Investigation of energy gap and observation of electron-phonon interaction in high-temperature superconductor $La_{1.8}Sr_{0.2}CuO_{4}$ - normal metal point contacts

1.4 MB·

by  I. K. Yanson

Investigation of energy gap and observation of electron-phonon interaction in
high-temperature superconductor La Sr CuO - normal metal point contacts
1.8 0.2 4
I. K. Yanson, L. F. Rybal’chenko, V. V. Fisun, N. L. Bobrov,
M. A. Obolenskii*, Yu. D. Tret’yakov**, A. R. Kaul’**, and I. E. Graboi**
Physicotechnical Institute of Low Temperatures,
Academy of Sciences of the Ukrainian SSR, Kharkov,
A. M. Gorky State University, Kharkov*,
and M. V. Lomonosov State University, Moscow**
7 Email address: [email protected]
1
(Dated: January 24, 2017; Published (Fiz. Nizk. Temp., 15, 803 (1989)); (Sov. J. Low Temp. Phys., 15, 445 (1989))
0
2 Electrical characteristics (I(eV),dV/dI(eV),d2V/dI2(eV)) are studied comprehensively for

n pressed submicron point contacts between fresh fractures of LaSrCuO ceramic pellets and a nor-
a
mal metal (Cu). Point contacts (PC) with the direct-type conductivity are investigated, which are
J
characterized by a considerable excess current due to Andreev reflection of quasiparticles at an NS
1
2 boundary of high transparency. Basic requirements for point contacts suitable for PC measure-
ments are formulated. The models of investigated point contacts permitting the interpretation of

] the observed characteristics are considered. The results of measurement of the energy gap reveal
n
o that LaSrCuO is a superconductor with a strong coupling since the maximum value of the ratio
c 2∆/kT (cid:39) 11. It is found that superconducting properties may vary appreciably over distances
-
r of several tens of angstroms, resulting in some cases in the simultaneous emergence of two gaps
p corresponding to two critical temperatures. The dV/dI(eV) and d2V/dI2(eV) curves display some
u
high-intensitysingularitieswhosepositionontheeV-axisispracticallyindependentoftemperature
s
. and correlates with the phonon spectrum obtained in neutron scattering experiments. This points
t
a to a strong electron-phonon interaction in LaSrCuO.
m
- PACSnumbers: 71.38.-k,73.40.Jn,73.40.Jn,74.25.Kc,74.45.+c,73.40.-c,74.20.Mn,74.70.Ad,74.72.-h,Dn,
d
74.50.+r.
n
o
c
[ I. INTRODUCTION where Λε = (lilε)1/2 is the energy relaxation length for

carriers in the dirty limit, and l (cid:28) l (l and l are the
1 i ε i ε
v Point-contact spectroscopy (PCS) is based on the in- elastic and inelastic mean free paths respectively).
3 vestigation of nonlinearity of current-voltage character-
0 The chemical potential of Cooper pairs in supercon-
istics of electrical point contacts (PC) with direct-type
0
ductors remains constant as long as the number density
6 conductivity (without potential barriers). The typical
0 ofsuperconductingelectronsdiffersfromzeroeveninthe
size of a contact, which is determined by the maximum
. presenceofanelectricfield. Thepenetrationdepthl of
1 size of the current concentration region (we denote the E
0 an electric field into a superconductor is determined by
contact size by d) must be small enough for the charge
7
the relaxation of quasiparticles with an energy of the or-
1 carriers ”remembering” about their energy on the sides
: derof∆,viz.,halftheenergygapwidth. ThevalueoflE
v away from the contact to appear in the region with a
isnormallymuchlargerthantheenergyrelaxationlength
i linear size of the order of the energy relaxation length.
