Physica C 483 (2012) 213–216

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Physica C

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Zero-bias anomalies on Sr0.88La0.12CuO2 thin films

L. Fruchter ⇑, F. Bouquet, Z.Z. LiLaboratoire de Physique des Solides, Univ. Paris-Sud, CNRS, UMR 8502, F-91405 Orsay Cedex, France

a r t i c l e i n f o a b s t r a c t

Article history:Received 26 March 2012Received in revised form 19 July 2012Accepted 13 September 2012Available online 23 September 2012

Keywords:Two-level systemsPoint-contact spectroscopy

0921-4534/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.physc.2012.09.011

⇑ Corresponding author.E-mail address: fruchter@lps.u-psud.fr (L. Fruchter

High-impedance contacts made on the surface of Sr0.88La0.12CuO2 superconducting thin films systemati-cally display a zero-bias anomaly. We consider two-level systems (TLSs) as the origin of this anomaly. Weobserve that the contribution of some TLS to the contact resistance is weakened by a magnetic field. Weshow that this could result from the increase of the TLS relaxation rate in the superconducting state, dueto its ability to create pairs of quasi-particles out of the condensate, when located close to the surface ofthe film.

� 2012 Elsevier B.V. All rights reserved.

Mesoscopic contacts, smaller than the electron mean free path,are highly sensitive to both interactions between the material exci-tations and the conduction electrons, and to their scattering byimpurities or defects present in the contact. Zero-bias anomalies,that are encountered in point-contact spectroscopy, are believedto often originate from the latter. As they may occur due to theexternal contamination of the contact, they are frequently not con-sidered and kept out of spectroscopic studies, and thus remainpoorly understood. However, they may also originate from defectsthat are characteristic of the bulk or the surface of the materialinvestigated by the point-contact technique, and provide a uniqueway to access the intimate nature of atomic disorder in some cases.They were observed in contacts between clean simple metals [1,2],and attributed in this case to scattering by two-level systems(TLSs).

A TLS is encountered whenever a defect in a crystalline solidexhibits two metastable configurations. Such configurations resultfrom the tunneling of a single atom, or a group of atoms, betweentwo positions with a small energy difference, separated by a largeenergy barrier, as compared to kB T [3]. They are the typicalexcitations of glasses. While TLS in insulating glasses manifestthemselves essentially by their interaction with phonons, in metal-lic glasses the coupling to conduction electrons is at the origin oftheir much faster relaxation than in dielectrics [4,5], as was firstmodeled in Ref. [4] (for a review, see Ref. [3]). As pointed out by Phi-lipps [6], glassiness is however not required and TLS may result fromsome short-range disorder.

Special attention has been paid to TLS in superconductors.Predictions for the interactions of TLS with the superconductingcondensate were first made by Black and Fulde [7]. In particular,

ll rights reserved.

).

the influence of superconductivity on ultrasonic attenuation wasconsidered. One of the predictions – the decrease of the attenua-tion in the superconducting state, due to the decrease of the TLSrelaxation rate as the interaction with the conduction electron issuppressed – was indeed verified for metallic glasses [8,9]. How-ever, the prediction that TLS with a large splitting energy shouldfind an additional channel for relaxation still lacks an experimentalverification. Here, we show that TLS at the surface of a supercon-ductor might be appropriate for the observation of such an effect.

We studied point-contact made at the surface of thin films ofthe electron-doped ‘‘infinite layer’’ Sr1�xLaxCuO2 compound (SLCO).These films grow epitaxially with the (001) direction normal to thefilm. To elaborate point-contacts, we used 50 nm thick films grownby rf-magnetron sputtering on a (100) KTaO3 substrate [10]. Aftergrowing the epitaxial film, a soft SLCO amorphous layer, about10 nm thick, was deposited in situ at room temperature. This layerprotects the films from degradation, which is otherwise observedafter a few weeks in air. It also provides an electrical insulatinglayer above the film which we used to elaborate contacts.

