Table Of ContentEPJ manuscript No.
(will be inserted by the editor)
7
0
0
2 Smearing origin of zero-bias conductance peak
n in Ag-SiO-Bi Sr CaCu O planar tunnel junctions:
a 2 2 2 8+δ
J influence of diffusive normal metal verified with the circuit theory
4
] Iduru Shigeta1,a, Yukio Tanaka2,3, Fusao Ichikawa4, and Yasuhiro Asano5
n
o 1 Department of General Education, Kumamoto National College of Technology, Kumamoto 861-1102, Japan
c 2 Department of Applied Physics, Nagoya University,Nagoya 464-8603, Japan
-
r 3 CREST, Japan Science and Technology Agency (JST), Nagoya 464-8603, Japan
p 4 Department of Physics, Kumamoto University,Kumamoto 860-8555, Japan
u 5 Department of Applied Physics, HokkaidoUniversity,Sapporo 060-8628, Japan
s
.
t
a Received 28 January 2006 / Received in final form 23 October 2006
m
- Abstract. We propose a new approach of smearing origins of a zero-bias conductance peak (ZBCP) in
d high-Tc superconductor tunnel junctions through the analysis based on the circuit theory for a d-wave
n pairing symmetry. The circuit theory has been recently developed from conventional superconductors to
o
unconventional superconductors. The ZBCP frequently appears in line shapes for this theory, in which
c
the total resistance was constructed by taking account of the effects between a d-wave superconductor
[
and a diffusive normal metal (DN) at a junction interface, including the midgap Andreev resonant states
3 (MARS), the coherent Andreev reflection (CAR) and the proximity effect. Therefore, we have analyzed
v experimental spectra with the ZBCP of Ag-SiO-Bi2Sr2CaCu2O8+δ (Bi-2212) planar tunnel junctions for
8 the{110}-orienteddirectionbyusingasimplifiedformulaofthecircuittheoryford-wavesuperconductors.
8 ThefittingresultsrevealthatthespectralfeaturesoftheZBCParewellexplainedbythecircuittheorynot
8 onlyexcludingtheDynes’sbroadeningfactor butalso consideringonlytheMARSandtheDNresistance.
0
Thus, the ZBCP behaviors are understood to be consistent with those of recent studies on the circuit
1
theory extendedto thesystems containing d-wave superconductortunneljunctions.
6
0
PACS. 74.25.Fy Transport properties (electric and thermal conductivity, thermoelectric effects, etc.) –
/
t 74.45.+c Proximityeffects;Andreeveffect;SNandSNSjunctions–74.50.+r Tunnelingphenomena;point
a
contacts, weak links, Josephson effects – 74.72.Hs Bi-based cuprates
m
-
d
n 1 Introduction Klapwijk (BTK) theory [24]. This model has sufficiently
o explained ZBCP behaviors in high-Tc cuprate supercon-
c The experimental studies of zero-bias conductance peak ductors. Another mechanism of the ZBCP plays a role in
: (ZBCP) behaviors have been frequently reported for var- thecoherentAndreevreflection(CAR),whichinducesthe
v
i ious unconventional superconductors with an anisotropic proximityeffectinthediffusivenormalmetal(DN)[25]at
X
pairing symmetry, for instance, p-wave and d-wave pair- a diffusive normal metal-insulator-superconductor (DN/
r ing symmetries [1–17]. The ZBCP that results from the I/S) junction interface. Then, there are two kinds of the
a
Anderson-Appelbaum scattering has been studied thor- ZBCP due to the formation of the MARS at junction in-
oughly via previous experiments [18–22]. However, only terfacesof d-wavesuperconductorsandof thatdue to the
untilrecentlywasthereanalternatetheorytoexplainthe CAR by the proximity effect in the DN.
origin of the ZBCP. In this theory, the ZBCP has been
The circuit theory includes both effects of the MARS
understood as the formation of the midgap Andreev res-
andtheCARduetoconstructingthetheoryatajunction
onant states (MARS) at a junction interface in a ballis-
interface under the condition of DN/I/S tunnel junctions
ticnormalmetal-insulator-superconductor(N/I/S)tunnel
for s-wave, p-wave and d-wave superconductors [26–34].
junction [23]. A basic theory of ballistic transport in the
Figure 1a illustrates the schematic drawing at a junction
presence of the MARS has been formulated in the case of
d-wave superconductors by way of the Blonder-Tinkham- interface of a dx2−y2-wave superconductor for the circuit
theory.Inthistheory,theZBCPfrequentlyappearsinthe
a Present address: Department of Physics, Kagoshima Uni- line shapes of normalized tunneling conductance σT(eV),
versity,Kagoshima 890-0065, Japan and we always expect the ZBCP to be independent of α
e-mail: [email protected] for low transparentjunctions with the small Thouless en-
2 I.Shigeta et al.: Smearing origin of zero-bias conductancepeak in Ag-SiO-Bi-2212 planar tunneljunctions
(a) (b) a normal state and RRd=0 is the total resistance of the
DN/I/S tunnel junction in the condition of Rd = 0. In
diffusive normal metal Ag thecaseofRd =0,thereisnoproximityeffectinthe DN,
and the junction resistances are given by the quasiballis-
SiO
tic formulas of reference [23]. Therefore, the theoretical
results serve as an important guide to analyzing the ac-
tualexperimentaldataofthetunnelingspectraofhigh-Tc
insulator cuprate junctions.