X
for quasiparticles with excitation energies of the order of
The nonequilibrium energy distribution of charge carri-
r phononfrequencies. Thisallowsthecarriersfromthetwo
a
ers formed in this case is such that the maximum energy
sides of an ScS contact, which ”remember” their energy
transfer in inelastic relaxation processes is equal to the
away from the constriction, to approach each other to
potential difference V applied across the contact. This
within a distance smaller than the inelastic relaxation
potential difference serves as an ”energy probe” in the
length. This determines the size of the region where
investigation of the spectral functions of the interaction
thesuperconductingorderparametervanishesevenifthe
between carriers and various excitations in conductors.
contact size is larger than Λ , and PCS is impossible in
ε
The PCS condition for normal metals has the form
the normal state [1]. A similar situation takes place in
d(cid:28)min(l ,Λ ), (1) ScN contacts also provided that d (cid:28) ∆ in the normal
ε ε ε
2
metal. olated in view of the extreme smallness of ξ. For this
reason, many aspects of the mechanism of formation of
Thus, PCS of high-energy excitations (with energies
gap singularities on IVC of point contacts with HTS re-
eV >∆) is possible in ScS and ScN contacts even if the
main unclear. The situation is also complicated by spa-
contactsizedoesnotsatisfycondition1. Themechanism
tial nonuniformity in the properties of HTS due to their
of emergence of singularities on current-voltage charac-
high sensitivity to the composition and structure, and is
teristics (IVC) due to inelastic interaction between the
probablyinherentinthoselayeredmaterialswhosecoher-
carriers and phonons or other excitations is not com-
ence length in the direction of the c-axis is smaller than
pletelyclear(seeRefs. [12]and[13]). Itisobviouslyasso-
thesizeofaunitcell. Nevertheless,itwillbeshownthat
ciated with a partial suppression of the superconducting
IVC of a point contact between LSCO and copper dis-
order parameter (reduction of the gap) for eV ≥ ¯hω
i
play singularities which allow us to measure the energy
(ω are the frequencies corresponding, for example, to
i
gap and to tract (at least qualitatively) its dependence
phononswithsmallgroupvelocitiesandhighdensitiesof
on temperature and magnetic field. The proximity ef-
states), which leads to a threshold decrease in the excess
fect in this case does not lead to an anomalously strong
current. Experiments [2, 4, 5] show that spectral singu-
gapsuppressionontheSNboundary, which couldbe ex-
larities appear in the form of narrow spikes (peaks) on
pected proceeding from the equilibrium pattern [7]. The
thedV/dI characteristicsatthebiaseV =h¯ω . Atypical
i
results of gap measurements on the whole confirm the
feature of phonon singularities on PC spectra is a weak
hypothesisaboutastrongelectron-phononinteractionin
temperature or magnetic field dependence of their posi-
this material.
tion on the energy axis while the position of the singu-
Since the information on a metal investigated by the
larities due to superconductivity degradation as a result
PCS method pertains to only a small region in the ma-
of heating depends strongly on these parameters.
terial with a size of the order of the contact diameter,
The present work reveals that the IVC of a point con-
the perfect structure and stoichiometry are insignificant
tact between La Sr CuO and a noble metal (Cu)
1.8 0.2 4 beyond this region (whose size can be only a few tens of
do indeed exhibit phonon singularities. The positions of
angstroms). From the methodological point of view, the
the peak on the dV/dI curves (or the positions of sin-
differenceintheinvestigationofceramics,polycrystalline
gularities on the d2V/dI2(V) curves which are close to
and monocrystalline samples consists in the number of
them),andsometimeseventheirrelativeintensities,cor-
touches required to identify a ”sensitive point” having
relate with the phonon states density function for this
goodsuperconductingpropertiesinthevicinityofacon-
high-temperature superconductor, which is known from
tact.
neutron studies. The intensity of these peaks is much
higher than the intensity of similar singularities on PC
spectra of ordinary superconductors investigated earlier
II. EXPERIMENTAL TECHNIQUE
(Nb,Nb SnandNbSe ),whichisanindicationofavery
3 2
strong electron-phonon interaction (EPI) in this mate-
A. Preparation of samples.
rial. TheabsenceofpeaksonthedV/dI(V)curvewhose
intensitywouldbecomparablewithphononpeaksaten-
Ceramic samples were obtained by coprecipitation
ergiesexceedingkθ testifytothedecisiveroleofEPIin
D from an aqueous solution containing stoichiometric
the superconductivity mechanism of this HTS. Prelimi-
amounts of La,Sr and Cu nitrates (X4 qualification)
naryresultsofourinvestigationswerereportedinRef.[6].
