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

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858 J.Zasadzinski

Fig. 15.28. STM mapping of the zero bias conductance near

a Zn impurity. The large central peak corresponds to the

tip right above the Zn atom.From [72]

barriers with a conductance per unit area greater

than 10

(

).This value isatleast two orders of mag-

nitude larger than found in planar junctions on con-

ventional superconductors. At the typical bias volt-

ages of interest, i.e., eV=2=80 meV per SIS junc-

tion, it is easy to realize currents of 10

(

)which

is the typical value for various nonequilibrium phe-

nomena to occur [77]. These include heating effects

where the electronic and bosonic (e.g. phonons) dis-

tribution functionshaveaneffectivetemperature,T

∗

higher than the bath temperature (this T

∗

should not

be confused with the pseudogap temperature). An-

other way to view this is to consider the electrical

power developed across a junction. The voltage scale

of interest is set by the gap value and thus the power

which rises as the junction resistance is low-

ered. The more transmissive a barrier, the higher the

heating effects become.

Another consequence of high injection rates is

that the electron distribution function is described

by a chemical potential greater than the equilibrium

value. These non-equilibrium distributions of elec-

trons and phonons both tend to reduce the supercon-

ducting gap value. Suzuki et al. [77] have modeled

these non-equilibrium effects using three different

phenomenological expressions for the reduction of

Fig. 15.29. Effects of high injection rates on the I-V char-

acteristics of an SIS tunnel junction between two d-wave

superconductors. For each curve the gap suppression is

proportional to the square of the junction current and p is

the proportionality constant.From Suzuki et al.[77]

the energy gap with current across the junction. The

effects for the different models are qualitatively sim-

ilar and lead to backbending of the I-V curve in the

sub-gapregion,similar to what is often observed.The

effect of quasiparticleinjection is shown in Fig.15.29

assuming a quadratic reduction of the gap (∝ pI

)

with junction current. Note the reduced size of the

measured gap value compared to the bulk value and

thebackbending of the I-V curves for larger values of

p. In Fig. 15.30 is shown a comparison of two differ-

ent nonequilibrium models for the reduction of the

gap value with measured data on a mesa stack. The

two models are a linear and quadratic gap suppres-

sion (LGS and QGS) with junction current. Another

importantresultisthatI-V curve rises sharply at the

gap voltage just at the threshold of backbending.This

can give rise to extremely sharp conductance peaks.

Various attempts have been made to reduce the

heating effects in mesa stacks. Considering the poor

thermal conductivity of Bi2212, one way to reduce

heating effects is to shrink the lateral area of the

mesa. This improves heat conduction away from the

15 Tunneling Spectroscopy 859

Fig. 15.30. Comparison of measured I-V characteristics

of a mesa stack of intrinsic junction on Bi2212 with two

nonequilibrium models for the suppression of the super-

conducting gap with temperature. From Suzuki et al. [77]

mesa. However, the junctions still have the same cur-

rent per unit area and thus direct injection can still

leadto nonequilibrium electrondistributions.Pulsed

current methods also help.A more suitable way to re-

duce nonequilibrium effects is to increase the junc-

tion resistance and thereby reduce the source of non-

equilibrium effects. Yurgens et al. [78] have shown

that this can be accomplished by intercalating HgB

between the double Bi-O layers in Bi2212 resulting in

up to a 100 fold increase in resistance. The resulting

quasiparticle spectra and T-dependent gap values,

(T), are very similar to break junctions shown ear-

lier. Note the strong dip features, similar to break

junctions shown in Fig. 15.25 which abruptly dis-

appear near T

. The dynamic conductance at various

temperatures is shown in Fig. 15.31 and the extracted

(T) is shown in Fig. 15.32. Theseintercalated mesas

do not exhibit any obvious closing of the gap at T

a result similar to STM and break junctions shown

earlier. Pristine junctions on the other hand show a

much more rapid decrease of the gap with tempera-

ture than expected from BCS theory.