Inthepresentpaper,wewilldiscussthe ZBCPbehav-
iorsinAg-SiO-Bi2Sr2CaCu2O8+δ (Bi-2212)planartunnel
junctions by using the circuit theory for dx2−y2-wave su-
q q perconductorsinthecaseofα=π/4,andthen,foranaly-
a a sisoftheZBCP,wewillfocusontheMARScaseinvolving
a
x a an influence of Rd, not the CAR or the proximity effect
d-wave superconductor Bi-2212 cases.
Fig. 1. (a) Schematic illustration of incoming and outgoing
processes at the junction interface for the diffusive normal 2 Experimental details
metal-insulator-unconventional superconductor tunnel junc-
tion. The unconventionalsuperconductor junctions can be in- Planartypetunneljunctionsarefabricatedinsomeexper-
corporatedintothecircuittheorybymeansoftherelationbe- iments, while other measurements rely on scanning tun-
tween matrix current and asymptotic Green’s functions [28]. neling microscopy and spectroscopy (STM/STS) for re-
This relation accounts for anisotropic features of the d-wave cent spectroscopic purposes. The STM/STS has the ad-
superconductors,assketchedforad-wavesuperconductor.(b) vantages of versatility adjustable junction resistance, si-
Planar type junction layout for the ab-plane direction. The multaneoustopographicalimagingat atomic scaleresolu-
Ag-SiO-Bi-2212 planar tunneljunction contains the SiO layer tions together with the spatial variations of local density
between the Ag thin film of the counterelectrode and the Bi- ofstates(LDOS),andmomentumspace(k-space)images
2212 single crystal enclosed with epoxyresin. The SiObarrier obtainedbyFouriertransformationofrealspace(r-space)
and Ag counterelectrode are deposited perpendicular to the
informations [35–42]. However, it suffers from a lack of
ab-planeof Bi-2212 single crystals.
stability against temperature and magnetic field changes,
so a planar tunnel junction is a more suitable device for
temperatureandmagneticfielddependence studies.Most
ergy ETh. Here, σT(eV) is defined as dividing tunneling ZBCP studies are on YBa2Cu3O7−δ (Y-123) thin film in
conductance σS(eV) in the superconducting state by tun- planartunneljunctionexperiments[43–46].Someofthese
nelingconductanceσN(eV)inthenormalstate,andαde- films are highly oriented, thereby making the study on
notes the angle between the normal to the interface and angular dependence of ZBCPs possible [47]. However, we
the crystal axis of d-wave superconductors. The nature chose to use Bi-2212 single crystals in tunneling spectro-
of the ZBCP due to the MARS and that due to the CAR scopic measurements, nevertheless, as the ZBCP is not
aresignificantlydifferent.ThecorrespondingσT(0)forthe commonly available or studied on such mediums as Y-
former casecan take arbitraryvalues exceeding unity. On 123.Bi-2212hasseveraladvantagesintermsofproperties
the other hand, σT(0) for the latter case never exceeds rather than other high-Tc cuprates. For example, Bi-2212
unity. Furthermore, the ZBCP width in the former case is very stable against losing oxygen, retains a cleavage
is determined by the transparency of the junction, while propertybetweenBiOplanes,possessesalargeanisotropy
the width in the latter case is determined by ETh. These ratio between the ab-plane and c-axis directions, and its
two ZBCPs compete with each other since the proximity single crystal does not twin like Y-123.
