Planar tunneling spectroscopy of the topological Kondo insulator SmB_6
aa r X i v : . [ c ond - m a t . s t r- e l ] J un Planar tunneling spectroscopy of the topological Kondo insulator SmB L. Sun, D.-J. Kim, Z. Fisk, and W. K. Park , † , ∗ Department of Physics and Materials Research Laboratory,University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA Department of Physics and Astronomy, University of California, Irvine, California 92697, USA (Dated: February 26, 2018)Several technical issues and challenges are identified and investigated for the planar tunnelingspectroscopy of the topological Kondo insulator SmB . Contrasting behaviors of the tunnel junc-tions prepared in two different ways are analyzed and explained in detail. The conventional approachbased on an AlO x tunnel barrier results in unsatisfactory results due to the inter-diffusion betweenSmB and deposited Al. On the contrary, plasma oxidation of SmB crystals produces high-qualitytunnel barriers on both (001) and (011) surfaces. Resultant conductance spectra are highly repro-ducible with clear signatures for the predicted surface Dirac fermions and the bulk hybridization gapas well. The surface states are identified to reside on two or one distinguishable Dirac cone(s) on the(001) and (011) surface, respectively, in good agreement with the recent literature. However, theirtopological protection is found to be limited within the low energy region due to their inevitableinteraction with the bulk excitations, called spin excitons, consistent with a recent theoretical pre-diction. Implications of our findings on other physical properties in SmB and also other correlatedtopological materials are remarked. I. INTRODUCTION
The conventional Landau-Ginzburg paradigm based onthe symmetries broken in ordered states breaks down inmany topological phases of matter discovered recently [1–4]. Three-dimensional (3D) topological insulators (TIs)comprise one such class of emergent quantum matter, inwhich the nontrivial topology in the bulk band structureleads to topologically protected metallic states at surfaces[5, 6]. Several dozens of 3D TIs have been discovered sofar, among which Bi-based materials [7, 8], such as Bi Se [9, 10], are best known. It is noteworthy that electron cor-relations do not play an important role in most of thesematerials. In recent years, Kondo insulators (KIs) [11]have drawn much attention due to a possibility that theymight also be topological [12]. Because strong correla-tions are at the heart of their underlying bulk physics,the surface states in these topological Kondo insulators(TKIs) are expected to exhibit more intriguing behaviorsthan in weakly correlated counterparts.SmB , known as a Kondo or intermediate valence in-sulator (or semiconductor), has long been studied [13].There is no doubt about the formation of a bulk hy-bridization gap below certain temperature and the ap-pearance of metallic states at low temperature as firsthinted by the resistivity plateau [14]. There had beenseveral scenarios proposed to explain this exotic behav-ior, including impurity states in the bulk [15]. However,the robustness of the plateau suggests that these con-jectures are unlikely as such states should be easily de-stroyed by disorders. Coming at the right time, the the-oretical proposal that certain Kondo insulators might be ∗ [email protected]; † Present address: National High Mag-netic Field Laboratory, Florida State University, Tallahassee,Florida 32310, USA topological [12], followed by subsequent band structurecalculations [16–18], has been given a particular attentionbecause it could readily explain the resistivity satura-tion behavior. These f -electron materials have inherentlylarge spin-orbit coupling and the hybridization gap getssmaller with increasing correlation strength, fulfilling therequirement for TIs, i.e., band inversion [6]. It was laterelaborated that the cubic crystal structure [19] and in-termediate valence nature [20] of SmB would make it aprime candidate for TKI. Consequently, a resurgence ofresearch interest has resulted in many new findings. Byall means, including transport measurements [21–25], itis now well established that the resistivity saturation isdue to the robust metallic states at surfaces [26, 27].However, their detailed topological nature still remainsto be unraveled unlike in the case of weakly correlatedcounterparts, e.g., Bi Se , in which various measure-ments, including angle- and spin-resolved photoemissionspectroscopy (ARPES) [9, 10] and scanning tunnelingspectroscopy (STS) [28, 29], have shown that the surfaceDirac fermions are indeed topological with the predictedspin-momentum locking nature. Although several pho-toemission measurements on SmB [30–36] have revealedthe formation of a hybridization gap below ∼
