Bennemann K.H., Ketterson J.B. Superconductivity: Volume 1: Conventional and Unconventional Superconductors; Volume 2: Novel Superconductors

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848 J.Zasadzinski

range of the composition phase diagram. All nearby

chemical phases are insulating and the parent phase

is an antiferromagnetic insulator. Thus the early ce-

ramic materials had thick, insulating dead layers on

the surfaces (thwarting attempts at STM measure-

ments) along with nanoscale sized grains which pro-

duced charging effects in tunnel junctions. One such

charging effect, the Coulomb’s staircase, exhibited

current-voltage (I-V) characteristics quitesimilar to

that expected from an s-wave superconducting gap,

leading to much confusion over the magnitude and

pairing state symmetry of the gap. A review of the

early tunneling efforts was given by Gray et al. [40]

and a later review by Kirtley [41] showed improve-

ments in junction quality resulting from the growth

of HTS crystals, such as La

2−x

CuO

By 1992 most of the interesting oxide supercon-

ductors had been studied by some form of tunnel-

ing spectroscopy using one or more of the junc-

tion configurations of Fig.˜refeps0. The review by

Hasegawa and Kitazawa [22] published at that

time showed that there was mixed success. The bis-

muthate, Ba

1−x

BiO

(BKBO), reproducibly exhib-

ited a clean, BCS-like gap structure (see Fig. 15.2)

indicating s-wave superconductivity. Higher energy

spectral features in the range 20 meV – 70 meV re-

sembled strong-coupling phonon structures which

were analyzed using the MMR procedure to obtain

F(!) [6]. But this was controversial because inter-

grain Josephson switching produced structures in

this energy range as well [42]. The issue was re-

solved by Samuely et al. [43] who applied a large

magnetic field to quench any Josephson switching

and the resultant ˛

F(!) spectra were in agreement

with Huang et al. [6]. Further support for electron–

phonon coupling in Ba

1−x

BiO

was found when

the tunneling spectral function was successfully used

to fit the d.c. electrical resistivity in overdoped com-

pounds with T

near 20 K [5]. However, BKBO is not

completely understood. The optical response is in-

consistent with standard electron–phonon coupling

and can only be explained by assuming weak cou-

pling to an unspecified high energy excitation near

0.4 eV [44]. Such an excitation might be related to

the nearby CDW phase that develops with even slight

underdoping from the optimal T

value of 30 K.

Comparing the state of the field in 1992 to the

present, some interesting developments and changes

in perspective have occurred. Early measurements

on the electron-doped cuprate, Nd

2−x

CuO

,in-

cluding tunneling, penetration depth, Raman and

photoemission were all consistent with s-wave pair-

ing [6, 45], however more recent results, including

tri-crystal ring experiments, indicate d-wave sym-

metry [7]. Thus there is a resurgence of interest in

this cuprate. Although high quality single crystals

and epitaxial thin films of YBa

had been de-

veloped early, the tunneling spectra were confusing.

Theenergygapstructureappearedverymuchbroad-

ened and in many cases a large ZBCP anomaly was

found. It was later discovered that this ZBCP was due

to the unusual effects that a d-wave gap has on quasi-

particle scattering processes (see the section on novel

d-wave effects). Now studies of the ZBCP are being

used to search for more exotic pairing states,includ-

ing broken time-reversed symmetry states.

Much clearer tunneling gap features were gener-

ally found on Bi

CaCu

(Bi2212)which was at-

tributed to the ability to cleave such crystals, leaving

an atomically smooth surface for vacuum or point

contact tunneling. Using STM or PCT methods re-

sulted in c-axis tunneling which eliminatedanyZBCP

anomalies as well.Nevertheless,there was much scat-

ter in the magnitude of the energy gap reported by

Hasegawa et al. [22]. It is now understood that this

spreadof gaps is due to a strong dependence of thein-

trinsic gap on doping concentration and it has taken

a new generation of high quality Bi2212 crystals to

unravel this mystery.At the present time there exists

a great deal of reproducibility among tunneling spec-

trainBi2212,notonlyin thesizeoftheenergy gapbut

in the overall spectral shape. Therefore this material

will be discussed in detail. The other cuprates men-

tioned will also be given further attention as they are

exemplary, providing a focus for the specific issues

of pairing mechanism and gap symmetry.

