Enhanced superconductivity at the interface of W/Sr RuO point contact 2 4 He Wang (王贺), Weijian Lou (娄伟坚), Jiawei Luo (骆佳伟), and Jian Wei (危健)∗ International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China and Collaborative Innovation Center of Quantum Matter, Beijing, China Y. Liu Department of Physics and Materials Research Institute, The Pennsylvania State University, University Park, Pennsylvania 16802, USA and Department of Physics and Astronomy and Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), 5 Shanghai Jiao Tong University, Shanghai 200240, China 1 0 J.E. Ortmann and Z.Q. Mao 2 Department of Physics, Tulane University, New Orleans, Louisiana 70118, USA n (Dated: January 6, 2015) a Differential resistance measurements are conducted for point contacts (PCs) between tungsten J tip approaching along the c axis direction and the ab plane of Sr2RuO4 single crystal. Three key 5 features are found. Firstly, within 0.2 mV there is a dome like conductance enhancement due to Andreev reflection at the normal-superconducting interface. By pushing the W tip further, ] n the conductance enhancement increases from 3% to more than 20%, much larger than that was o previously reported, probably due to the pressure exerted by the tip. Secondly, there are also c superconductinglikefeaturesatbiashigherthan0.2mVwhichpersistsupto6.2K,resemblingthe - enhancedsuperconductivityunderuniaxialpressureforbulkSr RuO crystalsbutmorepronounced 2 4 r p here. Third,thelogarithmicbackgroundcanbefittedwiththeAltshuler-Aronovtheoryoftunneling u intoquasitwodimensionalelectronsystem,consistentwiththehighlyanisotropicelectronicsystem s in Sr2RuO4. . t a m The layered perovskite ruthenate Sr RuO (SRO) has thatthetipwillexertsomepressureonthesurfacewhich 2 4 shown evidence for spin-triplet, odd-parity superconduc- may affect the SC,18 possibly due to local distortion of - d tivity (SC) which may be useful for topological quantum lattice.19,20 It is known that for SRO a very low uniaxial n computation.1–3 Thepossiblechiralorbitalorderparam- pressure of 0.2 GPa along the c axis can enhance the su- o eter for the two-dimensional SC is p ±ip as suggested perconducting transition temperature (T ) of pure SRO c x y c by the time-reversal symmetry breaking experiments.4,5 from 1.5 K up to 3.2 K,21,22 and recently in-plane strain [ Such chiral order is expected to generate edge currents, (0.23%) along (cid:104)100(cid:105) direction is also shown to enhance 1 but the expected magnetic field due to edge currents has T from 1.3 K up to 1.9 K.23 The pressure in abovemen- v c not been directly observed with local field imaging,6–8 tionedmeasurementswereappliedtobulksamples,while 8 though there is indirect evidence of edge currents re- forPCSthepressureisexertedlocally. Inthelattercase 9 7 vealed by in-plane tunneling spectroscopy9,10 and point itmaybelessaffectedbytheinhomogenityoftheapplied 0 contact spectroscopy (PCS),11both with assumptions to pressureandthesampleislesstendtodevelopingcracks, 0 fit the conductance spectra. thus locally higher pressure may be reached though ab- . solute pressure is not known. Here we report greatly 1 The surface properties of SRO is very critical for field 0 enhanced SC observed at the interface of the point con- imaging with scanning quantum interference devices, as 5 tact junction between a tungsten tip approaching along well as for the tunneling and point contact spectroscopy. 1 the c axis direction and the ab plane surface of a SRO It is known that the SRO surface can undergo recon- v: struction and the intrinsic SC may not be probed,12,13 single crystal. i X and it may even show ferromagnetism (FM) due to lat- SRO single crystals are grown by floating zone meth- tice distortion.14 Very careful in situ preparation of de- r ods and are from two different batches, details of sample a vices is required for making good tunnel junctions using preparation can be found in previous reports.24 Sample microfabrication techniques.9 Recently there is also the- S1 is from the first batch and is easier to cleave and oryproposalthatsurfacedisorderindeedcandestroythe shows no Ru inclusions. Sample S2 is from the second spontaneous currents.15 batch, toohardto cleave, andcontains alotof Ruinclu- One way to overcome the surface problem is to use a sions (for optical images see Appendix C). Only on the hard tip for the point contact (PC) measurement. If the cleavedsurfaceofS1doweobserveSCfeature. Tungsten tipishardenough,itmaypiercethroughthesurfacedead wire of 0.25 mm diameter is etched to form the tip, and layerandprobetheSCunderneath.16Infact,forthisrea- then fixed pointing to the ab plane of the SRO sample. sontungstentiphasbeenusedforPCSofheavyfermion ASichipwiththesampleandthermometergluedontop superconductors.17 A consequence of using a hard tip is is mounted on an attoCube nanopositioner stack. Since 2 at nominal