VOLUME 67, NUMBER 16 PHYSICAL REVIEW LETTERS 14 OCTOBER 1991

Features of the Density of States of High-T, Superconductors Probed by Vacuum Tunneling

Jin-Xiang Liu, Ji-Chun %'an, and A. M. GoldmanCenter for the Science and Application ofSuperconductivity and School of Physics and Astronomy,

University of Minnesota, Minneapolis, Minnesota 55455

Y. C. Chang and P. Z. JiangArgonne National Laboratory, Argonne, Illinois 60439

(Received 19 February 1991)

A scanning tunneling microscope has been used to study Bi2Sr2CaCu20 single crystals with transitiontemperatures of 85 K. Images of atoms and topographical features were obtained at low temperaturesand spectra were acquired in the vacuum tunneling mode. Interpretations of the conductance data sug-gest that 2A/k&T, =8.2. Most significantly, an additional conductance peak at 90 meV, suggesting a lo-calized state, is observed. The latter would appear to support the marginal-Fermi-liquid picture.

PACS numbers: 74.50.+r, 73.40.6k, 74.70.Vy

Tunneling measurements can provide critical data forthe elucidation of the microscopic mechanism responsiblefor superconductivity. For this reason, an uncountablenumber of studies have been performed on high-T, cu-prate superconductors [1]. In principle, tunneling can re-veal far more than the energy gap, which has been thefocus of most studies, in that density-of-states measure-ments can yield spectral functions central to the micro-scopic theory. However, the promise of tunneling has notbeen generally realized, as for any given material therehave been a wide range of values reported for the magni-tude of the energy gap, and a plethora of different curvesfor the density of states [1].

The central difficulty is that tunneling is a surfaceprobe, with information derived from a volume at the sur-face determined by the coherence length which can be asshort as one unit cell [2]. A controlled experiment shouldtherefore be accompanied by structural and chemicalcharacterization of the surface. This in and of itself will

not ensure a useful result, as the morphological andchemical complexity of the high-T, materials, togetherwith their sensitivity to disorder, can result in a surfacevery diff'erent from the bulk. The resultant data may notbe representative of the bulk properties. Consequently,conclusions drawn from all tunneling measurements re-ported to date, including the present one, must be viewedwith some caution. The emergence of photoemission[3,4] as an important probe of high-T, superconductivityhas been associated with the view that in such studies,surface conditions are largely under control.

A possible approach to transcending the difficulties oftunneling experiments would be to identify commonfeatures of data obtained from measurements subject toindependent systematic errors, possibly involving the useof diflerent tunneling geometries or the pursuit of entirelydiA'erent types of measurement. Historically, the com-parisons of electron-phonon spectral functions of conven-tional superconductors, as determined by tunneling, withphonon spectra determined by neutron scattering havebeen the most quantitative examples of this approach.Recently, such a comparison was carried out for Ba] —„-

K„Bi03and Nd2- Ce Cu04-y [5].An alternative approach would be to obtain tunneling

spectra by vacuum tunneling into a surface which is alsoclearly imaged, using the same tip, in the scanning-tunneling-microscope (STM) mode. In this Letter we re-port the results of such a study carried out on a high-quality Bi2Sr2CaCu20„single crystal. Current-voltagecharacteristics of a BCS-like nature with energy-gapvalues 6, = 30 meV were found, in agreement with previ-ous studies of this sort [6,7]. These spectroscopic mea-surements were obtained at positions near the center ofthe STM image, which itself was obtained at low temper-atures. Most significantly, a second peak in the conduc-tance at 90 meV, or around 3h„was observed. A featureof this sort has been predicted by the phenomenologicalFermi-liquid model [8].

The low-temperature STM, which was of tubulardesign, was placed inside a vacuum can immersed inliquid helium. It was calibrated by scanning the surfaceof a single crystal of graphite at 4.2 K. The supercon-ducting transition temperature T, and the transitionwidth (10%-90%)of the single crystal of Bi2Sr2CaCuqO„were determined, magnetically, to be 85 K and less than2 K, respectively. The tunneling structure was preparedin the following manner: The crystal was cleaved in airimmediately before being positioned in the low-temper-ature apparatus. The STM tip was then placed over ahighly faceted region on the cleaved surface such thatdirect tunneling into a combination of the c direction andthe a bplane would-be possible. This was intended to fa-cilitate some tunneling into the a-b plane, which wouldincrease the chances of probing superconducting proper-ties, as the coherence length is larger in that directionthan in the c direction. In some studies the tip was posi-tioned over a flat surface, thus confining the tunneling tothe c direction.

The techniques used to obtain the STM images resolv-ing atoms at low temperatures, as shown in Fig. 1, havebeen described in our earlier work [9]. Although sub-stantial detail is evident in Fig. 1, and the overall patternis in agreement with previous reports o'f atomic resolution

1991 The American Physical Society 2195

VOLUME 67, NUMBER 16 P H YS ICAL REVIEW LETTERS 14 OCTOBER 1991

~ I

b-

C

FIG. 1. Scanning-tunneling-microscope image of the a-b

plane of a BiqSr2CaCu20, crystal taken at 6.4 K. The tip biaswas +0. 1 V and the tunneling current was 1 nA. The a-axislattice parameter is estimated to be 5.0 A.