15.5.1 Nd

2−x

CuO

High quality tunneling spectroscopy measurements

of Nd

2−x

CuO

(NCCO) were reported by Huang

et al. in 1990 [6]. At that time there was little dis-

15 Tunneling Spectroscopy 849

Fig. 15.17. (a)Normalizedtun-

neling conductance of NCCO

in the gap region (dots)and

s-wave BCS fit (solid line). (b)

Phonon fine structure observed

at higher bias voltages in the re-

duced conductance and corre-

sponding fit from the MMR in-

version

Fig. 15.18. Comparison of phonon density of states ob-

tainedfrom neutron scattering with ˛

F(!),from Tral-

shawala et al. [5]

cussion of d-wave superconductivity.Thegap region

tunneling conductance shown in Fig. 15.17 is rea-

sonably described by a conventional, s-wave BCS fit

with thermal smearing and a small leakage conduc-

tance of 10%. However, the fit to BCS is not ideal

as is observed with BKBO. The gap parameter,  =

3.5 meV–3.7 meV, was found on 20 junctions mea-

sured on three different crystals. Using 3.6 meV as

the average leads to

2

=3.8 indicating moderate

coupling strength within an s-wave picture.

Inversion of the fine structure in the high bias

conductance was done using a modified version of

the MR procedure to include the small damping ef-

fect of a proximity layer on the surface. This MMR

procedure converged and led to the ˛

F(!)spec-

trum in Fig. 15.18. This is compared to the measured

neutron F(!) on the parent Nd

CuO

where good

agreement is found. It is important to stress that the

MMR procedure is iterative and if the high bias fine

structures are due to extrinsic sources then this pro-

cedure will not converge. Convergence is thus the

first sign that there is physical significance to the

fine structure. More importantly the ˛

F(!)spec-

trum leads to a calculated T

that is very close to the

measured value of 22 K [6]. The resulting coupling

constant,  =1.0, is close to that expected based on

the measured strong-coupling ratio. Thus there are

no inconsistencies in the tunneling data or the s-

wave analysis, and the conclusion of predominantly

phonon-mediated pairing in NCCO seems justified.

The observation of half-integral ﬂux quanta in tri-

crystal ring experiments on NCCO has led to the con-

clusion thatthis a d-wave superconductor[46].While

d-wave symmetry mightexplain thepersistent quasi-

particle sub-gap tunneling conductance in NCCO, it

appears that electron–phonon coupling still plays a

role in the superconductivity of this material. The

presentstate of affairs thus has contradictory aspects,

since it isnot obvioushowto make d-wave supercon-

ductivity and the observed electron–phonon cou-

pling compatible. For example, the measured strong-

coupling ratio in NCCO makes sense in an s-wave

850 J.Zasadzinski

picture but it is significantly smaller than the weak

coupling limit value of 4.26 for d-wave pairing [8].

This is to be contrasted with higher T

hole-doped

cuprates where the measured strong-coupling ratios

are larger than 4.26,as expected,and where such fine

structure from phonons is not observed in any re-

producible manner. Instead, the measured tunneling

spectra are consistent with pairing interactions that

are dominated by electron–electron interactions that

naturally give rise to d-wave superconductivity.

Perhaps in NCCO electron–electron interactions

are present, but necessarily weaker, since T

is quite

small compared to the hole-doped counterparts.

Nevertheless, it might be energetically favorable for

the competing interactions to settle on a d-wavepair-

ing state. However, it is unlikely that the resultant

momentum dependent gap would have the simple

BCS form considered in Sect. 15.2.1. Furthermore,

since d-wave superconductivity is sensitive to disor-

der, there might be local regions where a competing

s-wave state wins out. It is safe to say at present that

there are new questions to be resolved for NCCO.

15.5.2 Bi

CaCu

The generic spectral features of Bi2212 have already

been discussed for STM and PCT respectively, see

Fig. 15.20. These features can be separated according

to energy scale.When viewed at the highest energies

(out to 1 eV) the conductances are consistent with a

broad peak centered near the Fermi energy which is

mostlikely dueto theband structure DOS [31].While

the peak itself is obscured by the superconducting

gap, its effect is to produce a decreasing background

out to 300 meV. The sharp conductance peaks indi-

cate the gap for quasiparticle excitations.At energies

of the order two and three times the gap energy there

are dip and hump features with a strength that is

generally asymmetric in bias voltage. However, the

degree of asymmetry of the dip feature seems to de-

pend on the type of junction.Aswill be shown, some

STM measurements show nearly symmetric dip fea-

tures in the normalized data,whereas PCT junctions,

whichaverageoveramuchlargercontactarea,always

display a large asymmetry.

