Spin-Polarized Tunneling in Critically Disordered Be-Al Bilayers
SSpin-Polarized Tunneling in Critically Disordered Be-Al Bilayers
F.N. Womack and P.W. Adams
Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
G. Catelani
JARA Institute for Quantum Information (PGI-11),Forschungszentrum J¨ulich, 52425 J¨ulich, Germany (Dated: October 19, 2020)We report spin-polarized tunneling density of states measurements of the proximity modulatedsuperconductor-insulator transition in ultra thin Be-Al bilayers. The bilayer samples consisted ofa Be film of varying thickness, d Be = 0 . − . R ∼ h/ e revealed a super-linear Zeeman shift near the critical field. Ourdata suggests that critically disordered samples have a broad distribution of gap energies and thatonly the higher portion of the distribution survives as the Zeeman critical field is approached. Thisproduces a counter-intuitive field dependence in which the gap apparently increases with increasing parallel field. The disorder driven superconductor-insulator transi-tion (SIT) has been the subject of intense investigationfor more than 30 years now [1–6]. Early studies sug-gested a relatively simple picture of the SIT in homoge-neously disordered two-dimensional (2D) systems. As thedisorder of the superconductor is increased, the under-lying repulsive Coulomb correlations are enhanced untilthey eventually overwhelm the resident superconductingcorrelations. This was believed to occur at a relativelywell-defined critical disorder characterized by the quan-tum resistance R Q = h/ e [1, 7]. However, more recentstudies of the SIT have shown that the disorder-driventransition has contributions from both single-electron ef-fects and many-body quantum correlations which, underthe proper conditions, can lead to unexpected phases [8–11]. In particular, depending on the details of the filmmorphology, the SIT can either be dominated by an at-tenuation of the amplitude of the superconducting orderparameter or by a disruption of the phase of the orderparameter. In the latter case, the loss of long range phasecoherence can produce an insulating phase which is fun-damentally bosonic in nature [8]. For instance, inves-tigators have recently exploited multiply connected ge-ometries [12, 13] to show that superconducting pair cor-relations exist well into the insulating phase of highlydisordered Bi films [6, 8, 9]. But the details of howthis Bose insulator phase emerges with increasing dis-order remains unclear. Here we present a spin-polarizedtunneling study of the evolution of the superconductinggap in critically disordered Be-Al bilayers that are tunedthrough the SIT via a Zeeman field. Parallel magneticfield is used to induce a Zeeman splitting of the BCSdensity of states (DoS) spectrum while minimizing theorbital field broadening of the spectral features. As thecritical field is approached from below, we find that thesupra-gap spin band shifts super-linearly with increasingfield. This suggests that at low Zeeman fields the tunnel- ing conductance measures the average of a rather broaddistribution of gap energies [14]. But as the critical fieldis approached from below, only the highest energy por-tion of the distribution remains intact thereby producingan apparent increase in average gap energy with increas-ing field. The resulting spectra represent a direct probeof the pairing amplitude distribution across the SIT.Superconducting Be-Al bilayer films were formed byfirst depositing a thin Be layer of varying thickness ontoa fire-polished glass substrate followed by the depositionof a 1 nm-thick Al film. The depositions were performedby e-beam evaporation from 99.9% Be and 99.999% Altargets at a rate of ∼ . P < × − Torr. Planartunnel junctions were formed between the upper Al layerof the samples and a counter-electrode composed of anon-superconducting Al alloy using a 1 nm layer of SiOas the tunnel barrier. Bilayers with an Al thickness of1 nm and Be thicknesses ranging from 0.8 to 4.5 nm hadnormal state sheet resistances that ranged from R = 100to 10 Ω at low temperature. Magnetotransport measure-ments were made on a Quantum Design Physical Prop-erties Measurement System He3 probe. The maximumapplied field was 9 T and the base temperature of thesystem was 400 mK. The tunneling measurements werecarried out using a standard 27 Hz 4-wire lock-in ampli-fier technique.Our primary goal in this study was to use the Zee-man splitting of the BCS DoS spectrum to probe the su-perconducting phase of homogeneously disordered filmswhich are close to the disorder-driven zero field SIT. Inorder to resolve the Zeeman splitting, the superconductormust have a low spin-orbit (SO) scattering rate. We alsorequire that the transition temperature of the film be wellabove the base temperature of our fridge. Thin Al films a r X i v : . [ c ond - m a t . s up r- c on ] O c t meet these conditions; they have a T c ∼ . not necessarily by many-body effects. In order to circum-vent this limitation, we deposit the Al on a thin layer ofBe. Beryllium forms dense, adherent, amorphous films onglass substrates and, like Al, it has a low SO rate. How-ever, the transition temperature of Be films, T c ∼ . T c by virtue ofthe proximity effect [16].In general the critical field of a thin film superconduc-tor has both an orbital and a Zeeman component. Thelatter originates from the Zeeman splitting of the conduc-tion electrons [17]. In most circumstances, however, theorbital response of the superconductor dominates its crit-ical field behavior in the sense that the Zeeman criticalfield can be an order of magnitude larger that its orbitalcounterpart. This is particularly true in high spin-orbitscattering superconductors such as Nb and Pb due tothe fact that even relatively modest spin-orbit scatteringrates can dramatically quench the Zeeman response [18].But if one makes a low atomic mass