I ~ ~ ~ ~ I

-0. 1 0 -0.05I

0 ~ 00I ~ I I ~ I

0.05 0.10

in Bi2Sr2CaCu20 at room teinperature [10] and at lowtemperatures [6,7, 11], there was an instability which re-sulted in our not knowing the exact position of the tipduring a specific measurement of an I-V characteristi.It is known to be near the center of Fig. 1. Several tensof characteristics, interleaved with determinations of theimage, were obtained. The I-V characteristics were notstable indefinitely at nominally the same tip position, areflection of the instability. It should be noted that it wasnot possible to fix the position of the tip while tempera-ture was being changed.

Current-voltage characteristics were obtained with thefeedback off over a 100-ms interval. The maximum biasvoltage was 100 mV. The fact that by changing the verti-cal position of the STM tip it was possible to reversiblyvary the tunneling current at fixed bias and fixed tip posi-tion over about two decades is evidence that the STM tipwas not operating in a point-contact mode. The broaden-ing of the characteristics as the vertical position of the tipwas moved closer to the surface without touching it haspreviously been observed in our laboratory in STM stud-ies of Pb films which exhibited an unequivocal supercon-ducting gap. The eA'ect is probably a consequence of anincrease in pair breaking by the tunneling current itself,as the latter is increased. This suggests that thesefeatures are due to superconductivity, and are neitherCoulombic effects nor a consequence of a semiconductinglayer on the surface. When the point-contact mode wasentered by producing a tip crash, the atomic resolutionimages disappeared and I-V characteristics of the typeexemplified by representative curves a, b, and c of Fig. 2were lost and replaced by a multiple-peak structure simi-lar to that reported in Ref. [7].

The large peaks in the conductance of curves a, b, andc of Fig. 2 are identified, by analogy with low-T, super-conductors, as signatures of the energy gap. The conduc-tance near zero bias in some traces is quite low relative topreviously reported data on cuprate superconductors.The lowest zero-bias conductances correspond to a ratio

Bias (v)FIG. 2. Four representative plots of dI/dV Vcharac-teristics

normalized to unity at 100 mV and shifted vertically for clarity.The conductance peak resembling the BCS energy-gap featureis apparent in three curves (labeled a, b, and c) obtained at po-

sitions near the center of the faceted field imaged in Fig. 1. Thefeatures near + 90 meV are evident in these traces. Curve dwas obtained from a region which was unfaceted, as determined

by STM, and corresponds to the case of tunneling in the cdirection. The inset displays three I-V characteristics with

peak-to-peak tunneling currents of 20, 40, and 100 nA, respec-tively. These are normalized and shifted vertically for clarity.They differ in the tip-to-crystal distance. Curve a of the main

part of the figure is the derivative of curve 2 of the inset.

of the normal-state conductance to the zero-bias conduc-tance larger than 12, and in these instances density ofstates is approximately conserved. This would not be thecase if leakage, semiconductor, or Coulomb blockadeeA'ects dominated the data. A further argument againstCoulomb blockade effects is that no grains were imaged,as was the case in our previous work in which theblockade was directly associated with imaged grains [9].In our attempts at tunneling into the c direction, forwhich the tip was positioned at an unfaceted part of thesurface (curve d of Fig. 2), the widely reported lineardI/dV Vcharacteristic-s were found [12].

As is common to all published tunneling data on high-

T, superconductors, dI/ d V- V characteristics were broad-ened an order of magnitude in excess of what would beexpected from thermal processes (—0.5 meV at T=6.5K). For I-V characteristics, which were the leastbroadened, existing models such as the BCS theory incor-porating finite quasiparticle lifetime broadening orstrong-coupling effects [1,13] could not be satisfactorilyfitted to the data. However, for a few curves with lessdistinctive gap features, a fit could be made by replacingthe excitation energy E by E —II in the density of states,thus treating I as the broadening parameter [13]. Thisled to values of h, and I of the order of 32 and 7 meV, re-

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VOLUME 67, NUMBER 16 PH YSICAL REVIEW LETTERS 14 OCTOBER 1991

1 2

1 0(a)

8O

tD

~~g$

E

1 2

1 0

25 29 33 37 41 45 49 53I I I I I I I I I I I I I

36=90+2 me V

8O

)~~C5

4

O

82 84 86 88 90 92Bias Valtage(mV)

94 96

FIG. 3. (a) Histogram of the voltages of the feature associ-ated with the energy gap. (b) Histogram of the voltages of thesecond feature in the tunneling characteristic. The peak in thedistribution is at 90~ 2 meV which is approximately 3 timesthe gap voltage.

spectively, consistent with estimates in some previousstudies [1,6,7, 14].