Thus it can be said that intrinsicjunctionson fully

intercalated Bi2212 mesas (with 100-fold decreases

Fig. 15.31.Dynamic conductances atdifferent temperatures

for a stack of intrinsic junctions on a Bi2212 mesa interca-

lated with HgB

.FromYurgensetal.[78]

Fig. 15.32. Extracted gap vs. temperature in intercalated

and pristine intrinsic junctions. From [78]

in conductance per unit area) display conductance

spectra (including T-dependence) that are very sim-

ilar to those obtained from single junction methods

such as STM and break junctions. Such agreement

860 J.Zasadzinski

and reproducibility among the very different junc-

tion types on Bi2212 points toward these spectra as

revealing intrinsic properties. However, c-axis mesa

junctions on pristine crystals can exhibit markedly

different behavior,includingvery sharp conductance

peaks,no dip features and a rapid decrease of the gap

with temperature. [79] Not surprisingly, these [79]

and other studies [80] have led to very different in-

terpretations of the evolution of gap features with

temperature, concluding that the superconducting

gap closes at T

and that there is a single pseudogap

which has a different origin than the superconduct-

ing gap. Given the propensity of pristine junctions

to exhibit non-equilibrium effects, such conclusions

must betreated with caution at present.Further stud-

ies which compare single-junction methods and c-

axis, intrinsic junctions on the same Bi2212 crystals

are needed.

15.5.5 YBa

Much of the early tunneling work on high-T

cuprates involved YBa

(YBCO) since this

compound was easily grown as single crystals or thin

films [22]. However, interpretation of the results has

been more challenging than for Bi2212 most likely

due to the presence of another metallic layer in the

crystal structure arising from the Cu-O chains. As

discussed earlier, such normal metal layers can be

induced into the superconducting state via the prox-

imity effect. But of course this effect must now be

treated with a d-wave order parameter, where little

is known either from the experimental or theoretical

side. From planar junctions on etched single crys-

tals, a reproducible gap-like feature near 5 meV in

YBCO has been observed in addition to a higher

energy gap feature near 20 meV attributed to the

Cu-O plane [81]. These structures have been veri-

fied by STM and it was conjectured that the small

gap was due to the chain layer, either an induced su-

perconducting gap or a CDW gap [82]. Strong linear

increases in background conductance were also ob-

served but as discussed earlier, these are probably

due to inelastic tunneling channels.

Tunneling studies on YBCO films were among the

first to display a large ZBCP anomaly,an example of

Fig. 15.33. Splitting of ZBCP in zero field for YBCO junc-

tions as reported, Greene et al. [88]

whichisshown inFig.15.33.Thisobservation further

complicated the interpretation of tunneling spectra.

Several reviews of the various types of ZBCP phe-

nomena in different junction types and in different

cupratescan be found[83–85].A key observationwas

that the ZBCP was found only on films of YBCO ori-

ented such that the ab plane was not parallel to the

substrate plane. Thus the ZBCP was associated with

tunneling into the ab plane not along the c-axis [86].

As discussed in the section on novel d-wave effects,

the ZBCP could thus be associated with Andreev

bound states at the interface arising from quasipar-

ticle scattering events which change the sign of the

order parameter. The tunnel junction probes these

surface bound states. The ZBCP in Fig. 15.33 could

be split by a magnetic field and this was explained by

a doppler shift of the quasiparticle energy due to the

superﬂuid currents [87].