50 K andin-gap states, the exact topological nature is not unveiledyet. Also, clear signatures for the surface Dirac fermionssuch as linear conductance are lacking in several STS [37–39] and point-contact spectroscopy [40] measurements.The challenges encountered in studying SmB , or TKIsin general, are manifold. From the materials sciencepoint of view, these materials are much less favorable forthose surface-sensitive spectroscopic measurements thanthe Bi-based materials. More specifically, while the lay-ered structure of Bi Se allows an easy exposure of atom-ically smooth surfaces via cleavage, the 3D crystallinestructure of SmB makes it unfeasible. Also, it is knownthat the polar nature of the (001) surface, where thetopological surface states are predicted to exist, causesvarious complex issues including surface reconstruction[37] and time-dependent evolution [41]. Quantum oscil-lation measurements have shown the existence of surfacebands and their possible topological nature [42] but thenature of the bulk insulating state inferred from suchmeasurements is currently under debate [43]. From thefundamental physics point of view, the complexity has todo with the strong correlations in these materials under-lying their topological origin.We have addressed some of the aforementioned chal-lenges and obtained new spectroscopic information onthe topological nature in SmB [44]. Here, we adopt pla-nar tunneling spectroscopy (PTS) [45–47] because it isan inherently surface-sensitive probe [48]. In addition,the narrow tunneling cone in PTS geometry [49] mayallow momentum-selective measurements, which are use-ful when it is necessary to distinguish signals originatingfrom different Dirac cones, as seen in our work. In con-trast, despite its clear advantage of space-resolved spec-troscopic mapping capability [50], STS may not allowsuch measurements due to an inherently much wider tun-neling cone. There is another point to make in compar-ing spectroscopic techniques: in PTS (also in STS), acomplete energy range, i.e., both below and above thechemical potential, can be probed easily by reversing thebias polarity, whereas in ARPES it is non-trivial to ob-tain signals above the chemical potential. This differenceclearly stands out in our tunneling study [44].A basic underlying principle for PTS is Fermi’s goldenrule. A simple tunnel junction is comprised of a bottomelectrode (typically, the material of interest), a tunnelbarrier, and a top (or counter) electrode with a constantdensity of states (DOS) near the Fermi level ( N c (0)), thatis, a simple metal. Then, the differential conductance, G (V) ≡ dI/dV , is simply given by a convolution of theDOS of the material of interest ( N s ( E )) with respect tothe derivative of the Fermi function ( f ( E )): dIdV = A | M | e N c (0) ∞ Z −∞ N s ( E ) ∂f ( E − eV ) ∂ ( eV ) dE, (1)where A is the junction area and M is the tunnelingmatrix element. Thus, a measurement of tunnel conduc-tance can reveal detailed DOS structures.For high quality, the tunnel barrier should be sharplyinterfaced with both electrodes and its electrostatic po-tential should be much higher than the maximum biasvoltage. Typically, it is made of a thin layer of insu-lating oxide such as AlO x [45, 47]. Depending on theconstituent materials, depositing or forming such a thinbarrier layer may involve some challenges. This is par-ticularly the case with SmB , for which the conventionalAlO x barrier is found quite unfavorable. On the contrary,plasma oxidation of the crystal surface works quite wellto turn the top surface into a tunnel barrier. Combinedwith other cooperative factors including the excellent pol-ishability of SmB crystals and the use of superconduct- ing Pb as a counter-electrode, this approach allows us toobtain reproducible conductance spectra.In this paper, we shall focus on experimental develop-ments around the two approaches since detailed analysisand interpretation of the reproducible conductance fea-tures have been reported elsewhere [44]. In the next sec-tion, experimental details regarding the junction fabrica-tion and characterization are described. In Sect. III, re-sults from the above-mentioned two different approachesare presented. Those from initial attempts and also fromlater systematic diagnostic runs using an AlO x barrierare reported first, followed by the description of the datafrom junctions made of plasma-oxidized SmB surface.Sect. IV contains detailed discussion of the failures andsuccesses observed in these approaches as well as a briefdiscussion on the topological nature in SmB . A sum-mary follows in the last section. II. EXPERIMENTSA. Crystal Surface Preparation
Frequently, for PTS, the sample is in a thin-film formonto which a uniform insulating barrier can be easily de-posited. Here, we chose to use high-quality single crystalsgrown by a flux method [22]. Since the surface of a typ-ical as-grown SmB crystal is not so smooth as desiredfor tunnel junction fabrication, it has to be polished tomirror-like shininess. For this, as-grown crystals with lat-eral dimensions of 1 – 2 mm and thickness of ∼ R (cid:13) , 2850-FT).Polishing is done mechanically using alumina lappingfilms of particle sizes ranging from 12 – 0.3 µ m. Thecrystal is pressed manually with moderate pressure andrubbed against the lapping film. Isopropyl alcohol issprayed whenever lubrication is necessary. The polishinglasts for about 10 – 15 minutes using each lapping film,and the surface is subsequently inspected under an opti-cal microscope. If it appears to be smoother and moreuniform, the polishing proceeds with a lapping film ofsmaller particle. Figure 1 displays cross-sectional topo-graphic profiles obtained with an atomic force microscope(AFM). B. Junction Fabrication