film, such as Al,sufficiently thin and orients the field parallel to the filmsurface then the orbital response will be suppressed andone can realize a purely Zeeman-mediated critical fieldtransition [19]. The parallel critical field is given bythe Clogston-Chandrasekhar equation [20], H c (cid:107) = √ gµ B ,where ∆ is the zero temperature - zero field gap energy, µ B is the Bohr magneton, and g is the Land´e g-factor. Inthis series of experiments we have explored the Zeemanresponse of Be/Al bilayers with sheet resistances rangingfrom R (cid:28) R Q to R ∼ R Q .Shown in Fig. 1 are the bilayer transition tempera-tures T c as a function of the Be thickness. Note that forBe thicknesses greater than ∼ . T Be c ∼ . T Al c ∼ . T c increases with decreasing Be thickness d Be suggests that the bilayer transition temperature wasmediated by the proximity effect. But decreasing theBe thickness also increases the overall bilayer resistance,and bilayers with d Be (cid:46) R Q = h/ e [7]. Since R Q represents the threshold for the SIT we believe thatthe local maximum in Fig. 1 arises from the preemptiveeffects of increasing disorder. If the sheet resistance ofthe bilayers played no role in determining T c then onewould expect T c → T Al c as d Be → T c ( K ) beryllium thickness (nm) FIG. 1. Plot of the bilayer transition temperature as a func-tion of the Be layer thickness d Be . Inset: schematic diagramof the sample geometry. The thickness of the Be layer wassystematically varied between 0.8 nm and 4.5 nm, while theAl layer thickness was maintained at 1 nm. In Fig. 2 we plot the temperature dependence of thesheet resistance of a d Be = 0 . H c (cid:107) ∼ G is simply proportional to thesingle-particle density of states (DoS) [24]. The bias volt-age is relative to the Fermi energy and the conductanceshave been normalized by the conductance at 2 mV. Thesolid trace in the upper panel represents the tunnelingconductance in the superconducting phase of the bilayerand the dashed trace is the corresponding conductancein the high-field normal phase. The are three features ofthe tunneling spectra in Fig. 3 that are of particular im-portance to this study. The first is the Zeeman splitting R ( Ω / s q ) T (K) α t (nm) FIG. 2. Superconductor-insulator transition driven by a par-allel magnetic field for an Be-Al bilayer with a beryllium thick-ness of 0.8 nm and an aluminum thickness of 1 nm. Thesedata where taken at T = 400 mK. Inset: Relative depth ofthe zero bias tunneling anomaly α (defined in the text) as afunction of beryllium layer thickness. of the BCS coherence peaks [17, 25, 26]. The second is abroad logarithmic suppression of the DoS in the normalphase of the bilayer. This suppression arises from e − e interaction effects [22] and is often referred to as the zerobias anomaly (ZBA) or the Coulomb anomaly [3]. It isa direct microscopic measure of the disorder-induced re-pulsive correlations and has been well-documented in awide variety of 2D systems. The third is the pairing res-onance (PR) represented by the dips riding on top of thenormal state spectra [27, 28], as indicated by the arrowsin Fig. 3. Details of the PR have been published else-where [29], but for our purposes the resonance, whicharises from evanescent Cooper pairs, provides us with adirect probe of the spin properties of the normal state.In particular, we can use the PR to extract the effectivenormal state g-factor, which may differ from the naivevalue g = 2 due to Fermi liquid effects [30].As the beryllium thickness is decreased below 1 nmboth the resistance of the bilayers and the magnitudeof the ZBA increase precipitously. This is due, in part,to the fact that a 1 nm Al film deposited directly onthe glass substrate would not be electrically continu-ous. Therefore, for our chosen geometry the Be thicknesscontrols the level of disorder. In order to quantify thestrength of the ZBA we define the dimensionless param-eter α = [ G (2 mV ) − G (0)] /G (2 mV ) which measures therelative depletion of electron states at the Fermi energyin the high-field normal phase. A plot of α as functionof beryllium thickness is shown in the inset of Fig. 2.Note that α grows rapidly as d Be is lowered below 2 nm, G ( V ) / G ( m V ) V (mV) G ( V ) / G n ( V ) V (mV)
FIG. 3. Tunneling conductance as a function of bias voltagefor the bilayer used in Fig. 2 taken at T = 400 mK. The dataare normalized by the conductance at 2 mV relative to theFermi energy. The solid line represents the Zeeman-split BCSdensity of states in the superconducting phase of the bilayerin a parallel field of H (cid:107) = 6 T The dashed line representsthe normal state spectrum in a supercritical field H (cid:107) = 7 T.Note the substantial suppression of normal state tunnelingconductance near V = 0. The arrows point to the pairingresonance features in the normal state spectrum. Inset: nor-malized superconducting density of states after the normalstate spectrum was divided out of the raw superconductingdata. indicative of the approach to the zero-field SIT. As is ev-ident in Fig. 3 the depletion of single particle states dueto the ZBA and the depletion due to opening of the su-perconducting gap are comparable in magnitude in ourmost disordered samples.Shown in the lower panel of Fig. 3 is the superconduct-ing spectrum of upper panel with the normal state tracedivided out the data. In order to suppress the PR thenormal state spectrum was measured in a perpendicularsupercritical field. The four peaks, the two outer supra-gap peaks and the two inner sub-gap peaks, correspondthe Zeeman splitting of the BCS spin-up and spin-downsubbands [17, 25, 26]. The occupied and unoccupied sub-band peaks are located at eV = ± (∆ ± eV Z ) where eV Z = gµ B H (cid:107) is the Zeeman energy. Although thesedata where taken relatively close to the parallel criticalfield H c (cid:107) ∼ d Be = 0 . α ∼ .