temperature 0.35 K. SC is clearly shown by the resistance dip within ±0.2 mV without any applied field. With a 625 Oe magnetic field applied along the c axis (H ), SC is almost fully suppressed for the 9.3 ⊥ Ω PC as shown by the recover of the resistance peak at zerobias. However,forthe4.3ΩPCthereisstillasmall dip, suggesting that SC is not fully suppressed, i.e., SC is enhanced with increased pressure. Enhancement of SC is further confirmed by the tem- perature dependence of dI/dV at zero field as shown in Fig. 2b and Fig. 3b, where T is increased from the bulk c value of 1.5 k to about 2 K and 2.5 K for the 9.3 Ω and 4.3 Ω PC respectively. This enhanced T is consistent c with previous susceptibility measurements on bulk SRO sample under uniaxial pressure, where the mechanism of T enhancement was ascribed to anisotropic lattice dis- c tortion,21,22,25 similar to that found in the eutectic 3K phase.26,27 In Figs. 2 and 3, for easy comparison with theoretical description, dV/dI is converted to dI/dV. The magnetoresistance (MR) is shown in Figs. 1b, 1d, and 1f for the three PCs. The resistance starts to in- crease quickly at around 400 Oe, and there is clearly a hysteresis with steps which gets sharper and more pro- nouncedforhigherPCpressure. MRhysteresisisusually observed for ferromagnetic samples, and the observation of both SC and MR hysteresis was linked to the coexis- tence of SC and ferromagnetism (FM) for SC at the ox- FIG.1. (Coloronline)BiasdependenceofdV/dI (a,c,e)and ides interface.28 If indeed a FM-like internal field exists, magnetoresistance (b, d, f) of three different point contact could it be related to the long sought-after time-reversal (PC) resistance at the same location between the W tip and symmetry-breaking fields?6–8 SRO single crystal S1 at 0.35 K. The resistance at zero bias andzerofieldis9.3,4.3,3.2Ωrespectively. Forclarity,in(a) First the possibility of conventional vortex pinning and(c)thedV/dI curvesat625Oe(Green)areshiftedupby needs be considered. The field value above which dV/dI 0.2 Ω. Arrows in (b), (d), (f) show the sweeping direction of starts to increase quickly is around 400 Oe, in the same the magnetic field. The reproducibility of the measurements order of magnitude with the upper critical field H ||c c2 isdemonstratedbytheoverlappingofdV/dIcurvesin(a),(c), about 710 Oe for pure SRO crystal, but much larger (e) with bias ramping in both directions. The discontinuity than the critical field H ||c about 70 Oe (by specific around ±625 Oe is related to the ramping speed of the field, c1 heat measurements).29 Sharp increase of resistance may and can be smaller when the field ramping speed is reduced, indicate that vortices enter the PC interface and SC is while the hysteresis is almost the same. suppressed. However, it is not clear whether such strong pinning could be reduced by PC. The average distance (cid:112) between vortices is ∼ Φ /H, about 0.3 µm for 400 0 the tip and sample are both fixed to the copper housing, Oe, so the diameter of the PC should be much larger to relative displacement between the tip and sample is sup- include multiple vortices, which is inconsistent with con- pressed, which ensures a stable contact and reproducible ventional understanding of the PC. Moreover, it is diffi- PCS. The housing is suspended with springs at the bot- culttoexplainwhythestep-likefeaturesbecomesharper tom of a insertable probe for a Leiden dilution fridge. withhigherpressure. Besidestheexternalpinningdueto With such customization the sample position is not at defects, the intrinsic pinning due to chiral domain wall30 the field center of the magnet, and the field value is esti- seems also unlikely to reach 400 Oe. One variation of mated with the tabled values from the magnet manufac- vortex pinning is chiral domain wall motion, where with turer. Differential resistance (dV/dI) is measured with ramping field the DW wall moves and the edge current standard lock-in technique. can affect the transport of the PC,31 which seems rea- At the same location, by pushing the tungsten tip to- sonable. wards the SRO surface (more precisely it is the SRO Surface FM also needs to be considered since moving towards the tip), the PC resistance is reduced among other layered perovskite ruthenates in the series and the pressure is increased. The zero bias and zero A Ru O , SrRuO is a ferromagnetic metal with n+1 n 3n+1 3 field resistance (R ) is: 9.3, 4.3, 3.2 Ω respectively (see T =160 K, and Sr Ru O is at the boarder of FM and 0 c 3 2 7 Appendix A for a discussion of PC resistance). The bias shows pressure-induced FM.32 Thus it is natural to ex- dependence of dV/dI is shown in Figs. 1a, 1c, and 1e, pect that FM could be induced for SRO, or there might 3 FIG. 2. (Color online) (a) Bias dependence of dI/dV for the FIG. 3. (Color online) (a) Bias dependence of dI/dV for the 9.3 Ω point contact