These basic characteristics are evident for all dop-

ing levels, changing only in energy scale.An example

of PCT conductance data for a slightly overdoped

Bi2212 crystal is shown in Fig. 15.19 from the work

of Ozyuzer et al. [47]. Note the strong asymmetry

of the dip feature, being most pronounced for bias

voltages which remove electrons from the supercon-

ductor. The raw data have been compared to a BCS

d-wave fit which provides an excellent fit to the sub-

gap conductance.This indicates that the normal state

(or background) conductance is approximately con-

stant in the subgap region. The cusp at zero bias is

acharacteristicofad-wave gap and this feature has

been seen in the PCT data of Tl2201 (see Fig. 15.4) as

well as in many spectra on Bi2212.However, for bias

voltages eV >  there is no agreement. The simple

BCS d-wave fit cannot explain the asymmetric dip

Fig. 15.19. PCT tunneling conductance of overdoped

Bi2212 (dots)andd-wave fit (solid line), from Ozyuzer

et al. [47]

15 Tunneling Spectroscopy 851

feature or the decreasing background. In addition

the conductance peaks are wider than the fit curve

andthis is generallytrue for Bi2212data measuredby

STM, PCT, break junctions etc. A closer examination

of Tl2201 in Fig. 15.4 reveals an interesting similar-

ity in the deviation of the conductance data with the

d-wave fit.

The backgroundconductance in Bi2212cannotbe

measured to normalize away those features not asso-

ciated with strong coupling effects as done with Nb

or ZrN shown earlier. This is due to the fact that the

temperatures required to reach the normal state are

>90 K and the background can change when com-

pared to low temperatures.More importantly,the su-

perconducting gap might be evolving into a pseudo-

gap above T

in which case one needs to exceed T

∗

to reach the “true” normal state. For the analysis of

high-T

cuprates it becomes clear that the all effects

which might be contributing to the low temperature

conductance, e.g. d-wave superconductivity, strong

coupling effects, band structure DOS, pseudogaps,

etc.,willhavetobebuiltintoanymodelofthetun-

neling conductance. Such a model must also explain

all asymmetries. This situation is obviously much

more complex than found in conventional supercon-

ductors and leads to ambiguities in interpretation of

tunneling spectra.

In order to gain insight into the spectral features

the Argonne group has performed tunneling mea-

surements of Bi2212 over a wide doping range from

underdoped (T

= 70 K) to optimal doped (T

95 K) to overdoped (T

= 48 K) [48,49]. Doping de-

Fig. 15.20. To p:SIN and SIS tun-

neling conductances vs. dop-

ing obtained from PCT junc-

tions on Bi2212. Bottom:Gap

parameter vs. doping obtained

from all junction types. From

Miyakawa et al. [48,56]

852 J.Zasadzinski

pendent trends have been observed in the energy

gap and dip/hump features. The hole concentration

has been varied by oxygen content. Starting with op-

timal doped crystals, overdoping (underdoping) is

achieved by annealing in high (low) pressure oxy-

gen. Representative SIN conductances and SIS break

junctions are shown in Fig. 15.20. What is evident

is that the energy gap increases monotonically with

decreased doping, even in the underdoped region

where T

decreases. This is shown more clearly in

the bottom panel of Fig. 15.20 where the data points

represent averages of a large number of SIN and SIS

junctions. The error bars are small and this indicates

a high degree of homogeneity within a given crystal.

These gap values have also been reproduced in the

STMstudiesof Bi2212by DeWildeetal.[30]andRen-

ner et al. [50,51] and therefore Fig. 15.20 can be con-

sidered intrinsic from the perspective of tunneling.

There is always a question that tunneling might be

sensitive to surfaceeffects,but it should be notedthat

the same magnitudes and trend of gap vs.doping has

also been seen (over a more limited doping range) in

Raman spectroscopy which is a bulk probe [52].