with a total concentration of 1 mole. In order to avoid
It is well known that the energy gap ∆ in the quasi- the difficulties associated with an incomplete precipita-
particleexcitationspectrumofasuperconductorleadsto tion of cations, hot ethanol solution of oxalic acid was
significantnonlinearitiesofIVCofScN(orScS)contacts used. Thehighsolubilityofoxalicacidinethanolandthe
with a bias eV = ∆ (or 2∆). The mechanism of forma- laminating effect of the alcohol ensure almost complete
tionofthesesingularitiesonIVCisknownonlyforsmall precipitation, which was confirmed by chemical analy-
PC with d < ζ. In the pure limit, ζ−1 = ξ−1(0)+l−1 sis of the mother liquor. The obtained precipitate was
i
(ξ(0) is the coherence length at zero temperature). A separated in a centrifuge, dried at 150◦C to complete
similar condition for dirty contacts has the form d<ξ = sublimationoftheexcessofoxalicacid, anddecomposed
(ξ l )1/2. In the case of HTS, these inequalities are vi- at 750◦C . The powder obtained after the decomposi-
0 i
3
tionandagglomerateswaspressedandfrittedfor50hin
air at 1050◦C, and slowly cooled to 500◦C. According to
theresultsofx-rayphaseanalysis,thesampleswereone-
phase compounds having the K NiF structure and the
2 4
lattice parameters a=3.777 ˚A, c=13.241 ˚A. The density
ofthesamplesamountedto85%ofthetheoreticalvalue.
According to the results of resistive measurements, the
onset of the superconducting transitions was at 38 K,
the transition width varying within several degrees for
different samples.
B. Creation of point contacts and measurement of
their characteristics.
Apointcontactwasformedatthepointofcontactbe-
tweensharpedgesofanormal(Cu)andsuperconducting
(LaSrCuO) electrodes having an elongated shape and a
sizeofafewmillimeters(seeinsetinFig. 2). Thecopper
electrodwascutonanelectricsparkmachinefromabulk FIG. 1: Temperature dependence of resistance at V = 0 for
ingotandpolishedelectrolyticallyatthefinalstageinan contact No.1.
acid mixture whose composition is described in Ref. [5].
The S-electrode was cleaved with a scalpel from an orig-
the larger the volume of the contact occupied by it.
inal pellet and cemented to a damper made of beryllium
bronze with the help of a silver paste ensuring a reliable Second, it is important that the conductivity must be
electric contact. Then the two electrodes were mounted of the metal type at a large bias (eV > ∆), i.e., it must
inaspecialdevicepermittingtheirrelativedisplacement decrease with increasing voltage. In this case we assume
directly in the cryostat, which made it possible to renew that the voltage dependence RD(V) of the differential
the point of contact many times during a single measur- resistance is in qualitative agreement with the tempera-
ing cycle and to control the force of pressure. The time turedependenceoftheresistivityofthebulksampleasin
interval between the chopping of the S-sample and its PCS of normal metals, while the metal-type behavior of
mounting in the cryostat did not exceed 10 min. RD(V) for eV > ∆ corresponds to a linear dependence
The quality of a point contact was estimated from the ρ(T) of perfect LSCO single crystals for T > Tc. The
form of IVC and its derivatives as well as from the tem- deviations from the periodicity of the crystalline struc-
perature dependence of resistivity at zero bias (Fig. 1). ture lead to a violation of the coherent (”band”) motion
Firstly, it is necessary that the contact be formed in of charge carriers and necessitate the introduction of a
the region of emergence of the superconducting phase tunnel or jump-like mechanism of conductivity with a
with a high T∗ on the surface of a sample. For this rea- negativetemperaturecoefficient. Itshouldbenotedthat
c
son, the temperature of the superconducting transition most works on point-contact spectroscopy of HTS were
in the material in the immediate proximity of the con- carried out with the tunnel mode corresponding to RD
tact was measured in most cases. This temperature T∗ decreasing with voltage.
c
isnormallyslightlylowerthanthetemperatureT ofthe Third, a high (of the order of ∆/R ) and weakly de-
c 0
resistive transition in the bulk sample. It is determined pendent excess current I must be present on IVC in
exc
eitherfromasharpdropinthecontactresistanceatzero the superconducting state (Fig.2, IVC for contact No.2).