effect and the existence of the MARS are incompatible in Bi-2212 single crystals were prepared by the traveling
singlet junctions. solvent floating-zone (TSFZ) method, and the supercon-
The influence of the resistance Rd in a DN is signifi- ducting transitiontemperatureTc ofeachas-grownsingle
cantforthe resultingσT(eV).Hence,forthe actualquan- crystal was 87–90 K, which was decided by the resistiv-
titative comparison with tunneling experiments, we must ity and magnetic susceptibility measurements. For hole
take into account the effect of Rd. In the circuit theory dopingconcentration,as-grownsinglecrystalsarelocated
for d-wave superconductors, the ZBCP is frequently seen on slightly overdoped regions in the critical temperature-
in the line shapes of σT(eV). For α=0, the ZBCP is due dopingphase diagram[48].We havepreparedplanartun-
to the CAR. However, for α 6= 0, the robustness of the nel junctions by using these single crystals. Figure 1b
ZBCP does not depend on the DN resistance Rd. In such showsalayoutofaplanartunneljunctionfortheab-plane
an extreme case as α = π/4, the ZBCP arises from the directions. A single crystal with a size of approximately
MARS,andtheCARandthe proximityeffectareabsent. 10 mm × 3 mm × 50 µm was molded into a block of
TheσT(eV)isthengivenbyanelementaryapplicationof epoxyresin.Theblockofepoxyresinwascuttoexposethe
Ohm’s law: σT(eV) = (Rb +Rd)/(RRd=0 +Rd) [28,30], {110}-orientedsurfaceofthe singlecrystals.This cutsur-
where Rb is the resistance from the insulating barrier in face was polished roughly by sandpaper, then smoothed
I.Shigeta et al.: Smearing origin of zero-bias conductancepeak in Ag-SiO-Bi-2212 planar tunneljunctions 3
by diamond pastes with lubricant in the further process.
1.2
At that point, SiO was evaporated on the {110}-oriented
surface as a insulating barrier, and the thickness of SiO S) (a)
layer was modified between 0 ˚A and 300 ˚A for each pla- m 0.9
(
nar tunnel junction. Ag was deposited on the SiO thin S
ssss
film through a metal mask patterned with a counterelec- e
c 0.6
trode of strips with width of 0.5 mm. The thickness of n
a
the Ag layer was controlled to be 1500 ˚A. For the pla- ct
u
nar type junctions made in this manner, Au wires were d 0.3
n
attached to the Ag thin film with Ag paste, where the o
C T = 4.5 K
length L between the cross section of the tunnel junction
and Ag paste regarded as the reservoir in the circuit the- 0.0
ory is roughly 1–2 mm. The total number of measured ) (b)
S 0.5
samples was more than 50. In our experiments, the crys- m
talorientationatthe junction interface,expressedasα in (S 0.4
Figures1a and1b,couldbe predeterminedfroma sample ssss
e
rod configuration fabricated by the TSFZ method since c 0.3
n
thesamplerodgrowsuptothea-axisdirectionofBi-2212 a
t
c 0.2
singlecrystalsinthis method. This factwasconfirmedby u
d
takingintoaccountthesatellitereflectionsarisingfroman n
o 0.1 T = 5.4 K
incommensuratemodulatedstructureintheX-raydiffrac- C
tion pattern of Bi-2212 single crystals [49,50]. 0.0
WehavecollectedI–V anddI/dV–V dataforthepre-
(c)
pared planar tunnel junctions by the standard 4-terminal S) 25
mmeeathsuorde.dThbeyduIs/indgV–thVedcaotnavceonrtrieosnpaolnvdoinltgagtoeσmTo(edVul)awtieorne mmssmmss ( S 20
e
method. The temperature ranged from 4.2 K to 300 K, nc 15
using a temperature controller with a stability of more ta
than 0.1 K. Al-Al2O3-Pb planar tunnel junctions were uc 10
d
fabricated and their tunneling spectra were measured in n
o 5
advance, in order to compare differences about the pair- C T = 5.0 K
ingsymmetryofthesuperconductingorderparameterbe-
0
tween conventional superconductors and high-Tc cuprate -20 -10 0 10 20
superconductors.
Bias voltage V (mV)
Fig. 2. Comparison of typical spectral shapes for tunneling
3 Results and discussion
conductanceσS(eV)intheseveral{110}-orientedtunneljunc-
tions. An enhancement of the reproducible ZBCP was fre-
3.1 Tunneling conductance measurements quently observed below Tc in most of planar tunnel junctions
for the {110}-oriented direction. There are the dip and weak
We have measured tunneling spectra of Ag-SiO-Bi-2212 modulation structures at the outside of theZBCP.
planar tunnel junctions. Figure 2 represents typical tun-
neling conductance σS(eV) of the ZBCP in the super-
conducting state, which was obtained on several {110}- Figure 2, both sides of the backgroundaroundthe ZBCP
orientedtunneljunctions.TheSiOtunnelbarrierbecomes graduallyincreasewithleavingzero-biasvoltageandhave
graduallythicker from Figure 2a to Figure 2c. The values weak modulation structures. We conceive that the weak
of tunneling conductance tend to enlarge with decreasing modulation structures appeared by the specific current-
thicknessofthe SiObarrier,but wecannotverifythe def- path effect, due to the slight surface roughness at the
inite dependence of the ZBCP height on the insulating junction interface [9]. The coherent peaks at an energy
barrier thickness. Then, there is no large difference be- gap region and any other specific structures are not ob-
tween the {110}-oriented tunnel junctions for concerning served in tunneling conductance except for the ZBCP.