4. Note that at fields well below H c (cid:107) thepeaks shift linearly along the Zeeman lines. However,near H c (cid:107) the spectrum begins to display characteristics V p k ( m V ) H || (T) α = 0.4 FIG. 4. Position of the supra-gap (triangles) and sub-gap(circles) coherence peaks as a function of parallel field for abilayer with d Be = 0 . /µ B . of both the superconducting and normal phases. In par-ticular, the PR dip emerges and is superimposed on thesuperconducting spectrum. The position of the PR, eV ∗ = 12 (cid:20) eV Z + (cid:113) ( eV Z ) − ∆ (cid:21) (1)is quite close to, and partially overlaps with, the super-conducting sub-gap peaks near H c (cid:107) . This makes it dif-ficult to determine the sup-gap positions in the criticalregion. The supra-gap peaks, however, are positionedwell away from the PR, so we have chosen to focus ouranalysis on their field dependence.The supra-gap peak positions from the bilayer of Fig. 4are shown in Fig. 5 along with the corresponding peaksin a low disorder Al film, R ∼
100 Ω. The solid line inthis plot represents V Z with g = 2. At fields well be-low H c (cid:107) the supra-gap peaks in both films exhibit theexpected Zeeman shift. However, as the critical field isapproached the Al data falls below the Zeeman line whilethe Be-Al data rises super-linearly. The sub-linear fielddependence of the Al peak is due to FL renormalizationof the quasiparticle spin [30]. In fields well below H c (cid:107) the quasiparticle density in the Al is low and exchangeeffects are negligible and consequently g = 2. But asthe critical field is approached the quasiparticle density V p k ( m V ) H || (T) V * ( m V ) H || (T) g = 1.6 Δ = 0.51 mV FIG. 5. Position of the supra-gap coherence peak for thebilayer of Figs.2 and 4 (diamonds) and a low resistance pure4 nm thick Al film (circles). The dashed lines are providedas a guide to the eye. The solid line represents the expectedlinear Zeeman dependence. Inset: position of the normal statepairing resonance of the bilayer. The dashed line is a least-squares fit to Eq. (1) increases and the g-factor begins to approach its normalstate value, which is g ∼ . − . g and ∆ where varied. The fit clearly shows thatthe normal state g-factor in the bilayers is also well be-low 2. Therefore, the superlinear field dependence of V pk cannot be due to FL exchange effects. The super-linearfield dependence of V pk was only observed in highly dis-ordered bilayers having α (cid:38) .
2, which suggests that theeffect is a consequence of disorder-enhanced e − e interac-tions as manifest in the ZBA. In the strong disorder limitthe system begins to break up into weakly connected su-perconducting islands which have a broad range of lo-cal gap energies [14, 31, 32]. From this perspective, thesuper-linear field dependence of V pk arises from the factthat only the high energy tail of the gap distribution sur-vives as the critical field is approached. At low fields thetunneling conductance samples the entire distribution ofgaps but near the critical field the sampling is skewedtowards high gap values. To test this idea, we model thesupra-gap peak position as function of parallel field fromthe DoS obtained by averaging over a Gaussian distribu-tion of zero-field gaps. This approach is oversimplified atlow field, where different parts of the sample are all su-perconducting and can influence each other directly, butshould be qualitatively correct at high fields, where thesurviving superconducting regions are disconnected [31](a fully self-consistent calculation as those presented inRefs. [14, 31] is beyond our scope). The result of sucha calculation displays a supra-linear behavior resemblingthe experimental data, see the inset in Fig. 4.In summary, we have exploited the Zeeman splittingof the BCS DoS spectrum to obtain direct evidence for adistribution of pairing energies in a critically disorderedBCS superconductor. The effects of disorder serve toboth suppress T c and broaden the critical field transi-tion. Our data suggest that the Zeeman-tuned SIT isdominated by the tail of a broad distribution of localgap energies. 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