biaswithloweringtemperature(Fig. 1)orfromtheemer- Thelargemagnitudeoftheexcesscurrentisanindication
gence of a minimum near V =0 on the dV/dI(V) curve of the absence of potential barriers and normal leakage
(see, e.g., Fig. 5). The more clearly these properties are currents shunting the contact or, in other words, of the
manifested, the closer the superconducting region is to factthatthemostpartofthecontactregionisfilledwith
the physical boundary between copper and ceramic, and the superconducting phase. The constancy of the excess
4
TABLE I: Parameters of Point Contacts
No, of R ,Ω R , T∗, ∆ ,meV ∆ ,meV ∆ ,meV 2∆¯ /kT∗ 2∆¯ /kT∗ 2∆¯ /kT∗ Remark
N 0 c 1 2 m 1 c 2 c m c
contact + − Ω K + − + − + −
1 1110 1546 91 27.4 6.8 6.1 13.2 12.6 - - 5.46 10.93 - -
2 74 90 32 30 - - 12.3 13 2.5÷13 - 9.79 0.97÷5.03 -
3 126 107 92 31 - - - - 9.8 8.6 - - 6.89 -
4 159 153 - 19.6 - - - - 7.4 7 - - 8.53 -
5 1935 1962 715 20 4.2 3.6 7.7 7.2 - - 4.53 8.65 - -
5 2185 - 830 20 - - - - 6.4 6.0 - - 7.20 after application
of magnetic field
6 118 118 116 31 - - 10÷11 4÷11 - 3.74÷4.12 1.54÷4.12 -
maximumvalue. Inexperiments,resistancesoftheorder
of several kiloohms were attained (see Table I, contact
No.5), which corresponds to a contact size of the order
of a few tens of angstroms.
Fifth, the contact diameter d determined from the re-
sistanceR atzerobiasaccordingtotheSharvinformula
0
(cid:32) (cid:33)1/2
16(ρl)Cu
d= , (2)
3πR
0
mustcorrespondtoitsvaluecalculatedbyMaxwell’sfor-
mula
d=(1/2)(ρ /R ), (3)
LSCO N
where R is the resistance in the normal state, which
N
is determined by the superconducting bank almost com-
pletely. This condition presumes that a contact can be
modeled by a circular aperture in a thin partition which
dividesthenormalandthesuperconductingbanksandis
impenetrableforelectrons. Itisalsoassumedthatthesu-
perconducting phase comes close to the interface (sharp
boundary), filling the contact region completely. This
ideal pattern is not confirmed in experiments as a rule.
FIG.2: IVCforcontactsNos.1,2,and3(thenumbersonthe The departures from this pattern are so large that the
curvescorrespondtothenumbersofcontactsinTableI).The above condition is not satisfied even to within an order
IVCforcontactNo.1aretakenatdifferenttemperatures;IVC of magnitude.
for contacts Nos.2 and 3 are taken at T = 1.57 and 4.4 K,
Finally (the sixth criterion) phonon peaks on IVC
respectively. The dot-and-dash straight lines illustrate the
derivativesshouldnotbedisplacedappreciablyontheen-
methodofdeterminingR . Theinsetshowsthegeometryof
N ergyaxisuponachangeintemperatureormagneticfield,
the experiment.
whiletheirintensityandwidthmayconsiderablydepend
on these parameters. On the contrary, stray spikes due
current points towards the absence of a noticeable heat- to the superconductivity degradation along the current
ing of the contact region. linesontheeV-axistowardszerowithincreasingT orH,
Fourth, the resistance of a point contact must be as theirintensityandsharpnessremainingunchangedupto
high as possible to correspond to a small size d. In this temperatures close to T .
c
case, the probability of complete filling of the contact Current-voltage characteristics and their derivatives
region with a homogeneous superconducting phase has a were measured on a point-contact spectrometer oper-
5
FIG.4: Differentialresistanceversusbiasvoltageforcontacts
Nos.2-4(curve2repeatscurve2inFig.3onamagnifiedscale);
curves 3 and 4 were recorded at 5.0 and 4.2 K, respectively.