at 0.35 K and with increasing H and 4.3 Ω point contact at 0.35 K and with increasing H and ⊥ ⊥ (b)zerofielddI/dV withincreasingT.Curvesareshiftedfor (b) zero field dI/dV with increasing T. Curves are shifted clarityexceptforthezerofield0.35Kcurve. (c)Fittingwith for clarity except for the zero field 0.35 K curve. (c) Fitting EEItheoryinthe2Dlimitforcurvesin(a)withfittingtem- with EEI theory in the 2D limit for H = 0 (blue) and 625 ⊥ perature T =1.0 K, and (d) fitting for curves in (b) with Oe(yellow)curvesin(a)withT =0.8K,and(d)fittingfor fit fit T = 0.35 (1.0), 0.6 (1.1), 0.8 (1.24), 1.5 (1.65), 1.6 (1.85), differentTcurvesin(b)withT =0.35(0.8),1.5(1.5)K(T fit 1.8 (1.95), and 2.0 (2.2) K from top to bottom (T is indi- isindicatedintheparentheses). AfternormalizedbytheEEI fit cated in the parentheses). After normalized by the EEI fits fitswithcorrespondingT ,thedatacurvesareshownin(e) fit withcorrespondingT ,thedatacurvesareshownin(e)for fordifferentH and(f)fordifferentT.Curvesareshiftedfor fit ⊥ different H and (f) for different T. Curves are shifted for clarity. ⊥ clarity. ature dependences in Fig. 2 and Fig. 3, for the 9.3 and be some eutectic phase24 on the surface which leads to 4.3 Ω PC respectively. However, in Ref. [9] the gap is FM. Previously, experimental attempts to measure the about 0.7 mV instead of 0.2 mV, and the conductance bulk magnetic susceptibility of SRO with uniaxial pres- enhancement of the dome like feature is less than 1% surewerenotsuccessful,sinceabove0.4GpaSROsample (see see Appendix D for similar PC spectra with a Au tends to crush,33 while no drastic change of the temper- tip). The dome like feature may be fitted considering ature dependence of susceptibility was observed. On the chiral p-wave symmetry9, but here we focus on experi- other hand, doping the Sr with Ca does show a ground mental findings and methodology while leave the fittings stateofstaticmagneticorderduetorotationofRuO oc- in the future. 6 tahedra.34,35 Thus it is possible that the pressure under The broad background resistance hump as shown by the tip may be higher than 0.4 GPa16 and its influence dV/dI at 625 Oe in Fig. 4(a) (same as in Fig. 1a) is is comparable with that by doping. However, this is in- generally called zero-bias anomaly (ZBA), which is fre- consistent with the fact that the hysteresis diminishes quentlyobservedintunneljunctions9 aswellasPCs.36,37 together with SC at higher temperatures, which also in- The possible origins for ZBA in PCs include “extrinsic” dicates that the hysteresis is not due to eutectic phase magneticimpurities,two-levelsystems,Kondoscattering impurities. duetospontaneouselectronspinpolarizationetc,aswell Both field and temperature dependences of dI/dV re- as“intrinsic”densityofstates(DOS)effect,asshownfor semblethosefoundforin-planeAu/SROtunnelingjunc- chromium where DOS is reduced due to the spin density tions in Ref. [9], as shown by detailed field and temper- wave gap,38 and more recently for iron pnictides where 4 demonstrated. Another feature of the PC spectra is a small periodic “wiggling” outside ±0.2 mV, which also diminishes with increasing field and temperature, sug- gesting that it is probably due to interference of quasi- particlesattheNSinterface. Similarfeaturewasalsoob- served for multiple band superconductor MgB 16,18 but 2 detailed analyses are lacking. The ZBA background be- comeslesspronouncedwhenthePCresistanceisreduced from 9.3 Ω to 4.3 Ω, as shown in Figs. 3c and d, while the conductance enhancement gets larger. This is better illustratedbythenormalizedenhancement(Fig.4d),and by direct comparison of the zero field dV/dI (Fig. 4c). What parameters may change when the PC resistance is reduced from 9.3 Ω to 4.3 Ω? In the standard theory for PCS (see Appendix A for details), the PC resistance R =R +R , (1) PC Sh Max whereR istheSharvinresistancecorrespondingtothe Sh FIG. 4. (Color online) (a) dV/dI curves for the 9.3 Ω PC ballisticlimit,andR istheMaxwellresistancecorre- at 0 (blue), 625 Oe (black), and EEI fits (red dashed lines). Max spondingtothediffusivelimitandrelatedtotheresistiv- (b) dV/dI curves for the 4.3 Ω PC at 0 (blue), 521 (yellow), ity. ForthesimplestmetallicPC,R isconsideredtobe 625 Oe (black), and the EEI fit. (c) Zoom-in of the zero bias Sh energy independent as the energy dependence of veloc- resistancedipregimewithcurvesshiftedforclarityexceptfor the3.2Ωcurve. Thecurvesarereproducibleforbothramping ity cancels that of the DOS. This can be changed when directionsofthebias. (d)Zerofieldconductanceenhancement complicated Fremi surface is involved and the effective after normalized with the fitted EEI background. All at 0.35 DOS may be probed by R .38,39 Here for single crystal Sh K. SRO the mean free path is large, and if the interface is cleanandbarrier-free, thePCshouldbeclosetothebal- listic limit. As R ∝ (1/d)2 and R ∝ (1/d), where Sh Max