High-impedance contacts were made in two different ways. Thefirst, most direct way, was to scratch the soft protection layer at thesurface of the film with a tungsten tip, and press it mechanically.Such a method invariably yielded high-impedance contacts, withresistance from a few 100 X to a few kX. For the second method,a gold layer was evaporated on the film, then patterned, leavinga checkerboard of dots about 250 lm large. By applying the tipof an ultrasonic bonding machine on the dots prior to the measure-ment, or by pressing the tungsten tip on the gold contact andvibrating it in situ, holes could be created in the soft amorphouslayer and the contact resistance could be tuned down from insulat-ing to a few ohms. Although the resistance of such contacts couldbe found to increase upon aging at room temperature or thermalcycling, they were stable at low temperature and allowed for the

-40 -20 0 20 400

100

200

300

180 K

100 K

160 K140 K

120 K

80 K60 K

dV /

dI (

Ω )

V ( mV )

40 K

-10 0 10

230

240

250

260

270

V ( mV )

2 K 5 K 7 K 9 K11 K13 K

Fig. 1. Differential resistance for a high-impedance contact, showing a zero-biasanomaly developing at low temperature.

214 L. Fruchter et al. / Physica C 483 (2012) 213–216

study of the contacts over a large temperature interval. The spec-troscopy of the low-impedance contacts provided insight into thesuperconducting order parameter that will be discussed elsewhere.High-impedance contacts made by the two above methods yieldedsimilar results, and we present in the following data obtained fromgold dots only.

The contact resistance was measured using two additionalcontacts deposited on the film, in a geometry minimizing the contri-bution from the film resistivity, when it is in the normal state. How-ever, we could not avoid at high temperature a current-dependentcontribution to the contact resistance, likely originating from thefilm. The differential resistance was measured using standardlock-in techniques, using an AC excitation current, in order to avoidmeasuring the macroscopic contact non-linearity, and a point-con-tact voltage inducing a broadening well below the thermal one,Vac �; kBT=e.

Fig. 1 and 2 display typical results obtained with a large resis-tance contact from a gold dot made on a film with Tc = 20 K. System-atically, below T � 150 K, the contact resistance increases stronglyand develops a strong non-linearity with voltage bias. At lowtemperature, the smooth high-temperature non-linearity givesway to a sharp zero-bias anomaly, corresponding to a maximumof the differential resistance at V = 0. These data are representativeof several contacts made at the surface of several films. Besides TLS,scattering by paramagnetic impurities is also known to yield zero-bias anomalies (for a review, see Ref. [11]). However, the Zeemansplitting in a magnetic field of the degenerate spin states leads toa characteristic splitting of the zero-bias anomaly into two peaks,and a dip at zero-bias in the contact resistance, with width about2 glB H, in this scenario [12,13]. No such features were observed

50 100 150 200 250 3000

5

10

V = 40 mV V = 60 mV

T ( K )

102 [

dV/d

I(0) -

dV/

dI(V

) ] /

[ dV/

dI(0

) ]

0

100

200

300

dV/dI(0) (Ω )

Fig. 2. Differential resistance and its bias voltage dependence for the high-impedance contact of Fig. 1.

in a 9 T magnetic field, and therefore we conclude that such a Kondoscattering is not at the origin of the observed anomalies. In thefollowing, we show that scattering by TLS qualitatively and quanti-tatively account for our data.

First it is necessary to evaluate the regime applicable to ourcontacts. Point-contact spectroscopy requires that the contact ra-dius, a, is less than the mean free path, l, in the investigated metal.As a first approximation, the contact radius may be evaluated fromthe Sharvin formula for the contact resistance [14]

RS ¼4ql

3pa2 ð1Þ

which, using the fact that the product ql is a constant in the Drudeapproximation, is equivalent to