The polished crystal is loaded into a high-vacuumchamber. First, an Ar ion beam is used to clean the sur-face by etching out, if any, surface oxides or contaminantsresidual from the polishing process. We have adoptedtwo methods to form a tunnel barrier: (i) Deposition andsubsequent oxidation of a thin Al film to form AlO x ; (ii)Plasma oxidation of the crystal’s top surface. In the for-mer approach, the Al film is deposited by dc magnetronsputtering at room temperature unless otherwise speci- -404 0 1 2 3 4-404 H e i g h t ( ¯ ) (001)(011) Position ( m)
FIG. 1. Linear topographic profiles of the polished (001) and(011) surfaces of SmB crystals measured with an AFM, show-ing that the polished surfaces are smooth enough for the de-position/formation of a thin tunnel barrier. fied. The deposition rate ranges from 1.25 – 5.0 ˚A s − .Al films of various thicknesses, d Al , between 15 and 70˚A have been used to optimize the parameters in eitherplasma [51] or thermal oxidation process. The oxygenplasma is generated by dc glow discharge. For thermaloxidation, the crystal is left in the vacuum chamber filledwith 1 – 10 Torr of oxygen for half an hour. In the sec-ond method, the plasma oxidation is done similarly tothe first case but without the Al layer.Prior to the deposition of counter-electrodes, crystaledges are painted with diluted cement in order to preventthem from being shorted to the bottom electrode (SmB )and also to ensure that junctions could be defined overthe most uniform area (see Fig. 2). We adopt Duco R (cid:13) cement because of its confirmed stability over thermalcycling. Once the cement is cured, counter electrodesare thermally evaporated through a shadow mask that iscarefully aligned under a microscope. We use Pb (Ag)as a (non-)superconducting counterelectrode since it iseasy to evaporate thermally. The deposition is done ata moderate rate of 8 – 10 ˚A s − to prevent damagesto the barrier layer and the total thickness is typically2500 ˚A. Owing to its sharp superconducting DOS, Pbis found to serve as an excellent filter for the quality ofjunctions. The detailed junction structure is displayed inFig. 2, which also shows the wiring configuration for ourconductance measurements. C. Junction Characterization
There are several ways to check the quality of junc-tions. First, if they are made with well-defined structuresincluding a uniform tunnel barrier, their differential resis-tance ( R J ≡ dV /dI ) should be inversely proportional totheir area and, in turn, the R J A product would be nearlyconstant. Our optimized SmB junctions typically have R J A values in the range of 50 – 150 Ωmm . Those with FIG. 2. The structure of a typical tunnel junction on SmB .Top panel is an optical image of a real junction and thebottom panel is its schematic cross-sectional diagram. Thedashed rectangle indicates the junction area. Also shown isthe wiring configuration for conductance measurements usinga custom-built mixing circuit. too large R J A usually show large fluctuations as the biasvoltage is ramped and those with too small R J A tendto have leakage currents due to micro-shorts across thebarrier. If the R J A value at room temperature is foundto be in the favorable range, we proceed by recordingthe zero-bias conductance (ZBC) as a function of tem-perature. For a material which experiences noticeablechanges in its electronic states like the gap opening inSmB , the temperature dependence of ZBC is to reflectsuch changes inevitably. Once the temperature is stabi-lized at the base, G ( V ) is measured over wide ranges oftemperature and magnetic field. When Pb is used as acounterelectrode, if necessary, a magnetic field of 0.1 Tis applied to suppress its superconductivity. III. RESULTSA. SmB /AlO x /Ag(Pb) junctions Although an AlO x barrier has been widely adopted forPTS [45, 47], realizing it on a specific material of interestcould be non-trivial. The resulting junction might suf-fer from under- or over-oxidation. Slight under-oxidationwould hamper detecting the intrinsic DOS albeit less se-rious in superconductive junctions owing to the proxim-ity effect. Over-oxidation is also problematic because itcould form additional oxides originating from the mate-rial itself. Thus, in order to produce high-quality tunneljunctions, the oxidation process should be optimized suchthat the Al layer is completely oxidized while the SmB crystal remains intact.More than fifty junction fabrication cycles have beenexecuted repeatedly using two crystals with (001) or -100 -50 0 50 1000.40.60.81.01.2 G ( V ) / G ( - m V ) V SmB6 (mV) R J (k ) 0.55 3.94 18.9 FIG. 3. Normalized G ( V ) data taken at 1.7 K for three(001)SmB /AlO x /Ag junctions showing some features due toSmB . The R J values are given at −