Dashedverticallinesprojectphononsingularitiesontotheen-
ergyaxis. Themethodsofdetermining∆± (curve3)andthe
interval δ∆ over which the gap for contact No.2 is ”spread”
are indicated.
or by using a resistive heater (T > 4.2 K for measure-
ments in vapors). In the latter case, the pressure in the
FIG.3: ThefirstderivativesofIVCforcontactsNos.1and2. outer cryostat was kept at 30-40 mmHg higher than in
Curves1and1’wererecordedat4.1and10.8K,respectively, the inner cryostat. The magnetic field was produced by
while curve 1” was recorded in another series of experiments a superconducting solenoid and could be varied between
at1.6K (itrepeatscurve1inFig. 15bonareducedscalefor 0 and 50 kOe.
V). The vertical dashed lines project the positions of dV/dI
peaks onto the eV-axis.
III. PECULIARITIES OF IVC AND THEIR
DERIVATIVES
ating on the modulation principle. The signals pro-
portional to the first (V (eV) ∝ dV/dI) and second
1 LetusdescribesomepeculiaritiesofIVCforLSCO/Cu
(V (eV) ∝ d2V/dI2) harmonics of the modulating volt-
2 point contacts which do not refer directly to phonon or
age were registered (after amplification and synchronous
gapspectroscopy. Thecorrectinterpretationofthesepe-
detecting) on an x-y recorder. The initial component of
culiarities is important for appropriate interpretation of
the modulating voltage was compensated while measur-
PC spectra.
ing V (eV) with the help of a bridge circuit. Relative
1
nonlinearities of IVC were registered with an accuracy
notlowerthan10−3and10−5forthefirstandsecondhar- A. IVC asymmetry
monics channels, respectively. Measurements were made
in the temperature interval between 1.5 and 300 K in a Figure 2 shows IVC for three point contacts. The first
special cryostat formed by two Dewar flasks embedded derivativesforthesecontactsandcontactNo.4(seeTable
one into the other. Cryogen was delivered into the in- I) are represented in Figs.3 and 4.
nercryostatthroughacapillaryinavacuumjacket. The These characteristics are weakly asymmetric. The fol-
temperature was controlled either by varying the pump- lowing parameters are different for positive and negative
ing rate (T < 4.2 K for measurements in liquid helium) eV of equal magnitudes: (1) asymptotic resistances R±
N
6
determined by the slopes of the straight lines parallel to
excess current; (2) the values I± of excess current for
exc
thebiasofthesamemagnitude; (3)thedepthofthegap
minima of dV/dI, whose asymmetry usually correlates
with the asymmetry in R , and (4) the positions of R
N D
minima from which the energy gap ∆± is counted. It
can be seen that there is a correlation between I± and
exc
R±, while there is no correlation between these param-
N
eters and ∆±. The asymmetry is apparently due to the
dependence of the height of the small potential barrier
at the interface on the polarity of the applied voltage.
Sincethetransparencyofthebarrierforthecontactsun-
der investigation is close to unity, the asymmetry is very
small. Tunnel contacts exhibit, as a rule, much stronger
asymmetry in IVC and its derivatives [8]. It should be
noted that the excess current remains constant up to bi-
ases exceeding the energy gap by more than an order FIG. 5: ”Metal-insulator” transitions for the first derivatives
of magnitude. This is an indication of the absence of a of IVC for contacts No. 1(a) and 6(b) at different tempera-
noticeable heating of HTS in the contact region. The turesembracingthesuperconductingtransitiontemperature.
IVCforcontactsNos.2and3inFig.2hasanegativecur- The ordinate scale is in arbitrary units, and the curves are
vature (d2I/dV2 < 0), which points towards the metal displaced arbitrarily along the ordinate axis.
type of the resistance offered to quasiparticle excitations
with energies exceeding ∆ at T (cid:28) T∗. The curvature
c (in the case of a sharp boundary) and by the surface
is positive for the high-resistance contact No.1 in spite
LSCO layer depleted in oxygen. In both cases, a nar-
of the large excess current. Let us assess the lower limit
row minimum of dV/dI is observed at eV = 0 (see, for
of the diameter of this contact, assuming that the elec-
example, contact No.4 in Fig.4), whose depth increases
tron flight in the copper bank is ballistic (formula (2)).