DOS is enhanced due to strong electron correlations.39 d is the diameter of PC, and if the anisotropic electronic Here ZBA apparently coexists with SC in SRO, which state in SRO is not considered, the reduction of resis- is very sensitive to impurities, thus the origin of ZBA is tance from 9.3 Ω to 4.3 Ω would lead to an increase of more likely due to some “intrinsic” origin. d by roughly (cid:112)9.3/4.3=1.47 times in the ballistic limit ThebackgroundZBAcanbenormalizedwhenthebias (twice increase of the area); or by 2 times in the thermal dependence is replotted using ln(eV/kBT). In Figs. 2(c) limit(quadruple increase of the area). and 2(d), the normalized change of conductance shows With the increase of contact area, the PC may show a a linear dependence for eV (cid:29) kBT, similar to what larger critical current (IC) if the critical current density was observed in tunneling measurements for disordered is constant and I is only determined by the PC itself. C metalfilms,40 andalsoforlayeredcupratesandmangan- As the additional dI/dV dips shown in Fig. 3 is ascribed ites.41,42 In the tunneling case, the reduction of DOS is to the critical current effect45, I can be estimate from C due to electron-electron interaction (EEI). As proposed the dip position. At 1.6 K the dip position is about 1.2 by Altshuler and Aronov,43 for low dimensional systems and2.3mVforthe4.3Ωand9.3ΩPCs,sothecalculated the exchange interaction between electrons can cause I is around 0.28 and 0.25 mA respectively, inconsistent C quantum corrections to the conductivity as well as DOS, with the expected 2-4 times increase of I if I is pro- C C whichdependsonthedimensionalityofthesystems. For portional to the contact area. This may suggest that eV (cid:29) kBT, the DOS correction ∼ ln(eV/kBT) in 2D IC is determined by a fixed region, e.g., chiral domains (see Appendix B for details). When the full formula is under the PC, instead of by the area of the PC itself. used, we get good fits in the full bias range as shown by Thus, with increasing bias the region of SRO under the the dashed lines in Figs. 2(c) and 2(d) (also in Figs. 1a PC reaches its I , and R shows a finite increase due C PC and b). We note that in order for all normalized dI/dV to R , as described in Eq.(1). Max curves to collapse onto a single curve, enhanced temper- When the PC resistance is reduced further to 3.2 ature (Tfit) needs to be assumed for dI/dV measured Ω, even larger conductance enhancement is observed as at lower temperatures. This may indicate there is local shown in Fig. 1e and Fig. 4. After normalization by the heating in the small PC region, possibly due to inade- background, the conductance enhancement at zero bias quate filtering of the external microwave noise.44 is about 3% for the 9.3 Ω PC, 14% for the 4.3 Ω PC, The fitted ZBA can be considered as the normal state and 22% for the 3.2 Ω PC (Fig. 4d). The original dV/dI background and divided from the normalized conduc- curves without normalization and the EEI fits are also tance,9 the resulted curves are shown in Figs. 2(e) and shown in Figs. 4a and b, and the fits can very well re- 2(f), with the dome like conductance enhancement well produce the dV/dI curves when an effective tempera- 5 Fig.5c. Thereareclearlytworesistancedropsataround 4and6K,andwenoteasimilarbutsmallerdroparound 4kwasalsoobservedinRef.[9]. SincethebulkT ∼1.5 c K for S1, and even for the 3-K phase T ∼ 3 K, thus the c greatly enhanced T could be only due to the W/SRO c PC. In summary, an ultralow temperature point contact setup using nanopositioners was used to measure differ- ential resistance of W/SRO point contact junctions. We find: 1) a superconducting gap around 0.2 mV and a domelikeshapeofconductanceenhancement, consistent with chiral p-wave symmetry; 2) SC-like features per- sisting up to 6.2 K, much higher than the bulk T of c SRO, presumably due to the pressure exerted by the W tip and a mechanism similar to that of the 3K-phase; 3)abroadresistancehumpcoexistingwithsuperconduc- tivity, which is ascribed to density of states effect due to 2D electron-electron interaction, consistent with the highly anisotropic electronic system of SRO. We believe PCS may provide useful information beyond the surface problem for SRO. We thank Hu JIN for contribution in the earlier stage of this project, Liang LIU for various help with experi- ments and data analysis, Xin LU for helpful discussions on point contact measurements, and Fa WANG for dis- FIG.5. (Coloronline)(a)ForR =3.2ΩthreeSCtransitions 0 cussions on correlated systems respectively. Work at areshownbydV/dI curvesofatdifferenttemperatures. Red Peking University is supported by National Basic Re- curves are guide to the eye. (b) The position of the dV/dI peaks vs temperature. (c) Zero bias dV/dI vs temperature. search Program of China (973 Program) through Grant Both (b) and (c) are derived