Such an unusual doping dependence to the mea-

sured quasiparticle gap has stirred up considerable

debate, especially since it is directly related to the

issue of a pseudogap observed above T

in vari-

ous experimentalprobes of cuprate superconductors.

The various interpretations of the pseudogap can be

grouped into two broad classes [53] as shown in the

schematic phase diagrams in Fig. 15.21. In the top

picture, the pseudogap is depicted as a separate en-

ergy scale, distinct from superconductivity. Possible

origins ofsuch a pseudogap are charge density waves

(CDW), spin density waves (SDW) or more exotic

orbital antiferromagnetism or d-wave density waves

(dDW) [54,55]. In such a view the superconducting

gap more closely follows the doping dependence of

and therefore the measured quasiparticle excita-

tiongapin Fig.15.20mustrepresenta smoothchange

from purely superconducting character in the over-

doped region to some other type of gap in the under-

doped region. Tallon and Loram have suggested that

various bulk experimental probes such as specific

heat are consistent with this picture [53]. However,

it was argued by Miyakawa et al. [48,56] that such

Fig. 15.21. Schematic phase diagrams for cuprate super-

conductors.In (a) the pseudogap is a separate energy scale,

distinct from superconductivity.In (b) the pseudogap tem-

perature represents some form of precursor superconduc-

tivity

a view is not supported when the tunneling spectra

are examined in detail. In particular, two-gap mod-

els should exhibit two distinct features in the DOS

and therefore in the tunneling conductance,whereas

only a single, d-wavetype gap featureis observed.Al-

though the dDW state allows coherent mixing of the

two gaps, this is true only when mean-field theory

is applicable. The same disorder (ﬂuctuations) that

causes the mean-field dDW gap to become a pseudo-

gap would most likely affect the coherent mixing in

the superconducting state, leading again to distinct

spectral features in the DOS. Furthermore, robust

Josephson currents are observed in heavily under-

doped Bi2212 crystals, indicating that the excitation

gap is linked to a superconducting energy scale [57].

The second viewpoint is indicated in the bottom

graph of Fig. 15.21. Here the crossover temperatures

∗

and T

smoothly connect to the T

curvesuggest-

ing there is break between temperature scales associ-

ated with electron pairing and long-range phase co-

herence, as is likely in cuprates due to the low phase

stiffness [58]. In such pictures, pseudogap phenom-

ena are associated with some form of precursor su-

perconductivity and therefore the measured quasi-

particle gap of Fig.15.20 is the true pairing gap asso-

ciated with superconductivity[59].Thisviewpoint is

15 Tunneling Spectroscopy 853

Fig. 15.22. (a) STM conductances of

Bi2212 at various temperatures from

Renner et al. [62] and the KT fits of

Franz and Millis,[63]. (b) Resultant en-

ergy gap and scattering rates as a func-

tion of temperature

consistent with the fact that

2

∗

= 4.5-5.5, a reason-

able strong-coupling value [48,60] whereas putting

the measured T

in the denominator leads to un-

physically large values, as high as 20. It should be

mentioned here that the notation for the crossover

temperatures differs throughout the literature. The

notation used by Tallon et al. [53] is such that the

uppercrossoverislabeledasT

∗

. This crossover cor-

responds to the temperature where the uniform sus-

ceptibility ﬂattens out and is associated with the de-

velopment of short range magnetic order. Moreoften

itis referredtoasT

(asitishere)orT

anditismore

common to see the lower crossover listed as T

∗

.Itis

also possible that the upper crossover corresponds

to the development of some type of pseudogap as-

sociated with magnetic order, such as an incipient

SDW [61]. This would then suggest that there might

be two pseudogaps,with the lower crossover temper-

ature T

∗

generally associated with the development

of a pairing gap from superconductivity.

It might seem that a measure of the tunneling gap

vs.temperature would resolve the debate over the na-

ture of the pseudogap, however such measurements

are not easily interpreted. In Fig. 15.22 is shown the

temperature dependent tunneling conductances on

slightly underdoped Bi2212 by Renner et al. using

STM [62]. Qualitatively, the data appear to show a

superconducting gap smoothly merging into a pseu-

dogap of similar energy scale, indicating some form

of precursor superconducting state. The data have

been fit by Franz and Millis [63] using a Kosterlitz–

Thouless (KT) model to describe the phase ﬂuctu-

ations in the pseudogap state. In this model, long

range phase coherence is lost above T

by the pres-

ence of vortex/antivortex pairs which also serve to

scatter quasiparticles and turn the pairing gap into a

pseudogap.Support for this type of phase ﬂuctuation

model for the pseudogap comes from a.c. conduc-

tivity measurements of Bi2212 up to 600 GH

[64].