Interestingly there appears to be a splitting of the

ZBCP in zero field. Since magnetic fields produce

currents with a definite rotational direction, this in-

herently breaks time reversal symmetry. The obser-

vation of splitting in zero field thus suggests the pos-

sibility of spontaneously broken time reversal sym-

metry (BTRS).This can occur ifthepure d-wave state

changes to a formd +id



or d +is.In these cases there

is a continuous change of phase with rotation of the

wavevector, but without any nodes, and this must

be accompanied by supercurrents.A review of BTRS

15 Tunneling Spectroscopy 861

Fig. 15.34. (a) Vacuum and point contact junctions along

the (110) direction of YBCO. (b) Vacuum junction along

the c-axis. Data from [90]

and the use of Andreev bound state spectroscopy

to probe such exotic mixed pairing symmetries has

been given by Greene et al. [88]. In the case of YBCO

the BTRS state is probably due to the interface and is

not a bulk effect.Interface scattering which is accom-

panied by sign changes of the gap leads to depairing

effects and therefore suppression of the d-wave gap

near the interface. This effect is similar to the prox-

imity effect in N/S bilayers discussed earlier. If the

suppression of the d-wave gap is strong enough, a

sub-dominant pairing channel can develop, leading

to the mixed symmetry states and BTRS. However,

mixed symmetry can also be a property of the bulk

and whether this is occurring in cuprates is an area

of current research [89].

Another STM study of YBCO crystals attempted to

sort out the differences between c-axis and ab tun-

neling as well as impedance effects due to the Z pa-

rameter of the d-wave BTK model (see the section on

novel d-wave effects) [90]. In Fig. 15.34(a) is shown

a vacuum tunnel contact and point contact junction

along the (110) direction. The large ZBCP is due to

Andreev bound states but there is no splitting as was

found in the planar junctions on YBCO thin films.

This might be another indication that the BTRS state

is a surface effect which depends on details such as

surface roughness. In Fig. 15.34(b) is shown a tun-

nel junction along the c-axis. As discussed earlier,

this orientation should probe the full d-wave DOS in

the Cu-O plane without any ZBCP. The experimen-

tal data show a cusp like feature consistent with a

d-wave DOS and reasonable overall agreement with

agapparameter, =19meV.

The gap value measured by STM is in agreement

with other tunneling studies of YBCO and is con-

siderably smaller than that found in optimal doped

Bi2212 where  = 37 meV. The origin of this rather

large discrepancy in two cuprates with similar T

not completely understood. One possibility is that

the metallic chain layers in YBCO are reducing the

gap size in the Cu-O layers due to the proximity ef-

fect. Another possibility is that there is no universal

curve relating  to T

. The latter is likely especially

since the two quantities have such different doping

dependenciesin Bi2212.The dip/hump featurethat is

common to Bi2212 is also seen reproducibly in STM

measurements of YBCO films [91]. In that work the

gap parameter, =20-25 meV, and the dip is approx-

imately at twice the gap as is found in Bi2212.

15.6 Heavy Fermion Superconductors

The same electron correlation effects which lead to

the largeeffective massesinheavy fermionsupercon-

ductors (HFS) are expected to give riseto unconven-

tional superconducting order parameters. However,

experimental verification,especially from tunneling,

is lacking. Furthermore, HFS exhibit distinctly non-

universal behavior [92]. For the cuprates, tunneling

evidence for d-wave superconductivity is substan-

tial [7]. It includes the cusp feature and subgap shape

862 J.Zasadzinski

Fig. 15.35. Tunneling conductance from SIN junctions on

UPd

for various temperatures. From Jourdan et al. [97]

of the quasiparticle DOS,a reproducibleZBCP found

on ab plane junctions,and the fourfold symmetry of

the zero bias STM mapping near Zn impurities in

Bi2212. In addition there are phase sensitive, corner

SQUID measurements. No such analogue exists for

HFS. All of the point contact measurements on HFS

are in the metallic regime. The differences between

the shape of the Andreev reﬂection peaks for s-wave

and d-wave are subtle. In a comparative Andreev-

reﬂection study DeWilde et al. [93] found no evi-

dence for nodes in CeCu

or URu

. However,

deviations from s-wave BTK theory in UPt

were at-

tributed to nodes in the order parameter. The obser-

vation of Josephson currents between an Al tip and

CeCu

by Poppe [94] is consistent with the ab-

sence of nodes,while the absence of such currents in

UPt

supports the conclusion of DeWilde et al..