with lowering temperature. A small current through the
For R = 83 Ω and (ρl)Cu = 0.66·10−11Ω·cm2 we ob-
0 contactdestroysthissuperconductivity,andagapthatis
tain d ≥ 37˚A. On the other hand, by assuming that
not subjected to the proximity effect will be observed in
the motion of electrons in the normal HTS is diffusive
bothcases. SimilarnarrowminimaofdV/dI(0),strongly
(l (cid:28) d), we find from formula (3) the value d < 67 ˚A
i depending on temperature and magnetic field, were also
for the upper limit by putting l ≤ 10−3 Ω · cm2,
LSCO observed for ScN contacts between Ta and Cu [9].
R =750 Ω. Thus, the fifth quality criterion is satisfied
N A zero-point anomaly in R with a narrow minimum
D
for this contact. This criterion is obviously violated for
isapparentlyobservedincontactswithaSchottkytunnel
contacts Nos.2 and 3; consequently, their configuration
barrierformedduetospatialseparationofchargesatthe
differs considerably from the ideal model.
boundary. Figure 4 (curve 2) shows that this barrier has
an insignificant height, and we go over the conventional
form of dV/dI(V) with gap minima even at a compara-
B. Zero-point singularities of differential resistance
tively small bias.
InthevicinityofV =0,thedifferentialresistancenor-
mally has a peak corresponding to a small tunnel com- C. ”Metal-insulator” transition on R (V) curves
D
ponent of the current (curve 3 in Fig.4). In the case of a for T =T∗
c
sharp SN boundary, a potential barrier can emerge due
todifferentelectroniccharacteristics(p ,v )ofthemet- ItiswellknownthattheR (V)curveforapointcon-
F F D
als in contact. If there are no centers destroying Cooper tact formed by traditional superconductors at eV > ∆
pairs at the boundary, the proximity effect ”pulling” su- differs only slightly from the corresponding dependence
perconductivity into the normal metal must take place. in the normal state on the one hand and is qualitatively
The role of the normal metal can be played both by Cu similar to the temperature dependence of the resistivity
7
FIG. 6: Schematic diagram of point contacts between HTS ceramics and copper: structure (a), ScN and SNcN type contacts
modeling an ideal and real point contact (b,c); schematic of a real point contact with alternating real (N ) layer and two
1
different HTS phases (S and S ) (d, g); an aperture in an impenetrable partition modeling an ideal ScN contact (e); models
1 2
ofarealcontactoftheScNStype(f);thecoordinatedependenceofenergygapinequilibrium(solidcurve)andinthecurrent
mode(dashedlines)duringtheformationofPSC(i),andthecoordinatedependenceofchemicalpotentialµ ofquasiparticles
N
andµ ofCooperpairsforeV >∆intheabsenceofPSC(ii)(thesameparametersareshownon(iii)diagramforthecaseof
S
PSC formation).
ofthebulkmaterialaboveT ontheotherhand. Inpoint statechangesforthemetal-typedependenceforT <T∗.
c c
contacts containing HTS, a different situation, conven- (This effect can be clearly seen on the temperature de-
tionally referred to as the ”metal-insulator transition”, pendences of IVC in Figs.10, 12, and 13).
often takes place at T = T∗. Figure 5 shows differen-
c
tial resistances as functions of the bias voltage at differ- Asimpleexplanationofthiseffectcanbegivenonthe
ent temperatures embracing the superconducting tran- basisofpossiblenonuniformityinthepropertiesofthesu-
sition temperature of the contact. It can be seen that perconductor in the contact region. Let us suppose that
at T ≤ 27.4 K, the emergence of a minimum of dV/dI defectsofstructureandcompositionofHTSarelocalized
is accompanied by a change in the sign of the second on the periphery of the contact. However, it is these de-
derivative of IVC for large eV at zero bias, indicating fects that determine the resistance of the contact and its
the onset of superconductivity. The semiconducting (or semiconductor-type temperature dependence in the nor-
tunnel) type of the R (V) dependence in the normal malstate. Inthesuperconductingstate,theresistanceof
D
this region is shunted by supercurrent provided that the
8
electricfieldpenetrationdepthl issmallerthanthecon-
F
tact diameter d, and the sign of the derivative d2V/dI2
changes for eV > ∆ since it is now larger part of the
constriction. In this case, however, the differential resis-
tance in the superconducting state at a large bias must
beconsiderablysmallerthantheresistanceinthenormal
state. Unfortunately, this was not confirmed in experi-
ments. For example, the ”metal-insulator transition” is
observedforcontactNo.1inFig.13atT∗ =27.4K,while
c
the family of IVC recorded for this contact at different
temperatures indicates that the differential resistance at
a large bias practically remains unchanged upon a tran-
sition through T .
