores superconductivityin the area with dimensions on the order of the super-conducting coherence length. In some cases the super-conducting transition temperature T c at the surface candiffer from the bulk value. That is why it is importantto determine the local T c of the junction before makingany conclusions on such important parameter as the su-perconducting coupling strength 2∆ /k B T c . In the pub-lished spectroscopy measurements on YB the local crit-ical temperature T c values have not always been deter-mined, which could affect the calculation of the couplingstrength. A correct determination of this ratio requiresexperimental measurement of T c and ∆ in the same ex-periment.A representative temperature dependence of the PCspectra is plotted in Fig. 2 (lines). This is one of thehigh resolution spectra without any smearing parameter(Γ = 0). The open circles are obtained from the fits tothe BTK model. During the fitting procedure we firstdetermined the parameters ∆ and Z at the lowest tem-perature, here equal to 1.6 K. Later, for higher temper-atures only ∆ was used as a fit parameter, while Z wehad been kept constant. The inset of Fig. 2 shows the FIG. 1: Representative point-contact spectra measured onPt-YB hetero-contacts at T = 4.2 K (solid lines). The lowercurves are shifted in Y-coordinates for the clarity. Fits bythe BTK conductances are shown by open symbols with theresulting parameters Z = 0 . , . , . , Γ = 0 . , . , . temperature dependence of the superconducting energygap determined from the fit. The energy gap ∆(0) = 1 . T c = 7 . /k B T c = 4 .
07. Note thatfrom a number of measurements we always obtained T c close to 7 . ÷ . ± .
03 meV and 2∆ /k B T c valuesbetween 3.9 and 4.1. We can conclude that in YB thepoint-contact spectroscopy has revealed a single s -wave-gap superconductivity with intermediate strength of cou-pling. The temperature dependence of the superconduct-ing gap follows the BCS prediction well as documentedby the full line in the inset of Fig. 2.In the following we examined an effect of applied mag-netic field on the PC spectra and particularly on the su-perconducting energy gap. The magnetic field was ap-plied perpendicularly to the PC junction area and par-allel with a Pt tip. The estimated PC diameters werein the range of hundreds of nanometers while the co-herence length in YB is about 30 nm. Then, abovethe lower critical magnetic field the junction was in amixed state with many Abrikosov vortices penetratingthe junction. The vortex cores form a normal-state part FIG. 2: Temperature dependence of the high resolution (Γ =0) Pt-YB point-contact spectrum (solid lines) measured atindicated temperatures. Open symbols show the BTK fitswith the fitting parameters Z = 0 .
64, and ∆(0) = 1 . T ) is shownin the inset by the symbols. The solid line is the BCS predic-tion. N A of the junction with an area A . Their fraction ofthe whole junction written as n = N A /A is in a first ap-proximation proportional to the applied field divided tothe upper critical one ( H/H c ). n increases linearly withmagnetic field and at the upper critical magnetic fieldwhere the whole junction is in the normal state n = 1.The normalized point-contact conductance in the mixedstate will be the sum σ/σ N ( V, H ) = n + (1 − n ) σ , where n represents the normal-state channel and (1 − n ) σ is thesuperconducting-channel contribution. This simple em-pirical model (successfully applied for the study of two-gap superconductivity in MgB [22, 23]) has been used forthe fit of the normalized-conductance curves measured ina presence of magnetic field. Figure 3 shows the evolu-tion of one PC spectrum with magnetic field (lines) andfitting curves (symbols). The fit parameters Z, Γ and ∆have been determined from the zero-field PC spectrum.At higher fields only the values of the field-dependent pa-rameters n and ∆ have been varied. The resulting fielddependence of the energy gap is plotted by the open cir-cles in the Fig. 5. From relatively small fields it followsa square-root dependence, which is in accordance withthe Maki’s [24] generalization of the Ginzburg-Landautheory for dirty type-II superconductors.Similar measurements have been performed at 1.6 K.Thus, H c values, determined from the PC spectroscopyas the field where the superconducting features in thePC spectrum vanish, were obtained at these two tem-peratures. They are shown in the inset of Fig. 3 bythe stars together with the overall temperature depen-dence of the upper critical magnetic field H c ( T ) deter-mined from the specific heat measurements performed - 8 - 6 - 4 - 2 0 2 4 6 81 . 01 . 11 . 2 T = 4 . 5 K B T K f i t e x p e r i m e n t H = 0 T 0 . 0 2 T 0 . 0 4 T 0 . 0 6 T 0 . 0 8 T 0 . 1 T 0 . 1 2 T 0 . 1 4 T Normalized conductance
V o l t a g e ( m V ) H c2(T) T e m p e r a t u r e ( K )
FIG. 3: Effect of magnetic field on the Pt-YB point-contactspectrum (solid lines) measured at T = 4 . Z = 0 . , Γ = 0 .