from (a). No. 2011CBA00106 and No. 2012CB927400. The work at Tulane is supported by the DOE under grant DE- SC0012432. ture T is taken into account. Zoom-in the zero bias fit regime, the absolute amplitude of the dV/dI dip and of the “wiggling” part outside of the dip are clearly shown Appendix A: Basics of point contact resistance in Fig. 4c. For all three PCs, the dV/dI dip evolves to ZBA at around 0.2 mV (Fig. 4c), which is consistent There are many reviews on point contact spec- with the gap value of SRO from the weak-coupling the- troscopy46 and particular on unconventional heavy ory (2∆/e = 3.5k T ) with T ∼ 1.5 K. This value is fermionsystems.47,48 Hereweintroducethebasicsofthe B c c much smaller compared with previous PCS and ab plane PC resistance following Ref. 47. tunneling results where 0.7-0.9 mV were obtained,9,11 In the simple theoretical model, PC is formed with and also smaller compared with scanning tunnel spec- an orifice with diameter d between two bulk metallic troscopy(STS)measurementswhere0.3-0.5mVwerere- electrodes. Depending on the relative ratio between ported.12,13 d and different mean free path l, PC can be catego- For the 3.2 Ω PC, the surprising feature that the crit- rized into three regimes: ballistic (d < l ), diffusive elastic ical current effect persists to much higher temperatures (l < d < l ), and thermal (d > l ). In elastic inelastic inelastic is better illustrated in Fig. 5. In Fig. 5a, besides the the ballistic regime, the Fermi surface in the two elec- first dV/dI peak at around 0.2 mV, there are two addi- trodes has a difference of eV, similar to the tunneling tional dV/dI peaks, one persists up to about 5 K, while junction case; while in the thermal regime, the Fermi the other persists up to about 6.2 K. These two dV/dI surface evolves smoothly within the PC and there is a peaksarelikelytobeSCfeaturesasthemeasuredMRup well defined equilibrium temperature profile.49 to around 625 Oe also shows hysteresis, which decreases The current density in the orifice along its normal di- with increasing temperature and diminishes along with rection (z-axis) is the resistance dip near zero bias. At 8 K, the dV/dI (cid:88) within ±1.5 mV, and the MR of the zero bias dV/dI j =2e (v ) f (E), (A1) z k z k within ±625 Oe, becomes practically flat and changes k less than 0.03 Ω. The temperature dependence of the position of dV/dI peaks is plotted in Fig. 5b, and the wherev istheelectronvelocity,andf (E)istheFermi- k k zero bias dV/dI from the spectra in Fig. 5a is plotted in Diracdistributionfunction. Foravoltagebiasedballistic 6 PC, considering the energy difference eV, TABLE I. Summary of quasiparticle parameters of Sr RuO 2 4 (cid:90) EF+eV/2 (cid:90) dΩ (α,β,γ)2 and Tungsten. j =e dE v (E)f(E)N(E), (A2) z 4π z Fermi sheet α β γ Tungsten EF−eV/2 k (˚A−1) 0.304 0.622 0.753 1.55 F whereN(E)istheelectronicDOS.Inthesimplifiedcase, v (ms−1) 1.0×105 1.0×105 5.5×104 1.8×106 v (E) is inversely proportional to N(E), thus there is no F z m∗ (m ) 3.3 7.0 16 1 non-linearity caused by energy dependence of DOS. The e resulted Ohmic resistance is 16R 16ρl For a heterocontact between two different electrodes (1 R = q = , (A3) Sh (k d)2 3πd2 and 2), the resistance has contribution from both sides. F For geometrically symmetric PC with almost equal p , F where ρ is the bulk resistivity, l the elastic mean free path, Rq = h/2e2 = 12.9 kΩ the quantum resistance. R (T)(cid:39) 16ρl + ρ1(T)+ρ2(T). (A7) With the assumption that the Drude picture holds, ρl= PC 3πd2 2d p /ne2isaconstantforaparticularmetal(Notethatthe F Since the resistivity of simple metal tip like tungsten quantitiesp andnwereusedintheoriginalderivation). F is usually much smaller than that of the correlated elec- Thus, in the ballistic regime the diameter of the orifice d tron systems (in normal state), we may just keep the canbeestimatedusingthezerobiasresistanceR . Toget 0 resistivity term of the correlated systems being probed. a rough number, in the case of copper and other simple metals, d∼30/(cid:112)R (Ω) nm. The assumption of equal pF is very rough, the difference 0 between k of tungsten and SRO is shown in Table I. At finite bias, the electron can also be backscattered F Here k of tungsten is roughly estimated by assuming by phonons, magnons etc, at characteristic bias energy. F twovalenceelectronsandsimplesphericalFermisurface. So I-V curve of the ballistic PC can be nonlinear and For a heterocontact between a normal metal and second derivative is often used to identify phonon and a superconductor, Blonder-Tinkham-Klapwijk (BTK) magnonspectra. Moregenerally,forcorrelatedmaterials model50 is widely used to explain the conductance en- with complex Fermi surface, v (E) is no longer inversely z hancement within the gap energy and a tunnel barrier Z proportionaltoN(E),I-V curveisnonlinearandR (E) Sh parameterisusedtocharacterizetheinterface. Whether