c
There is also a contradiction in the estimate of l
E
which, if the above arguments are correct, should not
exceed a few tens of angstroms (it should be recalled
that the estimation of the size of contact No.1 gives
37 ˚A < d < 67 ˚A). On the other hand, differential re-
sistancesinexperimentsatlargerbiasareapproximately
equalalsoforcontactswithlowerresistanceandasizeof
the order of hundred angstroms and higher.
Inouropinion,thesecontradictionscanberemovedby
assumingthepossibilityofformationofphaseslipcenters
(PSC) along the current lines in HTS. The experimental
factsdescribedinthenextsectionalsopointtowardsthe
existence of PSC.
IV. CONTACT MODELS FIG.7: EquivalentcircuitdiagramandIVCofanScNScon-
tactwithPSC(modelseandf inFig.6)exposedtomicrowave
Although the mechanical contact between the elec- radiation.
trodes is formed over a large area, thus ensuring the sta-
bility of the construction, the electric contact emerges
only in small regions free of thin insulating (oxide and superconducting phase S with a lower critical tempera-
1
other) films. The surface layer of HTS consists mainly ture T , and deeper layers of the superconductor with
c1
of a poorly conducting or insulating material. For this the critical temperature equal to the transition temper-
reason,wehavetolookforrareregionswheredeepsuper- ature of the bulk sample (Fig.6d). The corresponding
conducting layers emerge at the surface (Fig.6a) for the modelsofe,f,andg contactsarealsopresentedinFig.6.
formationofacontact. Insomecases,asuperconducting Potential barriers with transparency of the order of 0.1-
crystalliteisindirectcontactwiththepuresurfaceofthe 1.0 can be present at the boundaries. It should be noted
normalmetal(Fig.6b),butthesituationwhenthesuper- thattheproximityeffectdescribedintheprevioussection
conducting phase is quite close to the physical boundary is observed for the model e. It can be expected that the
and yet does not touch it is more probable (Fig.6c). The fifth criterion of contact quality will be fulfilled for this
two phases are separated by a thin layer of supercon- model. On the contrary, for models f and g the influence
ducting metal phase of HTS, whose thickness is small in of the proximity effect on the electron made of the nor-
comparison with the inelastic mean free path. A more mal metal is insignificant in view of the smallness of the
complicated case of the superconducting phase with a coherence length in HTS, and the differential resistance
nonuniform composition is also possible, when the HTS of the contact for small and large bias voltages must be
surface is formed by a sequence of the normal phase, the of the same order of magnitude as in the normal state.
9
FIG.8: IVCandtheirderivativesforcontactNo.5before(a)
andafter(b)theactionofmicrowaveradiation(solidcurves).
Dashed curves illustrate the variation of dV/dI(V) and IVC
under the action of microwave radiation at T = 4.1 K; thin
lines make it possible to determine I , R , R and ∆ .
exc N 0 1,2 FIG. 9: R (V) dependence for different intensities of mi-
D
crowave radiation: 1-dV/dI structure reflecting Josephson
stepsonIVCofanSNSjunctionformedbyPSCinHTSelec-
Let us now consider the energy level diagram for the trodeuponmicro-waveirradiation;curve2correspondstothe
model f of a point contact in the current state at low maximum intensity of microwave radiation, which is almost
temperatures. As long as the energy of quasiparticles an order of magnitude higher than the microwave intensity
impinging on the superconductor from the normal metal levelforcurve1;curve3isthesameascurve1,butrecorded
is smaller than the equilibrium value ∆ of the gap, the after the action of high-intensity microwave radiation.