100 mV. d Al (oxidationconditions) is 50 (plasma, 4.2 W for 30 seconds), 50 (ther-mal, 1 Torr for 30 minutes), and 20 ˚A (plasma, 1.94 W for 20seconds), in the order of increasing R J . (011) surface orientation, respectively. Only a very smallportion (less than 4%) of the junctions show reproducibleconductance features, as displayed in Fig. 3. They com-monly exhibit both a gap-like suppression around zerobias and an overall asymmetric shape. While a broadpeak is seen in the negative bias branch, around − (17 ∼
20) mV, the conductance increases monotonically inthe positive bias counterpart. As this asymmetry can beattributed to a Fano interference effect [52] in a Kondolattice (or Anderson lattice, more broadly) [53–55], theconductance data must reflect intrinsic DOS in SmB tosome extent. The conductance curves appear to be lin-ear at low bias (in particular, see the curve for R J = 0.55kΩ), suggesting the existence of surface Dirac fermionsthat have V-shaped DOS, but detailed features are burieddue to large fluctuations. The overall features observed inthese curves are qualitatively similar to those revealed inthe best-quality junctions prepared by surface oxidation[44] (also, see Fig. 9), presumably because the adoptedprocessing parameters happen to allow the formation ofrather a clean tunnel barrier. However, due to the poorreproducibility, in the following we shall focus on under-standing how different parameters might affect the for-mation and quality of an AlO x barrier on SmB .Junctions with an AlO x barrier frequently have toolarge resistance ( R J A > ). This causes largeconductance fluctuations, rendering detailed DOS fea-tures buried in noise. One may consider decreasing thebarrier thickness as a solution but what actually happensis quite complicated as detailed later. Figure 4 shows anexample in which the conductance does not reveal anyDOS features of SmB . While the conductance is onlysemi-linear at high temperatures, a gaplike suppressionappears with decreasing temperature. The peaky shapearound ± -30 -15 0 15 305.56.06.57.0 (a) G ( V ) ( - - ) ( s h i f t e d ) V SmB6 (mV) (b) Z B C ( - - ) T (K)
H (G)
FIG. 4. Conductance of a (001)SmB /AlO x /Ag junctiondominated by the superconductivity in unoxidized Al. d Al =30 ˚A and the barrier is formed by thermal oxidation. (a) Con-ductance spectra as a function of temperature. For clarity, thecurves are shifted vertically. (b) Temperature- (bottom axis)or magnetic-field- (top axis) dependent ZBC. were oxidized. The ZBC data as a function of tempera-ture and magnetic field, shown in Fig. 4(b), indicate thatthe ZBC suppression disappears above ∼ ∼ directly. Then, why is its T c higherthan in the bulk Al (1.2 K)? This can be understood byconsidering that the unoxidized Al layer might be disor-dered, in which case the T c can go up [56]. This observa-tion may appear to point to the importance of completeoxidation of the Al layer. However, it turns out morecomplicated than it appears. For instance, the conduc-tance spectra from some other junctions reveal more com-plex features as plotted in Fig. 5. Here, the conductanceis asymmetric with some gap-like features including thebroad peak centered around a negative bias and the sup-pression around zero bias, whose origin might be similaras in Fig. 3. But there also appear additional features atlow bias ( ± -30 -15 0 15 300.60.70.80.91.0 G ( V ) / G ( - m V ) V SmB6 (mV)
H(T) 0 1
FIG. 5. Normalized conductance of a (011)SmB /AlO x /Agjunction at 1.37 K, exhibiting signatures due to both SmB and unoxidized Al. d Al = 40 ˚A and the barrier is formed bythermal oxidation. again we associate them with superconductivity in theunoxidized Al. To understand how those mixed featurescan appear, we speculate that, under some unknown con-ditions, the oxidation may result in a nonuniform barrierwith the Al being almost completely oxidized over someareas but remaining unoxidized in other areas.In order to investigate whether optimizing the oxida-tion parameters is a major issue, we performed experi-ments for a series of junctions with d Al decreasing from50 ˚A to 15 ˚A and Pb as the counter-electrode. Here,we adopt thermal oxidation instead of plasma oxidationfor the consistency of oxidation parameters (1 Torr, 30min.) among different runs. If the oxidation itself werethe issue, intrinsic DOS features could be observed repro-ducibly once d Al is optimized. Figure 6(a) shows theirnormalized G ( V ) curves at 4.2 K. Junctions with thickerAl exhibit the Pb coherence peaks but no features dueto SmB , which is possible again if part of the Al layeris left unoxidized. The Pb gap features are suppressedquite slowly with decreasing d Al down to 25 ˚A, belowwhich they disappear abruptly and only a broad dip de-velops around zero bias. Combined with results frommany other runs, we conclude that junctions with a verythin Al ( d Al <