may reflect the change of DOS.38,39 the Fermi velocity mismatch can be represented with an For PC in the diffusive or thermal regime, electrons effectiveZparameterisnotyetclear.48NotethatinBTK in the PC are scattered by impurities or defects, whose model the scattering in the metals and the interface is contribution to R can be estimated from the bulk re- PC not considered, even for finite Z. So its transparent in- sistivity, and the orifice just provides a geometric limita- terface limit (Z =0) corresponds to the ballistic limit of tion. In the limit d (cid:29) l , the Maxwell resistance inelastic the PC model, i.e., the point contact Andreev reflection is spectroscopy can only be applied to ballistic contacts. ρ R = . (A4) Since the BTK model can be used for various interface Max d transparencies, it has wider application than the simple Z = 0 point contact model. To take into account addi- As it depends on d−1 instead of d−2, it dominates over tional scattering at or near the interface, i.e., R , a R when d is large. And when inelastic scattering hap- Max Sh normal resistor in series45 or a normal current in paral- pens inside the PC, the equilibrium temperature in the lel20,51 canbeadded. Thusevenintheso-calledthermal PC can be elevated following regime,thegapvaluecanberoughlyestimatedwithcon- V2 sideration of a combination of the BTK model and PC TP2C =Tb2ath+ 4L (A5) model.45 In some cases it is believed that although the foot- where L is the Lorentz number. For a rough estimation, printofthePCcanbetensofmicrons,muchlargerthan when T (cid:28) T , assume a standard L = 2.45×10−8 bath PC l, but still ballistic limit can be applied because there V2K−2,theneV ∼3.63k T ,orT (K)(cid:39)3.2V (mV). B PC PC are multiple smaller PC junctions randomly distributed That explains for a thermal PC similar feature can be across the contact area,51,52 and the BTK model can foundindV/dI(V)andindV/dI(T). Forthegapenergy be used directly. Although conceptually this is differ- around0.2mVinthiswork,inthethermallimitarough ent from the picture that there is an interface barrier estimation of T at 0.2 mV is 0.64 K, which is below PC which contributes to the PC resistance like a real tun- the T of SRO, so the bias will not drive the PC out of C neling junction, but in both cases ballistic limit can be the SC state even in the thermal limit. applied as R is smaller than R . Max Sh Intheintermediateregime,Wexlerderivedaninterpo- When the SC has unconventional pairing symmetries, lation formula generalized BTK model is developed to fit the data by 16ρl ρ(T) taking into account various parameters including order RPC(T)(cid:39) 3πd2 + d . (A6) parametersymmetry,incidenceangle,Fermisurfacemis- 7 match, life time broadening due to inter or intra band scattering etc. PCS for unconventional SC has been re- viewed in Ref. 17, 18, 48, and 53. It is still not clear whether the order parameter symmetry can be verified strictly from the shape of the point contact Andreev reflection spectra.17,48 In this work we mainly report the temperature and field dependence of the PC spectra rather than quantitatively fit the data with the general- ized BTK model.9,10 FIG. 6. (Color online) Comparison of polarized optical mi- croscope images of two samples: S1 (left), S2 (right). Ru inclusions are clearly seen in the right image for S2. Appendix B: Fitting with electron-electron interaction The difference between PCS and planar tunneling is whether the in-plane momentum is conserved. Since there is no well-known theory for incorporation of quan- tum correction of DOS into PCS, here we use the theory for the planar tunneling junctions. Correction to tunneling conductance by electron- electron interaction (EEI) is quantitatively described by the Altshuler-Aronov (AA) theory,40,43 in the 2D limit, FIG. 7. (Color online) (a) Temperature dependence of the G(V,T)−G(0,T) = e2Rsq ln 4πδ [Φ ( eV )−Φ (0)], PC spectra for a W/SRO PC on S1 but obtained in another G(0,T) 8π2¯h DR 2 k T 2 run, showing similar gap features as in the main text. The sq B (B1) resistance is only about 1 Ω, but the gap around 0.15 mV, and the critical current effect are clearly demonstrated. (b) where R is the resistance per square of the metal film, sq Temperature dependence of the PC spectra for a Au/SRO δ the thickness of the insulating barrier, D the diffusion PC on S1, a split peak within ±0.5 mV is observed, similar constant,andΦ aintegralfor2DasdefinedinRef.[40]. 