spectralshapes ofthe ZBCP,whichwas observedinmost On the other hand, the typical σT(eV) tunneling into
of our planar tunnel junctions. The ZBCP had a peak the{001}-orientedsurface,whichwasthecleavagesurface
height of 2.0–3.3 times higher than the background and ofBi-2212singlecrystals,hadawell-knownV-shapedgap
a full-width at half maximum (FWHM) of 3.3–6.5 meV structure [51]. The d-wave pairing symmetry of an order
in our experiments. For the tunnel junctions that display parameterisevidentlysuggestedfromananisotropyofthe
the ZBCP, many peaks are higher and sharper than the tunneling spectra, such as the V-shaped gap structure in
limit allowed by the BTK theory. This ZBCP enhance- the {001}-orienteddirection and the ZBCP in the {110}-
ment clearly indicates an intrinsic property of the d-wave oriented direction. In contrast to Ag-SiO-Bi-2212 planar
pairingsymmetryinsingletsuperconductors.Asshownin tunnel junctions, a U-shaped gap structure with an en-
4 I.Shigeta et al.: Smearing origin of zero-bias conductancepeak in Ag-SiO-Bi-2212 planar tunneljunctions
observed only below Tc. These facts obviously show that
the ZBCP comes from not the magnetic impurity effect,
butthesuperconductivityofthed-wavepairingsymmetry.
Thus,theexperimentalresultsinFigures2and3coincide
20 with the expectation of the MARS theory for d-wave su-
) perconductors. Furthermore, we will compare our exper-
S
mmmm( imental results with previous research on planar tunnel
S 15 junctions for Bi-2212 single crystals [17]. S. Sinha et al.
ssss e reported that the ZBCP enhanced in ab-plane directions
c
n
a at liquid-helium temperatures and disappeared above Tc
t 10
cu with increasing temperature [52,53]. Their experimental
dn resultsoftheZBCPbehaviorsaresimilartooursneverthe-
o
C 5 lessthetunnelingdirectionintheab-planeatthejunction
60
interface was not controlled in their experiments.
50 K)
-20 40 T ( AnotherproblemfortheZBCPremains,regardingthe
Bias v-1o0ltage V0 (m10 20 10 2T0e3m0perature btminerutroefskartecfasnepcoetliif.tmaHbneeo-ilrwsoeowevtvreTeorrspc,aiiclafstsshyusempheBomrwTcenotRnriSydnuo(FcBctciTgouurRrssrSe[a5s)t42at–ht5ae6an]Sd.jIuTN3nh,cjeutthinZoecBnrteCiionPins-
V)
noZBCPsplittinginalloftheplanartunneljunctionsfor
the {110}-orienteddirection, on the condition of temper-
Fig. 3. Temperature dependence of the ZBCP for the {110}-
ature ranges of 4.2–300 K not applied to magnetic fields.
oriented tunnel junction in Figure 2c. As thetemperature de-
Thus, we have deduced that the BTRS does not occur
creased, the ZBCP height increased, the ZBCP width sharp-
ened,andtheweakmodulationstructuresenlarged.TheZBCP atthehigh-Tc superconductorjunctioninterfacefromour
experiments.
appeared below roughly T =60 K.
3.2 Application to the circuit theory
ergy gap ∆0 ≃ 1.4 meV was observed for Al-Al2O3-Pb
planar tunnel junctions at T = 1.8 K, where Pb was a
We will here discuss the smearing origin from a differ-
superconducting state and Al was a normal state. These
ent point of view against two theoretical analyses on the
tunnel junctions preserved resistances of more than sev-
experimental ZBCP. The actual ZBCP height depends
eral thousand ohms, so we consider that said junctions
on smearing processes of several possible sources. One of
correspond to ranges for high potential barrier height as
thesesubstantialsmearingeffectsis dueto theincreasein
the Bardeen-Cooper-Schrieffer (BCS) limit in the BTK
the number of quasiparticlesowing to thermal excitation.
theory, in which a tunneling spectral shape expects the
Although the tunnel junctions were studied at relatively
U-shape gap structure for s-wave superconductors.