The temperature dependence of the tunneling gap

thatresultsfromthisanalysisisofparticularinterest.

(T) decreases by more than 20 percent as T

is ap-

proached from below but does not go to zero.This be-

havior is also seen by SIS break junctions (Miyakawa

et al., Ref. [48]) and some intrinsic c-axis junctions

on Bi2212 (as will be shown in a later section). The

break junction data are shown in Fig. 15.23 for an

underdoped Bi2212 crystal with a T

=77K.Inthe

Miyakawa et al. work there was no attempt to fit the

data just above T

which was a well-defined temper-

ature where the Josephson current went to zero.Thus

in several tunneling studies of Bi2212,there appears

854 J.Zasadzinski

Fig. 15.23. Measured su-

perconducting gap vs.

temperature from SIS

break junctions in un-

derdoped Bi2212, from

Miyakawa et al.[48]

to be evidence that the pairing gap magnitude per-

sists into the pseudogap state,supporting the view of

precursor superconductivity.

However,aninteresting effectis foundin Fig.15.22

just above T

where the gap parameter which best fits

the data actually increases. The authors considered

this to be an artifact of fitting the broad tunneling

conductance and fixed the gap magnitude to that of

the low temperature value.Their interest was mainly

in the quasiparticle scattering rate [63]. In this KT

model, the broadening of spectral features above T

is due to the fact that the scattering of quasiparticles

has the effect of smearing out the spectral weight

function. More striking behavior is found in other

analyses of temperature dependent gap region tun-

neling conductances which use the ordinary quasi-

particle scattering rate,  , along with a d-wave gap

parameter to fit the data [65]. In those studies the

gap magnitude decreases as T

is approached from

belowbut thenincreasessubstantially aboveT

,often

reaching values that exceed the gap magnitude at low

temperatures. It is difficult to understand this in the

context of any superconducting ﬂuctuation model,

especially since the superconducting gap magnitude

should continue to decrease above T

.Rather,these

temperature dependent studies are suggestive of a

second gap in the quasiparticle spectrum, perhaps

associatedwith the uppercrossover temperature,T

In general it can be said that tunneling data from

STM, PCT, break junctions and some intrinsic junc-

tions (as will be shown) on Bi2212 are consistent and

support the phase diagram shown in Fig. 15.21(b).

Thus the pairing gap persists into the pseudogap

state but there is no long range phase coherence.

The inability oftunneling to clearly and reproducibly

map out the temperature evolution of the supercon-

ducting gap is probably due to the upper crossover

temperature, T

, which also gives rise to a pseu-

dogap. This second pseudogap has an energy scale

which is several times larger than the low-T super-

conducting gap, but is a much weaker effect on the

DOS and is therefore more difficult to detect experi-

mentally. Support for this view is also found in pho-

toemission studies of Bi2212 [66] and in theoretical

spin-fermion models [61].

The dip/hump feature shown in Fig. 15.19 is also

seen throughout the doping range in Fig. 15.20. In

PCTjunctionsthe dip is highly asymmetric withbias

voltage, always being very strong for bias voltages

which correspond to removal of quasiparticles from

the superconductor. This dip feature was observed

in some of the earliest tunneling studies of Bi2212

and at present there is still no consensus on its ori-

gin [67]. Because of the asymmetry, the positive bias

feature was ignored and the dip was thought to be

part of the background tunneling conductance, per-

haps a consequence of the van Hove singularity in

the DOS.However,later STM and PCT studies clearly

showed that the dip occurred for both bias polarities

which was more consistent with a strong-coupling

effect similar to that found with phonon structures

(e.g., see Fig. 15.7). For example we show the vacuum

15 Tunneling Spectroscopy 855

Fig. 15.24.NormalizedSTM conductanceof Bi2212foropti-

mal doped and overdoped samples from DeWilde et al.[30]