Point contact (N/S) studies of UBe

are not eas-

ily reconciled. Early work using Pt and W tips [95]

indicated  =0.13 meV, near the BCS value,but with

a more rapid suppression with temperature than ex-

pected for T

=0.89 K. The authors expressed con-

cern over possible heating effects due to high cur-

rent injection. The conductance curves did not show

an abrupt drop at the gap voltage and therefore this

could be a sign of nodes in the order parameter.More

recent studies using a Au tip revealed considerably

different behavior [96]. A much larger energy gap

was found, giving

2

=6.7, far in excess of the BCS

value and a giant ZBCP was observed, similar to that

expected from Andreev bound states. Both of these

observations are intriguinglysimilar with that found

on high-T

cuprates.

A successful tunnel junctionstudy of UPd

was

realized by Jourdan et al. [97] using a more conven-

tional planar junction geometry. This was possible

due tothe abilityto sputterdeposit high qualityfilms

of UPd

onto LaAlO

substrates with a T

=1.6

K, slightly reduced from the bulk value. A thin Al

overlayer was then used to provide the tunnel bar-

rier along with Pb counterelectrode, its supercon-

ductivity quenched by a small magnetic field. The

tunneling conductances are shown in Fig. 15.35 for

temperatures up to T

In addition to the conductance peaks, which give

agapvalue =0.235 meV, there are higher bias dip

and hump features at characteristic energy scales of

2 to 4 times the gap value. These effects are strik-

ingly similar to that foundon Bi2212although scaled

down in energy by a factor of more than 100. More

importantly, the dip feature appears to be connected

to a new spin excitation, a magnetic exciton, that de-

velops below T

. This is similar to the evidence for a

resonance mode in Bi2212seen in neutron scattering

and correlated with the tunneling dip feature. Also,

an effect which was not commented on by Jourdan et

al., is an apparent pseudogap type feature observed

at T

. All of these phenomena point toward a possi-

ble common mechanism for pairing between high-

cuprates and at least one HFS. Also, the tunneling

data are compatible with a d-wave gap symmetry

which is allowed from group symmetry considera-

tions as well as from the magnetic interactions sug-

gested as the pairing mechanism.

15.7 Organic Superconductors

When superconductivity was discovered in or-

ganic solids based on the bis(ethylenedithio)-

tetrathiafulvalene (BEDT-TTF) molecule, it was not

clear at all that these materials might be related to

high temperature superconducting cuprates. How-

ever, the accumulated evidence to date shows that

they bear intriguing similarities, including a similar

15 Tunneling Spectroscopy 863

Table 15.1. Energy gap parameters obtained from tunneling for several organic superconductors compared with mea-

sured T

Compound T

2

Reference

(K)

 −(BEDT−TTF)

Cu(NCS)

11 5.1 Bando et al.(1990)

ˇ −(BEDT−TTF)

1.35 8 Nowack et al. (1987)

ˇ −(BEDT−TTF)

IAuI 4.1 4 Nowack et al. (1987)

ˇ −(BEDT−TTF)

AuI

3.8 16 Hawley et al. (1986)

phase diagram [98]. A schematic of the “tempera-

ture vs. hole doping”phase diagram for cuprates has

been shown in Fig. 15.21. Changing the hole con-

centration is generally straightforward,e.g.changing

oxygen concentration in Bi2212. For the BEDT-TTF

family, pressure plays the role of doping. The fam-

ily (BEDT − TTF)

X consists of conducting layers of

BEDT-TTF molecules sandwiched between insulat-

ing layersof anions,forexample,X = Cu[N(CN)

]Br.