2 to that in Ref. [9]. The integral is (cid:90) ∞ cosh(x+A)−1 Φd(A)= dx cosh(x/2)2 micro image for S2, which is also harder to cleave than −∞ S1. This is consistent to the observation of Lichtenberg (cid:90) ∞ sinhydy in Ref. 54 that SRO with Ru vacancies is much easier to × dx , [coshy+cosh(x+A)](1+coshy)y2−d/2 cleaveandthesurfacedeadlayerprobablyisalsoeasierto 0 (B2) pierce through. We note that although here the surface where x=(cid:15)/kT and A=eV/kT. waspolishedbysandpapertoimproveimagequality, the The prefactor before the bracket in Eq. (B1) can be RuinclusionscaneasilybeobservedonthesurfaceofS2 lumped into one parameter S and it is the only fitting without any treatment. parameter. When eV (cid:29) k T but still within the 2D B limit, Eq. (B1) approaches Sln eV and S is just the kBT slope shown in Fig. 2. Since R = ρ/a, a the thickness Appendix D: Reproducibility sq of the metal film, the resistivity ρ=(e2νD)−1, the slope S ∝Rsqln(cν), where c is a constant. PC spectra for more than 10 locations were measured For the 3D limit, in several runs. In each run a few locations are tried to search for SC-like features. With increasing force the tip G(V,T)−G(0,T) e2ρ k T eV = √ ( B )1/2[Φ ( )−Φ (0)], eventually became blunted and bent, and small cracks G(0,T) 8 2π2¯h ¯hD 3 kBT 3 can also develop on the surface of the SRO. A set of PC (B3) spectrasimilartothatinFig.3isshowninFig.7a, fora (cid:112) which shows a linear dependence on eV/kBT when W/SRO PC on S1 but obtained in another run. Besides eV (cid:29)kBT. Wtip,Autip(0.5mmdia.) wasalsotriedonS1andthe PC spectra are shown in Fig. 7b. For the Au/SRO PC, gap value around 0.5 mV is observed, the conductance Appendix C: Optical images of the SRO surface enhancement is only about 1%, and instead of the dome like conductance peak, a split peak is observed, similar Optical images for SRO samples S1 and S2 are shown to that was reported in Ref. [9]. in Fig. 6 for comparison. Dense Ru inclusions of width ZBA is less obvious for Au/SRO PCs. For W/SRO about 1 µm and length a few µm are clearly seen in the PCs, ZBA is frequently observed, which could be due to 8 a thin oxide layer or a defective layer on the surface as observed in other PC measurements.51,55 For those PC spectra showing clear ZBA, there are two typical types as shown in Fig. 8. One type is similar to that in Fig. 2 with a logarithmic dependence consistent with 2D EEI, and SC feature sometimes coexists with ZBA; the other √ type has a V dependence which is consistent with 3D EEI, no SC feature is observed with this type of ZBA. For the 2D EEI type, e.g., for a 35 Ω PC on S2 as shown in Fig. 8, the slope 0.07 is close to the slope 0.11 for S1 inFig.2, and0.08in Fig.3, indicating similar2DEEIis probed, though here T = 2 K is higher than the bath fit temperature about 0.52 K, which is probably the reason that SC feature is not observed. FIG.8. (Coloronline)(a)Biasdependenceofthenormalized conductanceforpointcontactonS2withresistance35(blue) and13Ω(green)atT=0. 52K,and(b)theconductanceafter normalizedbythebackgroundEEIfits(thegreensymbolsare shiftedupforclarity). (c)EEI2Dfitting(blackdashline)for the 13 Ω PC with T = 2 K, slope 0.07. (d) EEI 3D fitting fit for the 35 Ω PC with T = 0.52 K, slope (3D) = 0.015. fit ∗ [email protected] F. Lichtenberg, Phys. Rev. Lett. 84, 1595 (2000). 1 Y.Maeno,H.Hashimoto,K.Yoshida,S.Nishizaki,T.Fu- 12 M. D. Upward, L. P. Kouwenhoven, A. F. Morpurgo, jita, J. G. Bednorz, and F. Lichtenberg, Nature 372, 532 N. Kikugawa, Z. Q. Mao, and Y. Maeno, Phys. Rev. B (1994). 65, 220512 (2002). 2 A. P. Mackenzie and Y. Maeno, Rev. Mod. Phys. 75, 657 13 I.A.Firmo,S.Lederer,C.Lupien,A.P.Mackenzie,J.C. (2003). Davis, andS.A.Kivelson,Phys.Rev.B88,134521(2013). 3 Y. Maeno, S. Kittaka, T. Nomura, S. Yonezawa, 14 R. Matzdorf, Z. Fang, Ismail, J. Zhang, and K. Ishida, Journal of the Physi- T. Kimura, Y. Tokura, K. Terakura, and cal Society of Japan 81, 011009 (2012), E. W. Plummer, Science 289, 746 (2000), http://journals.jps.jp/doi/pdf/10.1143/JPSJ.81.011009. http://www.sciencemag.org/content/289/5480/746.full.pdf. 4 G. M. Luke, Y. Fudamoto, K. M. Kojima, M. I. Larkin, 15 S.Lederer,W.Huang,E.Taylor,S.Raghu, andC.Kallin, J. Merrin, B. Nachumi, Y. J. Uemura, Y. Maeno, Z. Q. Phys. Rev. B 90, 134521 (2014). Mao,Y.Mori,H.Nakamura, andM.Sigrist,Nature394, 16 R.S.Gonnelli,A.Calzolari,D.Daghero,G.A.Ummarino, 558 (1998), cond-mat/9808159. V. A. Stepanov, P. Fino, G. Giunchi, S. Ceresara, and 5 J. Xia, Y. Maeno, P. T. Beyersdorf, M. M. Fejer, and G.Ripamonti,JournalofPhysicsandChemistryofSolids A. Kapitulnik, Phys. Rev. Lett. 97, 167002 (2006). 63, 2319 (2002), cond-mat/0107239. 6 J. R. Kirtley, C. Kallin, C. W. Hicks, E.-A. Kim, Y. Liu, 17 K.Gloos,F.Anders,B.Buschinger,C.Geibel,K.Heuser, K. A. Moler, Y. Maeno, and K. D. Nelson, Phys. Rev. B F. Ja¨hrling, J. Kim, R. Klemens, R. Mu¨ller-Reisener, 76, 014526 (2007). C. Schank, and G. Stewart, Journal of Low Temperature 7 C.W.Hicks,J.R.Kirtley,T.M.Lippman,N.C.Koshnick, Physics 105, 37 (1996). M.E.Huber,Y.Maeno,W.M.Yuhasz,M.B.Maple, and 18 D. Daghero and R. S. Gonnelli, Superconductor Science K. A. Moler, Phys. Rev. B 81, 214501 (2010). and Technology 23, 043001 (2010). 