15 ˚A) do not show any SmB features atall regardless of how it is oxidized. This observation iscontradictory to our initial speculation mentioned above.One might suspect the uniformity of the Al layer de-posited. To address this issue, we employed Auger elec-tron spectroscopy to measure the chemical homogeneityfrom several different spots on the surface of SmB sin-gle crystals coated with 20-˚A-thick Al. The statisticsclearly shows that the relative intensity of the Al peakis uniform on both (001) and (011) surfaces, ruling outthat possibility. Also, the fact that the superconductingPb features are still observed for d Al = 25 ˚A implies thatthe unoxidized Al is quite uniform over the junction area.This reasoning led us to speculate that the culprit mightbe at the interface between SmB and Al. To investigate this possibility, three more experimentsare conducted by preparing junctions with nominally thesame d Al (= 20 ˚A) but deposited in three different waysas follows. In one batch, 10 ˚A-thick Al is deposited andoxidized thermally, which is repeated twice with an an-ticipation that the Al layer could be oxidized more com-pletely and uniformly. However, as shown in Fig. 6(b),this method does not lead to any better data but fea-tureless and noisy signals. We then speculate this mightbe because the resultant AlO x layer is highly disordered.Thus, the next run is carried out by depositing 20 ˚A-thickAl under better base vacuum achieved by running a liq-uid nitrogen jacket inside the chamber. In this case, moreresidual moisture is expected to be removed so that theresultant AlO x barrier could be cleaner. Quite surpris-ingly, the superconducting Pb features reappear in thisjunction, contrary to the case in Fig. 6(a) with the same d Al but processed without the nitrogen jacket running.This implies that whatever causing the abrupt change inthe conductance behavior going from 25 ˚A to 20 ˚A inFig. 6(a) disappears. Because the conductance featuresare almost identical with the 25 ˚A case without showingany SmB features anticipated for thinner Al, this behav-ior can not be explained by the cleanliness of the barrieritself. In this regard, we note that the sample stage tem-perature during the deposition dropped to ∼
268 K due toconvective cooling by the running nitrogen jacket. Thisraises a possibility that Al atoms might diffuse into SmB (or vice versa) at room temperature, particularly in theinitial stage, whereas such diffusion is greatly reduced atlow temperature to allow them to form a sharper inter-face with SmB . In turn, if the Al layer were not oxidizedcompletely, the superconducting Pb features would reap-pear. To test this scenario in another way, the last trialis to deposit a thin (10 ˚A) Au layer prior to Al. This isa feasible scheme since different elemental atoms wouldhave much different diffusion constants. Here, both Auand Al layers are deposited at room temperature as usual.If the inter-diffusion were a real issue, this thin Au layermight alleviate it substantially by acting as a diffusionbarrier. Indeed, the Pb superconducting features reap-pear as shown in Fig. 6(b), very similarly to the previousone. These observations indicate that junctions havingnominally the same d Al behave very differently dependingon how the Al layer is deposited due to the inter-diffusionbetween Al and SmB . B. SmB /Oxi-SmB /Pb junctions As an alternative to the traditional AlO x barrier, wehave tried several other methods, including deposition ofa thin Nb layer as a diffusion barrier and/or buffer layerfor Al or oxidation of that layer to form a tunnel barrier.While some of these trials give better results, high-qualityjunctions are not obtained reproducibly by any approachexcept plasma oxidation of the SmB crystal surface [44].These tunnel junctions, denoted as SmB /Oxi-SmB /Pb, -30 -15 0 15 30 -30 -15 0 15 30 V SmB6 (mV) G ( V ) / G ( - m V ) ( s h i f t e d ) (b)(a) G ( V ) / G ( - m V ) ( s h i f t e d ) d Al (¯) = 5040302520 V SmB6 (mV)
20 (10+10)20 (268 K)10 (Au) /20d Al (¯) = 2025 FIG. 6. Normalized conductance spectra of SmB /AlO x /Pb junctions prepared by thermal oxidation with varying d Al . Thecurves are taken at 4.2 K and shifted vertically for clarity. The SmB crystal has either (001) or (011) orientation, which isnot specified here since the results do not seem to depend on it. (a) Evolution of normalized G (V) with d Al decreasing from 50to 15 ˚A. (b) Conductance spectra of junctions with nominally the same Al thickness (20 ˚A), revealing the impact of how theAl layer is deposited (three middle curves). The curves for d Al = 20 and 25 ˚A from (a) are also included for comparison. -50 -25 0 25 50-50 -25 0 25 50 (b)(a) (001) T(K) 100.00 90.00 80.00 70.00 65.00 60.00 55.00 50.00 45.00 40.00 35.00 30.00 25.00 20.00 15.00 10.00 7.25 6.80 6.20 5.20 4.19 3.24 1.72 G ( V ) / G ( - m V ) ( s h i f t e d ) V SmB6 (mV) V
SmB6 (mV) (011)
FIG. 7. Normalized G (V) of SmB /Oxi-SmB /Pb junctions for (a) (001) and (b) (011) surface orientations. The barrier isprepared by plasma oxidation of the SmB crystal. The data below T c (7.2 K) of Pb were taken with the superconductivitysuppressed by an applied magnetic field of 1000 G. The curves are shifted vertically for clarity. not only exhibit intrinsic DOS features due to SmB , asshown in Fig. 7, but also highly reproducible.The temperature dependence displayed in Fig. 7 pro-vides a detailed picture on how the electronic statesin SmB evolve from a bad metallic behavior at hightemperature to an insulating (or semiconducting) to asurface-conduction dominant state at low temperature.The bulk hybridization gap, as evidenced by the broadpeak around −