low temperatures (T/Tc ≃ 0.06, in the case of T = 5.0
Figure3representsthetemperaturedependenceofthe K) to minimize the effect of thermal excitations and to
ZBCPforthe{110}-orientedtunneljunctioninFigure2c. allow a more straightforward deconvolution of the ZBCP
Asthetemperaturedecreased,theZBCPheightenlarged, structure,theZBCPheightwasnotveryhigh,whencom-
the ZBCP width sharpened, the dip grew outside around pared to the expectation of the ballistic theory including
the ZBCP, and the weak modulation structures appeared the MARS mechanism [23]. In most of previous research,
around the ZBCP. As shown in Figure 3, the ZBCP ap- the origin of smearing processes was usually explained as
pearedbelowroughly60K.Inourtunnelingexperiments, aresultofthefinite lifetime ofquasiparticlesinsupercon-
theZBCPappearedatTc forseveraltunneljunctionsand ductors by introducing the broadening factor Γ, where E
below Tc for the other tunnel junctions with the decrease is replaced by E −iΓ using the Dynes’s method in for-
in temperature. Hence, the experimental results of the mulas of tunneling spectra [57,58]. Here, the Dynes’s pa-
temperature dependence also denote that the ZBCP is rameter Γ is introduced phenomenologically; accordingly
obviously caused by superconductivity. this method has not made clear how and where the finite
Here,wewilldiscussotherpossibleoriginsoftheZBCP lifetimeofquasiparticlescomesfromspecifically.However,
in tunneling conductance; for example, the magnetic im- this could be achieved to elucidate tunneling spectral be-
purity effect, known as the Anderson-Appelbaum model haviors, sometimes even under changing temperatures or
taking account of the s-d exchange interaction [18–20], magnetic fields, then used to fit theoretical curves of tun-
near the junction interface. However, the possibility of neling spectral formulas with many experimental tunnel-
the magnetic impurity effect is strongly contradicted be- ing spectra up to the present [59–69].
cause the ZBCP enhancement has not been measured in Up to this point, our experimentalresults for Ag-SiO-
the {001}-oriented direction, of which the tunnel junc- Bi-2212planar tunnel junctions revealthat Bi-2212is ev-
tions were also fabricated by using the same materials idently a d-wave superconductor and that the ZBCP for
and procedures as those of the {110}-oriented direction, {110}-orientedtunnel junctions obviously arises from su-
as described in Section 2. Moreover, the ZBCP has been perconductivity. We adapt the dx2−y2-wave pairing sym-
I.Shigeta et al.: Smearing origin of zero-bias conductancepeak in Ag-SiO-Bi-2212 planar tunneljunctions 5
(a) a = 0 (b) a =p /4 the proximity effect in wide directions around α = π/4,
D (+q ) D (+q ) even if actual tunnel junctions slightly retain the surface
- -
roughnessatthe junction interface.Therefore,inanalysis
for around α = π/4 corresponding to α ≫ 0.02π, those
facts justify usage of a simplified formula for the circuit
theory, just expressed by the Ohm’s law: an elementary
DN DN
sum of RRd=0 and Rd in a superconducting state. With-
outsolvingtheUsadelequationinsuchacase,thenormal-
Bi-2212 Bi-2212
ized tunneling conductance σT(eV) can be approximated
by the following simplified equations [30]:
σS(eV) Rb+Rd
D (- q ) D (+q ) D (- q ) D (+q ) σT(eV)= = , (1)
+ + + + σN(eV) RRd=0+Rd
zero MARS finite MARS Rb hIb0iS
finite CAR zero CAR RRd=0 = hIb0i, hIb0i= hIb0iN, (2)
finite proximity effect zero proximity effect hIb0iS = 1 ∞ dE1 π/2 dθ e−λθ2
Fig. 4. Schematic illustrations of the junction interface: (a) 4kBT Z−∞ π Z−π/2
α = 0 and (b) α = π/4. The trajectories in the scatter- E+eV
2
ing process for incoming and outgoing quasiparticles at the ×Ib0cosθ sech , (3)
(cid:18) 2kBT (cid:19)
DN/I/Sjunctioninterfaceford-wavesuperconductorsandthe
c∆o±rre=sp∆on0dcionsg[2p(aθir∓pαot)e]nftoiralt∆he±p(θa)irainregrseypmremseenttreyd.oWf aenchoordoseer hIb0iN = 4k1BT Z−∞∞dEπ1 Z−ππ//22dθ e−λθ2
parameter because of the dx2−y2-wave symmetry for Bi-2212 E+eV
compounds. The our experimental condition corresponds to ×T(θ)cosθ sech2 , (4)
thecase (b) for the situation at thejunction interface. (cid:18) 2kBT (cid:19)
T(θ) 1+T(θ)|Γ+|2+[T(θ)−1]|Γ+Γ−|2