8 P. J. Curran, S. J. Bending, W. M. Desoky, A. S. Gibbs, 19 K.Gloos,F.Martin,C.Schank,C.Geibel, andF.Steglich, S. L. Lee, and A. P. Mackenzie, Phys. Rev. B 89, 144504 Physica B: Condensed Matter 206-207, 279 (1995), pro- (2014). ceedings of the International Conference on Strongly Cor- 9 S. Kashiwaya, H. Kashiwaya, H. Kambara, T. Furuta, related Electron Systems. H. Yaguchi, Y. Tanaka, and Y. Maeno, Phys. Rev. Lett. 20 Y.Miyoshi,Y.Bugoslavsky, andL.F.Cohen,Phys.Rev. 107, 077003 (2011). B 72, 012502 (2005). 10 S. Kashiwaya, H. Kashiwaya, K. Saitoh, Y. Mawatari, 21 S. Kittaka, H. Taniguchi, S. Yonezawa, H. Yaguchi, and and Y. Tanaka, Physica E: Low-dimensional Systems and Y. Maeno, Phys. Rev. B 81, 180510 (2010). Nanostructures 55, 25 (2014), topological Objects. 22 S. Kittaka, H. Yaguchi, and Y. Maeno, Journal 11 F. Laube, G. Goll, H. v. L¨ohneysen, M. Fogelstro¨m, and of the Physical Society of Japan 78, 103705 (2009), 9 http://journals.jps.jp/doi/pdf/10.1143/JPSJ.78.103705. 39 H. Z. Arham, C. R. Hunt, W. K. Park, J. Gillett, S. D. 23 C. W. Hicks, D. O. Brodsky, E. A. Yelland, A. S. Das,S.E.Sebastian,Z.J.Xu,J.S.Wen,Z.W.Lin,Q.Li, Gibbs, J. A. N. Bruin, M. E. Barber, S. D. Ed- G. Gu, A. Thaler, S. Ran, S. L. Bud’ko, P. C. Canfield, kins, K. Nishimura, S. Yonezawa, Y. Maeno, D. Y. Chung, M. G. Kanatzidis, and L. H. Greene, Phys. and A. P. Mackenzie, Science 344, 283 (2014), Rev. B 85, 214515 (2012). http://www.sciencemag.org/content/344/6181/283.full.pdf. 40 M.E.Gershenzon,V.N.Gubankov, andM.I.Faleˇi,Sov. 24 Z. Mao, Y. Maenoab, and H. Fukazawa, Materials Re- Phys. JETP 63, 1287 (1986). search Bulletin 35, 1813 (2000). 41 A. A. Abrikosov, Phys. Rev. B 61, 7770 (2000). 25 H. Taniguchi, S. Kittaka, S. Yonezawa, H. Yaguchi, and 42 D.Mazur,K.E.Gray,J.F.Zasadzinski,L.Ozyuzer,I.S. Y. Maeno, Journal of Physics: Conference Series 391, Beloborodov, H. Zheng, and J. F. Mitchell, Phys. Rev. B 012108 (2012). 76, 193102 (2007). 26 Y. A. Ying, Y. Xin, B. W. Clouser, E. Hao, N. E. Staley, 43 B. L. Al’tshuler and A. G. Aronov, Sov. Phys. JETP 50, R. J. Myers, L. F. Allard, D. Fobes, T. Liu, Z. Q. Mao, 968 (1979); B. L. Altshuler, A. G. Aronov, and P. A. and Y. Liu, Phys. Rev. Lett. 103, 247004 (2009). Lee,Phys.Rev.Lett.44,1288(1980); B.L.Altshulerand 27 Y.A.Ying,N.E.Staley,Y.Xin,K.Sun,X.Cai,D.Fobes, A. G. Aronov, in Electron-Electron Interactions in Dis- T.J.Liu,Z.Q.Mao, andY.Liu,NatureCommunications ordered Systems, Modern Problems in Condensed Matter 4, 2596 (2013), 10.1038/ncomms3596. Sciences, Vol. 10, edited by M. Pollak and A. L. Efros 28 D. A. Dikin, M. Mehta, C. W. Bark, C. M. Folkman, (North-Holland, Amsterdam, 1985) Chap. 1, pp. 1–154. C.B.Eom, andV.Chandrasekhar,Phys.Rev.Lett.107, 44 L.Liu,J.Niu,L.Xiang,J.Wei,D.-L.Li,J.-F.Feng,X.-F. 056802 (2011). Han, X.-G. Zhang, and J. M. D. Coey, Phys. Rev. B 90, 29 K. Deguchi, Z. Q. Mao, and Y. Maeno, Journal of the 195132 (2014). Physical Society of Japan 73, 1313 (2004). 45 G. Sheet, S. Mukhopadhyay, and P. Raychaudhuri, Phys. 30 E. Dumont and A. C. Mota, Phys. Rev. B 65, 144519 Rev. B 69, 134507 (2004). (2002). 46 A. M. Duif, A. G. M. Jansen, and P. Wyder, Journal of 31 H. Kambara, S. Kashiwaya, H. Yaguchi, Y. Asano, Physics: Condensed Matter 1, 3157 (1989). Y. Tanaka, and Y. Maeno, Phys. Rev. Lett. 101, 267003 47 Y.G.NaidyukandI.K.Yanson,JournalofPhysics: Con- (2008). densed Matter 10, 8905 (1998). 32 S.-I. Ikeda, Y. Maeno, S. Nakatsuji, M. Kosaka, and 48 W. K. Park and L. H. Greene, Journal of Physics: Con- Y. Uwatoko, Phys. Rev. B 62, R6089 (2000). densed Matter 21, 103203 (2009). 33 S. I. Ikeda, S. Koiwai, Y. Yoshida, N. Shirakawa, 49 H.Pothier,S.Gueron,N.O.Birge,D.Esteve, andM.H. S. Hara, M. Kosaka, and Y. Uwatoko, Journal Devoret, Phys. Rev. Lett. 79, 3490 (1997). of Magnetism and Magnetic Materials 272 (2004), 50 G. E. Blonder, M. Tinkham, and T. M. Klapwijk, Phys. 10.1016/j.jmmm.2003.12.1027. Rev. B 25, 4515 (1982). 34 J. P. Carlo, T. Goko, I. M. Gat-Malureanu, P. L. Russo, 51 H. Peng, D. De, B. Lv, F. Wei, and C.-W. Chu, Phys. A. T. Savici, A. A. Aczel, G. J. MacDougall, J. A. Rev. B 88, 024515 (2013). Rodriguez, T. J. Williams, G. M. Luke, C. R. Wiebe, 52 Y. Bugoslavsky, Y. Miyoshi, G. K. Perkins, A. D. Caplin, Y. Yoshida, S. Nakatsuji, Y. Maeno, T. Taniguchi, and L. F. Cohen, A. V. Pogrebnyakov, and X. X. Xi, Phys. Y. J. Uemura, Nature Materials 11, 323 (2012). Rev. B 72, 224506 (2005). 35 J.E.Ortmann,J.Y.Liu,J.Hu,M.Zhu,J.Peng,M.Mat- 53 D.Daghero,M.Tortello,P.Pecchio,V.A.Stepanov, and suda, X. Ke, and Z. Q. Mao, Scientific Reports 3, 2950 R. S. Gonnelli, Low Temperature Physics 39 (2013). (2013), 10.1038/srep02950. 54 F.Lichtenberg,ProgressinSolidStateChemistry 30,103 36 K. Gloos, Low Temperature Physics 35, 935 (2009). (2002). 37 K. Gloos and E. Tuuli, Journal of Physics: Conference 55 S. Sasaki, M. Kriener, K. Segawa, K. Yada, Y. Tanaka, Series 400, 042011 (2012). M. Sato, and Y. Ando, Phys. Rev. Lett. 107, 217001 38 H. Meekes, Phys. Rev. B 38, 5924 (1988). (2011).