RS ¼4p3

ScSF

e2

�h

� �ð2Þ

where Sc ¼ pa2 is the contact surface and SF ¼ pk2F is the extremal

cross-section of the Fermi surface [15]. Like all other cuprates, SLCOis fairly anisotropic and the contact resistance should be dominatedby the two-dimensional Fermi surface. Additional complication isexpected in this case, as both an electron and a hole pocket contrib-ute to the conductivity. Nevertheless, one can use the total Fermi sur-face for the evaluation of Eq. (2). Using approximately 50% of the firstBrillouin zone, one obtains a typical value a ’ 400ðRS½X�Þ�1=2 Å. Forthe contact in Fig. 1, this yields a ’ 25 Å. This should not be largerthan the mean free path, as the coherence length inferred from uppercritical field measurements is of the order of 40 Å. Equivalently, Eq.(1), using q ’ 150 lX cm [16] yields l ’ 30 Å. Thus, these rough esti-mates show that one can expect the contact dimension and the meanfree path to be comparable. Therefore, there should be a diffusivecorrection to the Sharvin resistance (a fraction of the Maxwell resis-tance – also indicated by a temperature dependent contact resis-tance), which may be estimated from Wexler’s formula [11,17].This yields a correction factor to the above estimate for the contactsize, 1þ ð3pq=64RlÞ1=2 ’ 1:6, that further confirms a large diffusivecorrection to the ballistic resistance, on which spectroscopy isactually performed. This, however, does not prevent performingspectroscopy on TLS, as it was shown to be possible far into thediffusive regime [2,19].

The scattering by TLS of electrons injected from point-contactswas first considered in Ref. [18]. Inelastic scattering by the TLSwas found to result in a sharp peak in the point-contact spectrum,d2V=dI2, at V = E, where E is the TLS energy splitting. The effect ofthe temperature is a finite peak width � kB T. The data in Fig. 3clearly shows both a broadening and a shift to larger energy ofthe peak, as temperature increases, which rules out the inelasticscattering mechanism. It was pointed out that the elastic scattering

-10 0 10

-5

0

5

V (mV )

d2V

/ dI2

(arb

. uni

ts )

2 K 4 K 6 K 8 K10 K14 K19 K

-20 0 20

-1

0

1

V ( mV )

19 K22 K26 K30 K34 K

Fig. 3. Zero bias anomaly in d2V=dI2 for the high impedance contact in Fig. 1.

L. Fruchter et al. / Physica C 483 (2012) 213–216 215

of the electrons by a slow TLS may dominate its resistance [19]. TheTLS spectrum is determined in this case by the dependence of thetwo-level population on the energy of the incoming electrons,associated to two different cross sections for each state [2,20].The resistance for a collection of TLS with splitting energies Ej is:

1R

dRdV¼X

j

eCj

2Ejðrþ � r�j Þ tanh

12t

� �Sðv ; t; qÞ ð3Þ

where the sum is over all TLS within the contact, r�j is the cross sec-tion for the upper and lower levels, t ¼ T=Ej;v ¼ V=Ej;Cj is a con-stant, decreasing strongly with the TLS distance to the center ofthe contact, and q is a geometrical factor varying between q = 1/2when the solid angle at which the contact is seen from the TLS is2p, and q = 0 when the solid angle is zero. At T ¼ 0; Sðv ; t; qÞ exhibitsa d-function at V ¼ Ej, which broadens to a strongly asymmetricpeak, shifting to higher voltage as T increases. Real contacts likethe ones we have studied here are likely made of several mesoscop-ic contacts. We assume, however, that their resistance is dominatedby a single low-resistance contact, with a unique TLS with energysplitting E and geometrical factor q. The zero-bias anomaly maybe‘‘positive’’ (showing a minimum in resistance at zero bias, and apositive peak in d2V=dI2 at positive bias) or‘‘negative’’, for respec-tively rþj � r�j positive or negative. We always observed negativeanomalies. In Fig. 4, the amplitude and the position of the peak ind2V=dI2 may be tracked with temperature up to T ’ 25 K. For highertemperature, although some characteristic energy may be defined,d2V=dI2 saturates above this energy to a plateau (Fig. 3). As maybe seen in Fig. 4, the amplitude, the bias voltage and the profile ofthe peak may be reasonably accounted by Eq. (3). However the fitfor the peak bias voltage fails at large temperature, as the peak van-ishes. This is likely due to the contribution of the weak non-linearcontact resistance, which systematically develops belowT ’ 150 K, the origin of which is unknown. We are not, either, awareof any TLS spectroscopic study that could check the validity of Eq.(3) at temperature as large as Ej=kB (see e.g. Refs. [20,2]).