metry for an order parameter of Cooper pairs in Bi-2212 Ib0 = (cid:8) |1+[T(θ)−1]Γ+Γ−|2 (cid:9), (5)
compounds for the analysis of the circuit theory, because 4cos2θ
T(θ)= , (6)
of the experimental evidence for many other results in 4cos2θ+Z2
several measurement methods [70–74], as well as for the ∆∗+ ∆−
ZBCPenhancementofthe{110}-orienteddirectioninour Γ+ = , Γ− = , (7)
tunneling spectroscopic measurements. Here, we choose E+ E2−∆2+ E+ E2−∆2−
α=π/4astheorientationofBi-2212singlecrystalsatthe q q
junction interface, since the {110}-oriented surfaces were with ∆± =∆0cos[2(θ∓α)], where ∆0 denotes the maxi-
exposed at each junction interface as shown in Figures 2 mumamplitudeofthepairpotentialandθ istheinjection
and 3. For α=π/4 the CAR and the proximity effect are angleofthequasiparticlemeasuredfromthex-axis.Here,
completely suppressed and only the MARS remain, while an insulating barrier is expressed as a δ-function model
for α = 0 the CAR and the proximity effect are induced Hδ(x), where Z is an insulating barrier height given by
and the MARS is absent. The situations at the DN/I/S Z =2mH/(~2kF)withFermimomentumkF andeffective
junctioninterfaceareillustratedinFigure4.Here,itisim- mass m. In the above equations, kB is the Boltzmann’s
portanttonoteasfollows:(i)Itisvalidforthe restriction constantandthefactorcosθ isnecessaryforcalculatinga
of only α=π/4 in analysis for the circuit theory because normalcomponentrelativetothejunctioninterfaceofthe
the MARS channels quench the CAR and the proximity tunnelingcurrent.Furtherλisaddedinordertointroduce
effectveryeffectivelyatα>0.02πforthedx2−y2-wavesu- the probability of tunneling directions at the junction in-
perconductor [28]. (ii) The CAR and the proximity effect terface,wherewepresumetobetheGaussdistributionas
cannot influence against junction properties in our fabri- a weight function.
cated junctions. The mesoscopic interference effect, such The recent theoretical expectations of the circuit the-
as the CAR and the proximity effect, must be negligible ory motivate us to analyze experimental ZBCP spectra
since our junction configuration satisfies L ≫ L , where in the ab-plane directions. For the circuit theory with the
φ
the length L ≃ 1–2 mm mentioned in Section 2 and the d-wave pairing symmetry, the theoretical results indicate
phase-breaking length L ≃ 1–2 µm in Ag thin films at that the ZBCP height is strongly reduced by taking into
φ
liquid-heliumtemperatures[75,76].Inthiscase,quasipar- account the existence of the DN conductor, and the re-
ticles cannot interfere each other in the whole of the DN sulting σT(0)is notas highasthat obtainedin the ballis-
conductoronaccountofbreakingthephasecoherencybe- tic regime [28,30]. One of the typical examples is plotted
tween quasiparticles before phase coherent quasiparticles in Figure 5. In the case of α = π/4, the line shapes of
reach the Ag paste regarded as the reservoir[77]. σT(eV) areindependent of ETh because ofthe absence of
As a result,the MARS channelssufficiently giveinflu- the CAR and the proximity effect. The parameter values
ences in line shapes of σT(eV) rather than the CAR and change only for Rd/Rb in the tunneling spectral formula
6 I.Shigeta et al.: Smearing origin of zero-bias conductancepeak in Ag-SiO-Bi-2212 planar tunneljunctions
2.0 2.0
T T
ssss Z = 5.0 ssss Z = 5.0
e e
nc 1.5 llll = 0.0 nc 1.5 Rd /Rb = 1.0
ta aaaa =p ppp /4 ta aaaa =p ppp /4
c c
du T = 5.0 K du T = 5.0 K
n n c
o 1.0 o 1.0
d c c d c b
ze b ze a
mali 0.5 a mali 0.5
r r
o o
N N
0.0 0.0
-1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0
Normalized bias voltage eVD/DDD Normalized bias voltage eVD/DDD
0 0
Fig. 5. Variations of the normalized tunneling conductance Fig. 7. Variations of the normalized tunneling conductance
σT(eV)calculatedbythecircuittheoryundertheconditionof σT(eV)calculatedbythecircuittheoryundertheconditionof
Z =5.0, λ=0.0 and α=π/4 at T =5.0 K. a: Rd/Rb =0.0, Z =5.0, Rd/Rb =1.0 and α=π/4 at T =5.0 K. a: λ=0.0,
b: Rd/Rb =1.0 and c: Rd/Rb =5.0. It is important that the b:λ=10.0 and c: λ=90.0.
DN resistance Rd effectively suppresses the ZBCP height but
doesnotchangetheZBCPwidthontheconditionofα=π/4.