The many I-V characteristics obtained in this workwere different, certainly the result of the tip being posi-tioned at locations with different atomic environments,and possibly a consequence of tunneling into differentcrystalline directions exhibiting different pair potentials[1,15]. Alternatively, there may be inclusions at a partic-ular location of other Bi-Sr-Ca-Cu-0 phases withdifferent (higher) transition temperatures. A statisticaldistribution of the voltages at which the peak of the gapfeature was found is plotted in Fig. 3(a). The spread isfrom 30 to 50 meV. Traces exhibiting the largest gapswere those which were most broadened. The best-definedpeaks in the conductance were those with the lowest gaps(5=30 meV), leading to a ratio of 2d/kT, =8.2, ap-proximately the value found in high-resolution photo-emission measurements [3,4], and in several tunnelingstudies of Bi2Sr2CaCu20„[6,7, 14].

The second peak was found in all of the dI/dV V-characteristics exhibiting a gap feature. Its position involtage at a given lateral position of the tip was indepen-

dent of the tip-to-crystal distance, which was also true ofthe main peak. Figure 3(b) shows a histogram of thevoltages at which this peak was found, derived from 38d1/dV-V curves. The distribution is centered around90+ 2 meV, a value 3 times that of the lowest energy-gapfeature. Effects with possibly the same physical origin asthe 90-meV feature have been observed in other studies.A dip (not a peak) has been seen in the density of statesnear 90 meV in a photoemission study [4], and a peak inthe density of states at approximately 4h, has been report-ed in a break-junction ineasurement [16]. The latter in-volves a superconductor-insulator-superconductor (SIS)tunneling configuration rather than a superconductor-insulator-normal (SIN) geometry. The observation of a4h, peak in a SIS configuration is consistent with a 3h,peak in a SIN configuration, implying the presence of acommon feature in the quasiparticle spectral densities.The fact that both of these other studies are presumablysubject to systematic errors different from those of thepresent work, provides support for the idea that the peakat 3A is not an artifact. However, it should be noted thatthere was no sign of a 3h, feature in either the work ofRef. [7], which was an investigation similar in nature tothe present study, albeit with lower signal-to-noise ratio,or in optical experiments [171.

It is significant that the histograms for the main and90-meV peaks are not the same. The former disperse up-ward from 29 to 30 meV, whereas the latter is symmetricabout 90 meV, and exhibits far less dispersion. Thesecond peak most frequently occurs at voltages 3 timesthat of the lo~esi, value observed for the main peak. Theobservation of atomic images implies that tunneling be-tween the tip and the superconductor is directional. Be-cause data have been acquired with the tip positioned inthe vicinity of a highly faceted region of the surface,traces at slightly different positions should result in tun-neling into states for which the lowest energy correspondsto nonvanishing wave vectors (k). The lowest values ofthe conductance peak would then correspond to tunnelingin which the threshold corresponded to @=0 and the peakvoltage in this instance would be a measure of the energygap A. Tunneling in which the threshold corresponded tok&0 would give rise to conductance peaks at energiesgreater than the smallest observed, and because of therandom positions of the tip, the histogram of peak volt-ages would scatter upward from the minimum value, as isobserved.

Dispersion with k would not be expected for a featurein the spectral density associated with a spatially local-ized excitation, such as that described in the marginal-Fermi-liquid phenomenology [18]. In this model, a bo-sonic spectrum of particle-hole pairs, which have a bind-ing energy of twice the energy gap in the superconductingstate, provides a scattering channel for quasiparticles,leading to the feature at 3h. in the single-particle spectralfunction. Because these excitations are spatially local-ized, the energy of their signature in the conductance

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would be k-vector independent. Thus dI/dV-V tracescorresponding to diA'erent k vectors and diA'erent valuesof the voltage of the main peak would have their high-voltage features at the same fixed voltage. If the 90-meVfeature were a band-structure effect, or were associatedwith an elastic process, it would disperse with k the sameway the main peak does, resulting in a similar histogram.It could conceivably be a signature of an inelastic process,but would have to involve a localized excitation. In thisinstance, it would be hard to see why it would occur at anenergy 3 times that of the superconducting gap.

In summary, a STM study has been carried out on aBi2Sr2CaCu20 crystal at low temperatures. The ar-rangement of the surface atoms was observed and thedI/dV vs B characteristics yield the ratio 2A/k8 T, = 8.2,and reveal a peak in the density of states at 3A. Thelatter implies the existence of a localized excitation suchas that suggested in the marginal-Fermi-liquid picture.

The authors would like to thank C. Varma, P. Little-wood, and E. Abrahams for pointing out to them thesignificance of a 3b, peak in the conductance. They wouldalso like to thank L. Glazman, P. Littlewood, D. Lynch,C. Olson, G. C. Spa]ding, O. T. Valls, C. Varma, X.Wang, and F. Yu for useful discussions. K. McGreercontributed to the early stages of this research. Work atMinnesota was supported in part by the MaterialsResearch Group Program of the National Science Foun-dation under Grant No. NSF/DMR-8908094, and by theDepartment of Administration of the University of Min-nesota. 3-C.W. was also supported by a University ofMinnesota Graduate School Doctoral Dissertation Fel-lowship. Y.C.C. was supported by the National ScienceFoundation Office of Science and Technology under Con-tract No. STC-8809854. P.Z.J. was supported by theU.S. Department of Energy, Office of Basic EnergyScience/Materials Science under Contract No. W-31-109-ENG-38.

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