Although there seems to be a general agreement to attribute theorigin of the zero-bias anomaly, in the absence of paramagneticimpurities, to TLS, the elastic scattering model by Kozub and Kulikis actually challenged by the two-channel Kondo model [21]. Forthis model, a non-trivial T = 0 fixed point governs the low tempera-ture properties. It was found, however, that experimental data suchas in Fig. 4 cannot easily decide between these two models [2]. It hasbeen proposed, instead, that the evaluation of the TLS relaxationrate can tell which of the two mechanisms is pertinent [22].

0 5 10 15 20 250

Am

plitu

de (

arb.

uni

ts )

T (K)

0 10 200

5

10

V (m

V )

T (K)0 5 10 15

d2 V/d

I2

V (mV)

Fig. 4. Amplitude and bias voltage (right inset) for the peaks in Fig. 3. Diamonds arefor H = 0 T; circles are for H = 9 T. Left inset shows the data at 4 K. Lines are fits usingEq. (3) with q = 0.1 and E = 1.7 meV.

What is, then, the effect of a magnetic field on the contact spec-trum? In the two-channel Kondo model, a magnetic field breaks thespin degeneracy, yielding a linear decrease of the contact resistanceat zero bias with applied magnetic field [1,23]. It is however difficultto go beyond the scaling approach to evaluate the magnitude of theeffect. In Kozub and Kulik’s model, no effect of the magnetic field isexpected when the TLS results from two structural defect configura-tions. It was, however, pointed out that TLS may also result fromelectronic disorder [24]. In this case, a magnetic field, which reducesthe amplitude of mesoscopic fluctuations, will also reduce the mag-nitude of the zero-bias anomaly, as for the Kondo model.

In our case, we observe that the effect of the magnetic field onthe zero-bias anomaly varies greatly from contact to contact. InFig. 4, only a slight decrease of the amplitude anomaly could be ob-served upon applying the magnetic field. For some contacts, themagnetic field is able to depress the amplitude much morestrongly, as can be seen in Fig. 5. Within the Kondo model, it is dif-ficult to explain such a dispersion: the effect of the magnetic fieldis intrinsic to the scattering mechanism, so we expect comparablemagnitudes of the effect for contacts showing comparable spectra,as observed in Ref. 23. In the case of mesoscopic electronic disor-der, the magnetic field should either show variable fingerprints,with random sign – which is not observed – or an average effect,resulting from the summation over many fluctuators [24]. As forthe Kondo model, we expect for the latter case comparable magni-tudes for comparable spectra. Therefore, we consider anothermechanism for the effect of the magnetic field, taking into accountthe interaction of the TLS with superconductivity.

Both samples in Fig. 4 and 5 showed bulk superconductivity atTc � 20 K. The applied magnetic field, 9 T, drives the sample to itsnormal state over a large temperature range [25]. As the magneticfield destroys superconductivity, TLS that are strongly coupled tothe superconducting condensate can either gain or loose a channelto relax. Indeed, it is known that the enhanced TLS relaxation inmetals is analogous to the Korringa relaxation of nuclear spins inter-acting with conduction electrons, and the relaxation rate dependson the square of the density of electronic states at the Fermi energy[4]. As a consequence, the superconducting gap eliminates thisrelaxation channel for the TLS, as long as the TLS energy, E, is smallerthan the gap [7]. However, when E > 2D, the relaxation may occurby the creation of a pair of quasi-particles. The relaxation rate beingthe one for a time-reversal-invariant interaction of a pseudospinwith the condensate [7], the coherence factor is of the order of unity[26] and the relaxation rate is larger in the superconducting statethan in the normal state, up to a factor �2. The first mechanism isat the origin of the variation in the superconducting state of the

-5 0 5

0

9 T

d2V/

dI2 (

arb

. uni

ts )

V ( mV )

0 T

0 10 200A

mpl

itude

( ar

b. u

nits

)

T ( K )

Fig. 5. Effect of the magnetic field on a high impedance contact spectrum (T = 7 K).The inset displays the amplitude of the peak in d2V=dI2. Diamonds are for H = 0 andcircles for H = 9 T.