21 mV as well as the low-bias conductancesuppression, appears to form below ∼
50 K but signaturesfor the surface states do not stand out until the temper-ature is lowered further down to ∼
25 K, as seen moreclearly in G ( V b , T ) curves [44]. Afterward, the surfacestates appear to undergo quite a complicated multi-stepevolution, which we associate with their interaction withthe bulk excitations, called spin excitons [57].In order to investigate what kind of tunnel barrieris formed in these junctions, we have carried out x-rayphotoelectron spectroscopy (XPS) measurements on theSmB crystals oxidized similarly. Figure 8 shows XPSdata on both (001) and (011) surfaces. In Fig. 8(b),some of the boron atoms are found to be oxidized to formB O [58]. On the other hand, no clear evidence is foundfor oxidized Sm atoms as shown in Fig. 8(c). Whilethe formation of some samarium oxides such as Sm O can not be completely ruled out due to their chemicalcomplexity [59], we think that the B O layer serves asa tunnel barrier, as also supported by a band structurecalculation [60] showing that B O has a large (6–9 eV)band gap.Also shown in Fig. 7, SmB /Oxi-SmB /Pb junctionsexhibit linear conductance shape at low bias reminiscentof the V-shaped DOS of Dirac fermions, which is dis-tinctly different between the two surfaces, i.e., double-versus single-linear. As has been explained in detail inRef. [44], this is interpreted as due to the difference inthe number of distinct Dirac cones, which is detected pre-sumably due to PTS’ momentum-selective nature [49].Our observation is in good agreement with both theo-retical calculations [16–19] and quantum oscillation mea-surements [42].Another significant spectroscopic feature is the linear-ity ending well below the hybridization gap edges. Asdescribed in Ref. [44], the surface states in SmB areprone to the interaction with bulk excitations, spin ex-citons, abundant due to its close proximity to an anti-ferromagnetic quantum critical point [61] as detected inrecent neutron scattering measurements [57]. Our con-ductance spectra clearly exhibit the features evidencingsuch interaction, also seen in some ARPES measurements[32, 62].The features discussed above are quite reproducible.Figure 9 shows conductance data obtained from junc-tions prepared in different runs. The bulk gap featuresincluding the broad peak at −
21 mV and the suppressionaround zero bias are clearly observed. Also, features dueto the topological surface states are detected, includingthe double- versus single-linear conductance shape and the kink-hump structure originating from their interac-tion with bulk excitations. The two junctions for a givensurface orientation show slightly different Dirac pointsand kink locations as well, which might originate fromthe difference in chemical potential and also in lengthscale for the interaction depending on detailed conditionsfor the plasma oxidation.
IV. DISCUSSION
In the last section, several issues and challenges areidentified in producing high-quality tunnel junctions onSmB . A great number of junctions based on the conven-tional AlO x barrier exhibit unpredictable behaviors rang-ing from trivial conductance shape such as parabolic orsemi-linear, superconducting features due to the under-oxidized Al layer, to features somewhat intrinsic toSmB . A few systematic studies with various d Al showthat the culprit is the inter-diffusion between SmB andAl. Here we address these issues in more detail by con-sidering realistic junction structures and tunneling pro-cesses.Let us begin by discussing what might happen as d Al is varied. In Fig. 10(a), we consider two limiting cases.When the Al layer is too thick, regardless of what actu-ally happens at the interface, some Al will remain unox-idized underneath the top AlO x layer. Then, the tunnel-ing will occur between the top electrode and the unoxi-dized Al instead of SmB , which is why some junctionsexhibit features due to superconducting Al (Fig. 4) orPb (Fig. 6). When the Al layer is too thin, even if agood-quality AlO x barrier is formed at the top, due to theinter-diffusion layer underneath, electrons will go throughdiffusive transport instead of single-step elastic tunnelinginto SmB . This explains why the Pb superconductingfeatures disappear abruptly as d Al is decreased from 25˚A to 20 ˚A (see Fig. 6(a)).Figure 10(b) illustrates structures of the three junc-tions with nominally the same d Al (20 ˚A), whose conduc-tance spectra are plotted in Fig. 6(b). First, depositingand oxidizing a thinner (10 ˚A) Al twice to ensure a thor-ough oxidation does not work since the first Al deposi-tion has already resulted in an inter-diffusion layer, whoseoxidation would produce some non-conducting complexoxides. Thus, even if the second Al layer