23 meV and ∆(4.5 K) = 1.15meV. Inset shows the temperature dependence of H c fromour specific heat (squares) and point-contact measurements(stars). The line is the WHH model. on the same crystal, displayed here as solid squares [25].The consistency between H c ’s obtained from the bulk-sensitive specific heat measurements and surface sensitivepoint-contact-spectroscopy measurements points the factthat also the latter reflects the bulk properties and is notaffected by any kind of surface degradation. The lineover the H c ( T ) data points is the classical Werthamer-Helfand-Hohenberg model curve [24]. Our H c values arein a reasonable agreement with the results of other groups[9, 26]. In particular our zero-temperature upper criticalfield H c (0) = 0 .
28 T is slightly smaller than 295 mT and315 mT of Lortz [9] and Kadono [26], resp., despite ourhigher T c than their T c = 7 . d V /dI ( V ) is proportionalto the EPI function. The first mechanism requires cleanballistic contacts and reveals approximately the samespectrum in the superconducting as well as in the nor-mal state. The latter mechanism prevails in the strongly-coupled superconductors, where intensity of the peaks in d V /dI ( V ) related to the phonons (bosons) mediatingthe superconducting coupling is significantly increased inthe superconducting state as compared with the normalstate and moreover, the peak positions are shifted in en-ergies by the value of the superconducting energy gap∆. With a relatively strong superconducting coupling of2∆ /k B T c = 4 ± . samples we expected thatstrong coupling features could also appear in the elas- m H = 0 T m H = 0 . 1 T d V / dI
2 (a.u.)
V o l t a g e ( m V )
N o r m a l s t a t e , m H = 0 . 4 T Y B 6 - P tT = 4 . 2 K
P t - E P I s p e c t r u m
FIG. 4: Second derivative d V /dI ( V ) spectrum measured at T = 4.2 K on a Pt-YB point contact in superconducting (at0 and 0.1 T) and normal (at 0.4 T) state. The down-mostcurve plots the EPI function of a Pt-Pt homo-contact [14]. tic component at the characteristic phonon energies. Bytrial and error we looked for the dV /dI spectra showinga ’smooth’ linearly increasing background, a typical fea-ture of a good quality metallic point contacts with moredirect than tunneling conductance. Figure 4 plots a set ofsecond derivatives d V /dI ( V ) of the point-contact spec-tra obtained at T = 4 . hetero-contact. Thecurves taken at H = 0 , . H = 0 . H c (4.2 K) =0.18 T (see inset of Fig. 3), represents the normal-statebehavior. All spectra shown here reveal well defined non-linearities in the 30 mV window. In the zero-field spec-trum a sharp peak is visible at the bias (energy) ω /e =8.6 mV, an intense peak is placed also around ω /e ≈
13 mV followed by a hump at about 18 mV and a peakaround ≈
23 mV. The structure is superimposed on thetypical point-contact background which is related to thenonequilibrium phonon generation near the point-contactorifice [8].Point-contact spectra measured through a junction be-tween two different metals are proportional to the EPIfunction of both electrodes. For comparison we show inFig. 4 also the point-contact spectrum of the electron-
FIG. 5: Magnetic-field dependence of the superconductingenergy gap of YB (left ordinate) resulting from the measure-ments shown in Fig. 3 - open circles. The solid line is a squareroot field dependence. The full circles indicate a position de-velopment of the phonon mode of YB in magnetic field fromthe spectrum in Fig. 4 (right ordinate applies). phonon interaction obtained on the Pt homo-contact, thecurve is reproduced from Ref. [14]. In this spectrum thePC background was already subtracted. Two dominantPt phonon modes are visible with peaks at ∼