tunneling results of DeWilde et al. [30] in Fig. 15.24

for two crystals, one near optimal doping (T

=93

K) and another that is overdoped (T

=77K).The

data from many junctions at various locations on

the surface have been normalized by a smooth back-

ground and plotted together. There is generally good

agreement among the different junctions. The nor-

malization has removed some of the asymmetry but

not all of it. There remains a difference in the peak

heights and the strength of the dip but it is clearly

seen for both voltage polarities and is approximately

at 2. Also, the normalized data indicates that the

dip drops below unity by about 15%, again consis-

tent with strong coupling effects. This magnitude is

about ten times larger than observed in Nb, but this

is consistent with the much larger gap size.

Oneoftheearliestnotionsaboutthedipfeature

was that it might be a proximity effect.As Figs. 15.14

and 15.15 show,dip features can arise from the prox-

imity effect however in those cases the main con-

ductance peak is either an induced gap (McMillan

model) or a bound state (Arnold model) in the N

layer and therefore would always be at a lower energy

than the true gap.Also the conductance peak voltage

would depend on details of the surface N layer and

thus would be material dependent,an effect which is

not observed. Most importantly, the dip/hump fea-

ture in proximity effect models would be a closer

measure of the underlying superconducting gap and

for tunneling data on Bi2212 this would give an over-

estimateof thegapvalueby a factorof twoor three.As

noted before,Raman scattering which is bulk probe,

matches the gap vs. doping curve in Fig. 15.20 and

therefore the tunneling conductance peak gives the

correct value of the superconducting gap. Thus the

Fig. 15.25. SIS tunneling conductances at various dop-

ing levels showing the shift of the dip feature with T

Voltage axis is rescaled in units of /e, from [68]

856 J.Zasadzinski

dip/hump features are not consistent with any prox-

imity effect interpretation.

Further insight into the dip is found in SIS

break junctions where the feature is much more

pronounced. More recent data from the Argonne

group [68] is shown in Fig. 15.25. Here the voltage

axis has been rescaled in units of /e. If the dip in

the SIN spectra was exactly at E =2, then it should

appear at 3 in the SIS plots but Fig. 15.25 shows

that there is a systematic shift of the dip feature with

doping. This dip in the SIS junctions is found to be

at 2 +§ where § =4.9kT

. This scaling is nearly

the same as found in neutron scattering for the reso-

nance spin excitation [69,70].Thus it appears that the

dip feature can be considered a strong coupling ef-

fect analogous to phonon structures, but the bosonic

excitation that is responsible for this feature, the res-

onance spin excitation, is itself well defined only in

the superconducting state. As will be shown later, a

similar effect is seen in a heavy fermion supercon-

ductor.

15.5.3 Bi

CaCu

S™ Mapping

There has been a systematic improvement in the

quality of STM data on HTS cuprates in general and

on Bi2212 in particular. These are a consequence

of improved quality of crystals as well as vacuum

tunneling methods. In general, the Bi2212 crystals

can be cleaved in-situ in a UHV environment and

then measured at low temperatures. These latest gen-

eration STM measurements are providing unprece-

dented atomic resolution images of the cleaved sur-

faces which have an exposed Bi-O layer. An example

is shown in Fig. 15.26 where the Bi and O atoms can

be resolved [71]. The modulation of the Bi-O struc-

ture along the b-axis is indicated by the light and

dark fringe pattern and along the light fringes there

is a sinusoidal pattern which is not understood.Thus

suchatomically resolvedimagesprovideauniqueop-

portunity to examine the local superconducting DOS

and perhaps link the spectra to particular kinds of

defects. By examining the superconducting conduc-

tance spectra at different locations,adefect structure

is foundthat appears to be intrinsic to the Bi2212 ma-

terial.

Two such spectra are shown in Fig. 15.27 for a

slightly overdoped Bi2212 crystal from Hudson et

al. [71] The dashed line conductance looks very sim-

ilar to superconducting spectra obtained by PCT and

previous STM studies. Note the dip features found at

about 2 with the same strength as observed earlier

by DeWilde in Fig. 15.24. However, there is an addi-

tional feature, a small peak, observed just before the

dip. The origin of this feature is not understood,but

it bears a resemblance to general strong coupling fea-

tures, and it might be that the improved resolutionof

this STM spectrum is providing moredetailed strong

coupling features. This gives further credence to the

notion that the spectral region near the dip is due

to some type of quasiparticle emission process and

Fig. 15.25 is suggesting that the boson emitted seems

to be the resonance spin excitation.