This is because the ZBCP comes from the formation of the circuit theory, Rb depends on Z by way of equation (6)
MARS. and also the following equation [30]:
2R0
2.0 Rb = π/2 , (8)
dθ T(θ)cosθ
sssse T Rd /Rb = 1.0 aaaa =p ppp /4 Z−π/2
nc 1.5 llll = 0.0 T = 5.0 K which has Sharvin resistance R0 at the junction inter-
a
ct d face. Therefore, for the actual quantitative comparison
u with tunneling experiments, these facts suggest that we
d c
on 1.0 b must take into account the effect of Rd. As shownin Fig-
d c ure 2, the resulting ZBCP height from experiments is not
e as highas that obtained in the ballistic regime,so we can
z a
ali 0.5 expectthattheinfluenceofRd canreplacethatofDynes’s
m parameter Γ [57,58] as a broadening factor in tunneling
r
o spectral formulas for the ZBCP. Therefore, we will ana-
N
lyzeourexperimentalZBCPresultsintermsofthecircuit
0.0
theory extended to the systems containing d-wave super-
-1.0 -0.5 0.0 0.5 1.0
conductor tunnel junctions.
Normalized bias voltage eVD/DDD
0
Fig. 6. Variations of the normalized tunneling conductance 3.3 Fitting results for the circuit theory
σT(eV)calculatedbythecircuittheoryundertheconditionof
Rd/Rb =1.0, λ=0.0 and α=π/4 at T =5.0 K. a: Z =5.0, Figure 8 shows the spectral fit of the circuit theory for
b: Z =2.0, c: Z =1.0 and d:Z =0.0. d-wave superconductors to our experimental data. In ad-
dition,in orderto make a comparisonbetweenthe circuit
theory for DN/I/S tunnel junctions and the ballistic the-
of equations (1–7). As shownin Figure 5, the effect of Rd ory for N/I/S tunnel junctions, the fitting result for the
is obviously significant for the ZBCP height of the result- ballistic theory is also given in Figure 8. This result was
ing σT(eV), but is independent ofthe ZBCPwidth of the found by calculating the equations cited in reference [51].
resulting σT(eV). On the other hand, the ZBCP width The open circles represent the experimental data for the
is determined by an amplitude of ∆0, Z and λ on the {110}-oriented tunnel junction in Figure 2c, normalized
condition of α = π/4. Figures 6 and 7 represent typical by a parabolic background. The solid line represents the
variations of line shapes of σT(eV) for Z and λ, respec- fitting curve for the circuit theory extended to the sys-
tively.DifferentfromthecaseofRd inFigure5,theheight tems containing d-wave superconductor tunnel junctions.
andwidthoftheZBCPchangesimultaneouslywithalter- The broken line represents that for the ballistic theory
ations to the value of Z or λ. Here we note that, for the extended for d-wave superconductors, as well. The fitting
I.Shigeta et al.: Smearing origin of zero-bias conductancepeak in Ag-SiO-Bi-2212 planar tunneljunctions 7
Table 1. Typicalvaluesofthefittingparametersineachtun-
2.5
neling conductance formula of (A) the circuit theory and (B)
T
theballistictheory,whencomparedtotheexperimentalresult
ssss
e Experimental data for the {110}-oriented tunnel junction in Figure 2c. The “—”
anc 2.0 Circuit theory meansthattheparameterasRd/Rbdoesnotexistinthespec-
ct tralformulaoftheballistictheory.Itisimportanttonotethat,
u Ballistic theory
d forthecircuittheory,theΓ valueasthebroadeningfactorcan
on 1.5 equalto 0.0 meV,in spite of obtaining good fitting results.
d c
e ∆0 (meV) Γ (meV) Z λ Rd/Rb α
z
ali 1.0 (A) 25.0 0.0 2.2 13.0 0.35 π/4
m
(B) 22.0 1.7 2.3 13.0 — π/4
r
o T = 5.0 K
N
0.5
0 5 10 15 20
Bias voltage V (mV) 1.0
D
y
Fig. 8. Experimental tunneling spectrum at T =5.0 K with t
the tunneling spectra of the circuit and ballistic theories for bili
d-wavesuperconductors.Theopencirclesrepresenttheexper- ba
imental result of the {110}-oriented junction for the Bi-2212 o
r
single crystal in Figure 2c.The experimentalspectrum isnor- g p 0.5 a
malized by a parabolic background. The solid line represents n
the tunneling spectrum calculated by the circuit theory ex- eli b
n
tended to the d-wave pairing symmetry; and the broken line, n
u c
that of theballistic theory extendedas well. T
d
0.0
resultsindicategoodagreementbetweentheexperimental p-ppp /2 p-ppp /4 0 p ppp /4 p ppp /2
dataandtwotheoreticalcurves.Othertunneljunctionsof Incident angleq qqq (rad)
the same compound have been also studied in this fash-
ion, and the results are very reproducible. The slight dis- Fig.9.TunnelingprobabilityDasafunctionofincidentangle
crepancy between the experimental data and theoretical θ for a: λ=0.0, b: λ =1.0, c: λ=13.0 and d: λ=90.0. The
calculations in Figure 8 seems to come from the simpli- dotted line c is corresponding to the fitting results in both of
fication of the insulating barrier in the theories. Here, a thecircuit theory and the ballistic theory in Figure 8.