quasiparticles undergo an Andreev-type reflection at the
jump ∆. The resistance in this bias region (eV < ∆) is
current through it is eV = 2∆, while the frequency of
equal to the sum of Sharvin’s resistances on the side of
Josephson’s alternating current is 2ev/¯h as usual. The
thenormalmetalandtheresistanceofathinlayerofnon-
emergence of such PSC leads to additional mechanisms
superconducting HTS, which apparently plays a decisive
ofthemanifestationofphasesingularitiesonIVCaswell
role. As soon as eV becomes higher than ∆, quasipar-
as to a nonequilibrium suppression of the excess current
ticle excitations with an energy exceeding the gap will
at phonon energies, which forms the basis of EPI spec-
be responsible for the transport of excess current over
troscopy for these materials. It should be noted that the
the maximum possible superconducting current density
behavior of the chemical potential of pairs and quasipar-
to the depth l into the bulk of the superconductor. It
E
ticles near a sharp Sn boundary for eV >∆ is similar to
is natural to assume that the maximum value ∆ of
max
that of half PSC but without the Josephson effect.
the gap corresponds to the drift of carriers along well-
conductingbasalplaneswhichshuntthespreadingofthe TheemergenceofthePSCcanbeprovedbyanalyzing
currentinthetransversedirection. Ifthe”easy”linesfor the interaction between the Josephson current and an
the superconducting current are interrupted by defects, external electromagnetic radiation. An equivalent cir-
phase slip centers (lines or surfaces) emerge in the vicin- cuit diagram for such a PSC consists of a resistance R
1
ity of these lines, at which the electrochemical potential connected in series with a Josephson element (Fig.7a).
of pairs undergoes a jump. Such a PSC is actually a Thecurrent-voltagecharacteristicsoftheseelements(ina
Josephson SNS junction. The threshold of quasiparticle given current regime) are shown schematically in Fig.7b,
10
FIG. 10: dV/dI(V) curves for contact No.3 at different tem- FIG. 11: dV/dI(V) dependence for contact No.3 with a
peratures. smaller temperature step in the vicinity of T = Tc1 where
∆ vanishes.
1
and c; the resultant IVC is given in Fig.7d. Its first
widthofthepeaksisapproximatelyequaltoaJosephson
derivative contains a series of peaks whose width is of
quantum. High intensities of microwave radiation smear
the order of a Josephson quantum h¯ω , while the peak
j the clear-cut spatial structure of PSC due to nonequilib-
separation is determined by the height of Shapiro steps
riumeffects(curve2). Noreturntothepreviouspattern
in current and by the values of R The latter may gen-
1 at low-intensity microwave radiation is observed (curve
erally depend on V, which will lead to a change in the
3), which is an indication of the magnetic flux trapping
separation between R peaks.
D in the contact region, although the effect is reproduced
Figures 8 and 9 present IVC and R (V) for contact qualitatively.
D
No.5 (see TableI) exposed to microwave radiation and It is appropriate to consider a few remarks of general
in the absence of it. The differences between curves 2 nature. First, if we exclude the artefacts due to a possi-
and 2’ in Fig.8 are apparently due to the magnetic flux ble partial transport of the superconducting material to
trapping as a result of suppression of superconductiv- the surface of the normal electrode, in the experiments
ity near PSC by a high-intensity microwave field. After where Josephson effects were observed on ScN contacts
the action of this radiation, a single broad minimum is the latter are obviously due to the formation of a phase
observed instead of two minima of 3.8 and 7.4 meV on slip surface in the bulk of the superconducting electrode
R (V)inthisintervalofbiasvoltage. Thespikesappear in the vicinity of the SN boundary, this concerns espe-
D
on the R (V) dependence not at zero voltage; in other cially the superconducting materials with a short coher-
D
words, there is a certain threshold in current (curve 1 ence length, viz., HTS, compounds with heavy fermions,
in Fig.9). The separation between the steps consider- etc. The threshold in constant current is not necessary
ably exceeds h¯ω , increasing with the step number as in this case since PSC can be formed by the microwave
j
a result of the increase in R on this bias interval. The radiation itself in the absence of a transport current also
1