The solid line curve of Fig. 15.26 has a slightly

different spectral shape, generally weaker supercon-

ducting features and a small peak near zero bias.

These types of ZBCP are common for junctions

where the tunneling direction is into the ab plane

as was discussed in the section on novel d-wave ef-

fects. They correspond to surface induced Andreev

bound states which result when a quasiparticle scat-

tering off a vacuum interface changes the sign of its

Fig. 15.26. STM image of Bi-O plane,from Hudson et al.[71]

15 Tunneling Spectroscopy 857

Fig. 15.27. STM conductance spectra for the tip over a su-

perconducting region (dashed line) and a defect region

(solid line). Note the zero bias conductance peak for the

spectrum at a defect, from [71]

order parameter as can happen with d-wave symme-

try.Similareffectsare foundfor scattering off defects

either adjacent to the Cu-O plane or within it. Even

for elastic scattering,the quasiparticle can change its

wavevector such that the sign of the order parameter

is changed. The intrinsic defect regions are proba-

bly associated with defects that originate within the

Bi-O layer where the excess oxygen has been placed

to dope the material. Such a defect can still cause

potential scattering within the Cu-O plane.

A more striking result is obtained when a Ni or

Zn impurity is introduced directly into the Cu-O

plane [72]. Scattering off such defects leads to large

a ZBCP in the local density of states due to Andreev

bound states and a suppression of superconductivity.

An example of the spatial profile over a Zn impurity

is shown in Fig. 15.28. It is important to understand

that this is not a standard atomic image but is a spa-

tial plot of the zero bias conductance and therefore

the insulating Bi-O/Sr-O layer is acting as part of the

tunnel barrierand superconductivityof the underly-

ingCu-Oplaneis beingprobed.Thesuperconducting

regions far from the Zn impurity have a low conduc-

tancesincethisis insidethesuperconducting gapand

appear as dark regions. The brightest regions corre-

spond to the largest ZBCP where superconductivity

is weakest and the bound states exist. The dominant

peak corresponds to the tip being just above the Zn

atom. A striking feature of this image is the fourfold

symmetric pattern which is a consequenceof d-wave

symmetry.

15.5.4 Intrinsic c-Axis Junctions on Bi2212

The cuprates are layered materials,with Cu-O planes

separated by charge reservoir layers. Thus the doped

cuprates can be viewed as stacks of metallic layers

separated by thin insulating regions. Figure 15.1(e)

is a schematic representation of such a stack for a

single Cu-O plane per unit cell as in Tl2201.Whether

intrinsic tunneling phenomena can be observed in

experiments depends on the nature and magnitude

of the tunneling matrix element. For example, co-

herent tunneling occurs when transverse wavevector

is conserved and this leads to the standard Bloch

waves and band dispersion along the c-direction.

Nothing unconventional would be expected in this

case. Transport along the c-directionwould be of the

Drude type. In Bi2212,the c-axis resistivity is larger

than the maximum metallic resistivity and therefore

adjacent Cu-O bi-layers are coupled incoherently. A

single crystal along the c-axis can be viewed as a

set of incoherently coupled tunnel junctions [73].

Lithographic methods have been developed to iso-

latestacks of junctions in a mesa configuration which

contain a relatively small number (≈ 5–20) of such

SIS junctions in series. For example, three Cu-O bi-

layers in Bi2212 would act as two SIS junctions in se-

ries. These stacks exhibit Josephson effects and when

the Josephson critical current for an individual junc-

tion is exceeded, that junction switches over to the

single-electron (or quasiparticle) branch. Studies of

such intrinsic junctions were pioneered by Kleiner et

al. [74,75] and have led to an active field of study. A

thorough review of the extensive literature has been

given by Yurgens [76].

It might be assumed that such a stack of junc-

tions would provide ideal quasiparticle characteris-

tics since the Cu-O layers are perfectly aligned and

there are no exposedsurfaces whichpotentially could

effect standard tunneling geometries.However,these

intrinsic junctions have highly transmissive tunnel