junction interface between a superconducting state and a
normal state is clearly defined, and a δ-function is used
as a potential barrier. An actual tunnel junction is more for 2∆0/kBTc a value of about 6.5 was obtained, typical
complicated. for high-temperature superconductors [80]. The value of
Table1denotesthecorrespondingparametervaluesin Z = 2.2 is comparatively small in variable ranges (see
each theory. The difference in two fitting results is essen- Fig. 10 in Ref. [30]), so this result corresponds to rel-
tially recapitulated in values of Γ and Rd/Rb. Here, we atively the low barrier height for our tunnel junctions.
emphasize that an introduction of the Dynes’s parame- Corresponding to a finite value of Z, a finite potential
ter Γ in tunneling spectral formulas may not necessarily heightexistsatthejunctioninterface.Therefore,thetun-
suggestthe concretesmearingoriginin experimentaltun- nelingdirectionsofelectronsandholesalsorestrictaround
nelingspectrainthecaseof(B)fortheballistictheory.On normal to the junction interface. Consequently, the finite
the other hand, in the analysis in the case of (A) for the value of λ = 13.0 was obtained. Furthermore, we con-
circuittheory,theDynes’sparameterΓ asthebroadening sider how the σT(eV) depends on the spread of k-space
factor does not need to be introduced into the tunneling in which tunneling electrons reach. The tunneling prob-
spectralformulabecausetheresistanceRd oftheDNcon- ability D as a function of the incident angle θ results
ductor plays an important role as the suppression of the in D ∝ exp(−λθ2)cosθ when U ≫ EF, where U is the
ZBCP height in tunneling conductance. height of a tunneling barrier and EF is Fermi energy [5].
Here, we note several features for the fitting param- The term exp(−λθ2)cosθ is also contained in the equa-
eter values obtained from the circuit theory. The am- tions cited in references [51,81]. As seen in Figure 9, the
plitude of ∆0 = 25.0 meV in the {110}-oriented direc- directional dependence of tunneling probability becomes
tion is appropriate for comparison to ranges of roughly strong with increasing λ. When λ = 0, tunneling elec-
∆0 = 16–40 meV for energy gap values in the {001}- trons range most in k-space. On the other hand, when λ
oriented direction [78,79] and to the value of ∆0 = 22.0 is enough large, electrons are restricted in the narrow re-
meV obtained through the analysis of the {110}-oriented gion along an x-axis through the Γ point in the Brillouin
direction by using the ballistic theory in Table 1. Thus, zone. The planar type junction detects the electric state
8 I.Shigeta et al.: Smearing origin of zero-bias conductancepeak in Ag-SiO-Bi-2212 planar tunneljunctions
in narrow k-space, while the point contact spectroscopy Rd in the formula of tunneling conductance. As a new
and the STM/STS detect the electric state in wide k- interpretation about smearing origins, the circuit theory
space. Therefore, it is reasonable that we have estimated gives that the smearing factor in tunneling spectra could
λ = 13.0 as the parameter of the D from the analysis beunderstoodastheeffectoftheDNconductorintunnel
ofthe circuittheoryford-wavesuperconductors.Further- junctions,ratherthanthatofDynes’sbroadeningparame-
more,the ratio of Rd/Rb =0.35may be not so large,but terΓ.Thus,thecircuittheorywelldescribesthephenom-
this value is sufficient to smear the spectral shape of the ena of quasiparticle tunnelings in anisotropic supercon-
ZBCP by the influence of Rd in systems of d-wave super- ductors, rather than the ballistic theory, and such is very
conductortunnel junctions because the theoreticalZBCP applicable to analysis of the actual experimental data of
height is effectively suppressed as shown in Figure 5. As tunneling spectra of high-Tc cuprate tunnel junctions.
a result, in Figure 8, we received fitting results between
the experimental ZBCP result in the {110}-oriented di-
rections and the circuit theory. Hence, through analysis Acknowledgments
of the circuit theory, we are able not only to exclude the
Dynes’sparameterΓ fromthetunnelingspectralformula,
We would like to thank T. Arai, T. Uchida and Y. Tomi-
but also able to obtain good fitting results of the ZBCP
nari for supplying Bi-2212 single crystals. We appreciate
for the {110}-orientedtunnel junctions.
T. Aomine, T. Fukami, S. W. M. Scott, S. Keenan, M.
In this situation, we were successful in explaining the
BrineyandA.Odaharaforhelpfuladviceanddiscussions.
ZBCP behaviors by using the circuit theory for α = π/4
We are additionally grateful to T. Asano for supporting
including only the MARS and the influence of Rd in the SQUID measurements on some single crystals.
tunneling spectral formula, in which the CAR and the
proximityeffect arecompletely suppressed.Other mecha-
nisms may be responsible for the observed ZBCP smear-
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