13 mVand 23 mV and also a hump at about 18 mV can berecognized. Comparing the YB -Pt zero-field spectrumwith the spectrum of Pt one can see that the maxima ob-served above 10 mV are positioned at the characteristicphonon energies of Pt without any energy shift. Whenthe superconductivity in our YB sample is suppressedin increasing magnetic field, the intensities and the po-sitions of these maxima are practically unchanged. Thisis strongly suggestive that in our PC spectra the inelas-tic scattering of electrons on the Pt phonons dominatesat energies above 10 meV. On the other hand the low-energy sharp peak observed in the superconducting stateat ω /e ≈ . ± . ∼ ∼ H ) (open sym-bols) in increasing magnetic field. At higher fields, above H c the phonon contribution in the spectrum due to theenergy-dependent superconducting gap is absent and asmall non-linearity at about 7.6 mV which is still presentas dispalyed in Fig. 4 is due to an inelastic quasi-particlescattering on this phonon mode. It is visible togetherwith the phonon modes of the Pt tip. In contrast to thereports in Refs.[10, 11] no structure was observed at ∼ d V /dI ( V ) spectra on our Pt-YB hetero-contacts. Yet no structures apart of the smoothlyincreasing background was observed at higher voltagesabove 30 mV.It is noteworthy that that our measurements have re-vealed only the strongest peak of the complete EPI spec-trum of YB , while the other branches due to the quasi-particle interactions with the optical phonon modes ofthe boron octahedra are not pronounced. That theyhave been observed in our PCS studies on the non-superconducting LaB [8] can be explained by the ex-tremely high quality of the LaB crystal with the resid-ual resistivity ratio RRR ∼ = 200 while in the case of YB RRR = 4. In the case of our point contact measurementson the LuB single crystals with RRR = 70 we have ob-served a dominant EPI peak at about 14 meV comingfrom Lu vibrations and two small maxima at 24 and 30meV from optical boron branches [27].Our finding strongly suggests importance of the low-energy yttrium phonon mode with energy of 7.6 meV inthe superconducting coupling of YB , while other phononmodes coming from the boron octahedra vibrations arenot significantly coupled to the electronic quasi-particles.This result is in a full agreement with the conclusions ofthe ”thermal spectroscopy” of Lortz et al. [9] based onthe heat capacity and resistivity measurements. V. CONCLUSIONS
Point-contact spectroscopy measurements have beenperformed to study the superconducting coupling in YB . The values of the superconducting energy gap∆ = 1 . ± .
03 meV and of the strength of supercon-ductivity 2∆ /k B T c = 4 . ± . d V /dI ( V )spectra observed on the Pt-YB point contacts at ener-gies above 10 mV are related to the inelastic scatteringof electrons on the phonons of the Pt tip the low-energymode, observed in the superconducting state at 8.6 mVis shifted to lower energies in the same way as the super-conducting energy gap of YB is gradually suppressedby the magnetic field and shows up as a small feature at7.6 meV when YB is driven to the normal state. Thisfinding is a direct experimental evidence of the phonon-mediated superconductivity in YB by the low energyyttrium phonon mode near 7.6 meV. Our measurementsconfirm the results of the deconvolution of the electron-phonon interaction from the specific-heat and resistivitymeasurements by Lortz et al. showing that YB has beena superconductor with an Einstein lattice of Y ions rat-tling in the spacious cage of boron octahedra. Acknowledgments
This work was supported by the following projects:CFNT MVEP - the Centre of Excellence of the Slo-vak Academy of Sciences, FP7 MNT - ERA.Net II.ESO, the EU ERDF (European Union Regional Devel-opment Fund) grant No. ITMS26220120005, VEGA No.2/0135/13 and the APVV-0036-11 grant of the SlovakR&D Agency. The liquid nitrogen for the experimenthas been sponsored by the U.S. Steel Koˇsice, s.r.o. [1] J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani,J. Akimitsu, Nature (London) , 63 (2001).[2] A. J. Arko, G. Crabtree, J. B. Ketterson, F. M. Mueller,P. F. Walch, R. R. Windmiller, Z. Fisk, R. F. Hyot, A. C.Mota, R. Viswanathan, D. E. Ellis, A. J. Freeman, andJ. Rath, Int. J. Quantum Chem. Symp. , 569 (1975).[3] C. Buzea and T. Yamashita, Supercond. Sci. Technol. ,R115 (2001).[4] I. Baˇtko, M. Baˇtkov´a,, K. Flachbart, V. B. Filippov, Yu.B. Paderno, N. Yu. Shitsevalova, T. Wagner, J. Alloysand Comp.
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