216 L. Fruchter et al. / Physica C 483 (2012) 213–216

ultrasonic absorption in amorphous superconductors [9,28]. How-ever, to the best of our knowledge, there has been to date no obser-vation by ultrasonic attenuation or velocity measurements of thesecond mechanism. Presumably, this is due to the fact that it mayconcern glassy superconductors that are so disordered, that theyactually are gapless or no longer superconducting. The situationmay be more favorable when disorder is probed at the surface of asuperconductor, as in the present case.

As shown in Refs. [18,19], the relative intensities of the elasticand inelastic contributions of the TLS to non-linearity are governedby the TLS relaxation rate, the former being favored in the case ofslowly relaxing systems. We then expect that an increase of therelaxation rate, as would be the case for the quasiparticles-pairgeneration mechanism, should favor the latter. The enhancedinelastic scattering in the superconducting state should be accom-panied by a shift to lower energy and a narrowing of the zero-biaspeak. This is indeed what we observe (Fig. 5). Within such a pic-ture, the TLS in Fig. 4 is only weakly coupled to the condensate,whereas the behavior in Fig. 5 is one of a strongly coupled TLS.

The requirement E > 2DðTÞ for the pair generation is however astrong constraint. Using Dð0Þ=kBTc ’ 3:5, as found for optimallydoped SLCO [29,30], requires E J 12 meV for Tc = 20 K, which isquite a large value. The superconducting gap may however belocally smaller, considering that the TLS may be present in somepart of the film which is strongly disordered, or close enough tothe interface so as to experience a depressed gap. We tried to eval-uate the gap from point-contacts for which TLS did not dominatethe spectrum. Likely as a counterpart of the relative easiness forTLS observation, these films do not easily provide contacts fromwhich the superconducting gap may be straightforwardly deduced.Nevertheless, such contacts exhibit a gap �5 meV for samples withTc ’ 20 K, in line with previous estimate [31]. So, the observation ofthe additional relaxation channel for TLS with E � 2 meV does re-quire that the superconducting gap at the TLS is strongly depressedwith respect to that of the bulk. There is also a requirement on thelocation of the TLS, which should be located within the supercon-ductor’s coherence length from the interface: further away into thesuperconductor, the point contact resistance would be set by theAndreev reflection mechanism, whereas it can experience boththe quasi-particles from the normal metal and the superconduc-ting condensate close to the interface. We note that somepoint-contacts have been observed, between a metal and asuperconductor, exhibiting both Andreev reflection and noise fromTLS, as well as a large broadening parameter, suggesting pair-breaking effects [27].

It should be possible to bring such a mechanism into play forconventional superconductors, and observe a direct TLS signatureas well as their interaction with superconductivity. We would liketo suggest some ways to perform this. What one needs is actually ahigh density of TLS segregated in a metal, subject to the proximityeffect from a superconductor. This may be, as in the present case,defects at the surface of a superconductor, or a sandwich madeof a superconductor covered by a thin glassy metal layer, both

systems probed using point-contact spectroscopy. Alternatively,one could think of a short normal metal wire with a TLS, coupledto a superconducting bank, although we are not aware of any TLScreated in a controlled way in a metal wire. When using a glassymetal, it should be kept in mind that the contact dimension shouldbe as small as the reduced mean free path in the disordered mate-rial, in order to allow for spectroscopy: this suggests using tech-niques able to finely scan surfaces, such as AFM in contact mode.

Acknowledgement

The authors are grateful to G. Collin for valuable contributionson materials elaboration and structural studies.

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