turned intoa good tunnel barrier, the conductance data would notreveal any information on the electronic states in SmB but featureless noise. Second, when the Al layer is de-posited while the liquid nitrogen jacket is running, thelowered sample temperature reduces the inter-diffusion.Thus, most of the 20 ˚A-thick Al layer remains intact,part of which is left unoxidized under the thermal oxida-tion conditions adopted, as depicted in the middle panelof Fig. 10(b). This explains why the Pb superconduct-ing features reappear. Lastly, the thin Au layer (10 ˚A)prevents the inter-diffusion as it may act as a diffusionbarrier, as illustrated in the right panel of Fig. 10(b). *** S m d O K LL B s C s O s (a) I n t e n s i t y ( C P S ) Binding Energy (eV) (001) (011) (001) (011) S m d / S m d / (c) I n t e n s i t y ( C P S ) Binding Energy (eV) (001) (011) B O B s (b) I n t e n s i t y ( C P S ) Binding Energy (eV)
FIG. 8. XPS data from plasma-oxidized SmB crystal surfaces. (a) Spectra over the entire binding energy range. The peakslabeled with asterisks are due to the epoxy mold. (b) Detailed data to show the chemical states of B atoms. (c) Peaks arisingfrom Sm 3 d electrons. G ( V ) / G ( - m V ) ( s h i f t e d ) J2, 1.75 K J1, 1.72 K (001) (a) V
SmB6 (mV)
J4, 1.74 K J3, 1.72 K (011) (b)
FIG. 9. Reproducibility of conductance spectra in SmB /Oxi-SmB /Pb junctions. Normalized conductance curves shownfor two junctions prepared in different runs, shifted verticallyby 0.2 for clarity. The inter-diffusion layer may consist of some alloy-likestructures in which the Al atoms randomly occupy thelattice sites in SmB . While the length scale over whichsuch diffusion occurs remains to be investigated, it is clearthat the lattice translational symmetry is broken in thatregion, preventing the formation of coherent heavy bandsin a Kondo lattice. In turn, there will not be any topo-logical surface states since, theoretically, they can ariseonly under the formation of coherent states in the bulkor a hybridization gap [12, 26]. The topological surfacestates might still exist beyond the inter-diffusion layer,similarly to the case of ion-damaged SmB crystals [23],but they would not be felt by tunneling electrons unlikein transport measurements, in which the current is set to flow along the surface. The reason why the SmB features are not still observed when the inter-diffusion isreduced by depositing 20-˚A-thick Al at low temperaturemay have to do with the length scale relevant for tun-neling electrons. We speculate that the unoxidized Allayer might be still too thick ( >
10 ˚A) to allow tunnelingelectrons’ wave functions to extend down to the surfacestate region.In order to enhance our microscopic understanding, wespeculate on what trajectories the electrons will followwhen forced to move from the counter-electrode (Ag, forsimplicity) to SmB , as illustrated in Fig. 11. First,when a good tunnel barrier is formed like in the case ofplasma oxidized SmB , the single-step elastic tunnelingis predominant as depicted in the left panel, resultingin clear features reflecting the DOS of SmB . On theother hand, if the deposited Al forms an inter-diffusionlayer, electrons can not tunnel but diffuse through it, asdepicted by the trajectories in the right panel of Fig.11. They will lose energy via inelastic scattering eventsin that region, effectively rendering those features lostin the current-voltage characteristics. If the Al layer isthick enough to leave a part of it unoxidized on top of theinter-diffusion layer, or if the diffusion is largely reducedat low temperature or due to a diffusion barrier, theytunnel into the unoxidized Al layer instead of SmB .A possible solution for both inter-diffusion and under-oxidation is depositing a thinner ( <
10 ˚A) Al layer atliquid nitrogen temperature and thermally oxidizing itcompletely. A potential issue would be uneven coveragedue to the reduced kinetic energy of sputtered Al parti-cles. Other possibilities include reactive sputtering of Alunder a small oxygen partial pressure or direct deposi-tion of Al O using RF sputtering. Also, one can thinkof using different materials for the tunnel barrier sincethey may not suffer from the issues raised by Al. Theextent of diffusion and sticking of sputtered particles ona given substrate (SmB in our case) relatively dependson the pair of materials. Although Al has some seriousissues when paired with SmB as we report here, it is awell-known material to grow on Nb to form an excellent FIG. 10. Schematic cross-sectional diagrams of the SmB /AlO x /Pb junctions prepared by thermal oxidation. (a) To illustratecontrasting behaviors between junctions with an Al layer in the thicker (40 ˚A) or thinner (15 ˚A) limit. The left panel is for d Al ≥
25 ˚A, thick enough to leave a part of the Al layer unoxidized on top of the inter-diffusion layer. The right panel showsthe opposite case, namely, d Al <
25 ˚A, where the Al layer is too thin to leave an unoxidized layer. (b) Structures of threejunctions with nominally the same Al thickness (20 ˚A) but deposited and oxidized in different ways. Left panel: 10 ˚A-thick Alis deposited and oxidized, which is repeated twice. Middle panel: 20 ˚A is deposited at low temperature ( ∼
268 K). Right panel:10 ˚A-thick Au is deposited prior to the Al layer at room temperature. TSS denotes the topological surface states. tunnel barrier [47].The success of plasma oxidation of the SmB crystalas a means to form a tunnel barrier has to do with thestability of resultant B O with large enough band gap[60] as mentioned earlier. Such methods of utilizing self-oxides as a tunnel barrier have been known for somematerials in the literature [47] and was attempted onSmB with some success [63]. In our case, the emergenttopological surface states in SmB and their robustnessagainst non-magnetic perturbations [22] are very bene-ficial. While it remains to investigate detailed proper-ties of the B O layer formed on SmB , the cleanlinessand reproducibility of the conductance features suggeststhat it has a high-enough potential barrier sharply in-terfaced with both SmB and Pb, as illustrated in theleft panel of Fig. 11. Here, the majority of electronsundergo a single-step elastic tunneling and, thus, the dif-ferential conductance maps out the DOS of SmB whenthe Pb is in the normal state. Also, it is interesting tonote that, after the plasma oxidation, the surface statesmust have moved down to underneath the B O layer, at-testing their robustness, thus, topological nature. If theywere trivial metallic states at the surface, they would notbe able to survive such harsh processes as polishing andplasma oxidation.As revealed in our conductance spectra and analysis[44], the topological surface states in SmB are not in-tact under the existence of bulk excitations, unlike in theweakly correlated counterparts. Furthermore, the tem-perature dependence of the conductance, both G ( V ) and G ( V b ), indicates that their spectral density undergoes a rather complex evolution due to the interaction with spinexcitons [61], which must also impact many other phys-ical properties measured. For instance, the temperaturedependence of DC resistivity in SmB has been inter-preted as exhibiting temperature-dependent activationenergy gaps [64] when analyzed using the conventionalArrhenius expression as for typical semiconductors. Weconjecture that such non-trivial temperature dependencemight originate from the complex evolution of the surfacestates rather than the bulk hybridization gap itself. Also,the helical spin texture [36] might be influenced greatlyby the same interaction.Finally, we mention broader implications of our find-ings on other topological materials in which strong corre-lations govern their ground states. Their phase diagramsare generally complex due to competing/intertwined or-ders (e.g., the Doniach phase diagram for Kondo lat-tices [65]) and, thus, it is not uncommon that topologicalphases may emerge in close proximity to quantum criticalpoints. In such cases, there can be strong bulk excitationmodes due to critical fluctuations, which will inevitablyinteract with the topological surface states as we observein SmB . Therefore, this possibility should always betaken into account in studying strongly correlated topo-logical materials. V. SUMMARY
PTS, being both surface-sensitive and momentum-selective, is a technique suitable for the investigation0
FIG. 11. Diagrams to illustrate the tunneling process in SmB junctions. For simplicity, only transmissive (not reflective)trajectories are considered. Left panel: When the junction isof high quality with the barrier formed by plasma oxidationof the crystal, a single-step elastic tunneling is predominant.Right panel: When the barrier is formed by depositing andoxidizing a thin Al layer, the charge transport is dominatedby multiple diffusive steps in the inter-diffusion layer as illus-trated by the two different trajectories. of electronic properties of the topological surface statesin SmB . The conventional method of depositingand oxidizing a thin Al layer is found to pose severalchallenges. Not only is the complete oxidation of Alnon-trivial but also the inter-diffusion of Al with SmB is found to be a fundamental issue, as tested in a fewsystematic studies with various thickness and depositionschemes for Al. While it is possible to overcome thesechallenges with a better system, we have successfullyidentified an alternative method. Here, the key pro-cessing step is to form a self-oxide. Namely, the topsurface of a SmB crystal is plasma-oxidized to form atunnel barrier, i.e., B O layer as confirmed by an XPSanalysis. This method produces high-quality junctionswith excellent reproducibility. The tunnel conductance of such junctions reflects spectroscopic properties of thebulk and the surface states as well [44]. While the bulkhybridization gap is found to open up below ∼
50 K withthe full gap size of ∼
21 meV, signatures for the surfacestates begin to appear at a much lower temperature, ∼ ± .Further investigations using even higher-quality tunneljunctions should promise to unveil more details. VI. ACKNOWLEDGMENTS
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