Similar to cuprates, the insulating layers dope holes

onto the organic layer making them metallic and the

entire system highly anisotropic. This hole concen-

tration can be changed with X as well as with in-

creasing pressure.A Greek prefactor symbol denotes

the packing pattern of the BEDT-TTF molecules.The

parent insulatingphase is antiferromagnetic and for

some compounds the state above T

can be an un-

conventional metal with evidence of a pseudogap.

Tunneling measurements on organic superconduc-

tors have not displayedthe requisite sharpness to dis-

criminate among various gap symmetries. However,

good estimates of gap magnitudes can be obtained

and these have been used to generate the strong cou-

pling ratios shown in Table 15.1 [99–101].

What is immediately clear is that in three of the

organic materials,

2

is significantly larger than the

BCS value of 3.53. The extraordinarily large value

found in ˇ − (BEDT − TTF)

AuI

was considered by

some to be unphysical. However, these large values

are reminiscent of that found in underdoped Bi2212

wherevaluesashighas20areobtained.Thissug-

gests another important similarity to cuprates which

might help explain the anomalies. In cuprates the

anomalously large strong coupling ratios are gener-

ally understood to be due to ﬂuctuation effects which

are stronger in two dimensions. In addition, d-wave

symmetry is more susceptible to scattering of any

type and such ﬂuctuations therefore have a more se-

vere effect on reducing T

.Thusitisnotthatthegap

is too large but rather that the measured T

is too

small. Such large ratios found in organics thus are

consistent with pseudogap phenomena and possibly

with unconventional order parameters.

15.8 Other Materials

While the high-T

cuprates and bismuthates have

captured most of the attention over the past 15 years,

along with organic and heavy fermion superconduc-

tors, a number of other interesting superconductors

have been discovered and are worthy of some com-

ment. The fullerenes certainly represent an exciting

class of materials. A comprehensive review of the

chemical, structural, electronic and optical proper-

ties of these systems is available [102]. Another re-

view which focuses on the electronic properties in-

dicatesthatwhile electron–phonon coupling is viable

as a mechanism forsuperconductivity,aquantitative

tunneling spectroscopy measurement does not ex-

ist [103]. Inelastic tunneling measurements which

utilize C

and C

as part of a multilayer tunnel

junction barrier have revealed the intramolecular

vibrational modes which extend up to nearly 200

meV [104]. If these extremely high frequency modes

were participating in the pairing, they would be very

difficultto detect in superconducting tunneling spec-

troscopy since the strength of the phonon structure

is proportional to



[1].

864 J.Zasadzinski

Fig. 15.36. Tunneling conductance for MgB

from a point

contact junction.Data from [109]

Other compounds of interest are the intermetallic

borocarbides RNi

C (R = rare earth). These lay-

ered systems display rich phase diagrams showing

coexistence or competition between superconduc-

tivity and magnetic order of the rare earth spins. At

presentthere seem to be no surprises in the tunneling

spectra, with most measurements of the gap consis-

tent with weak coupling, BCS theory [105,106]. Re-

cent tunneling measurements of TmNi

C exhibit

very clean gap region spectra, consistent with BCS,

and which show no particular change below 1.5 K

where antiferromagnetic order sets in [107].

The discovery of superconductivity at 39 K in the

simple intermetallic compound MgB

has led to a

ﬂurry of activity [108]. At the time of this writing

there exist several reports of the energy gap from

tunneling. Values of the gap parameter  vary from

2 to 8 meV which could be due to a number of rea-

sons including compositional inhomogeneities. An

example of a relatively clean gap feature is shown in

Fig. 15.36 from PCT measurements [109].

Although the authors assumed this was SIN tun-

neling, the presence of a zero bias feature in this and

other junctions suggests an incipient Josephson cur-

rent and possibly SIS tunneling. In the latter case

thegapvaluewouldbe =2.2 meV far below the

BCS value of 5.9 meV but consistent with STM mea-

surements which display a clean gap [110]. Unpub-

lished reports indicate that this small gap nonethe-

less closes at the bulk T

which is a strong indica-

tion formultiband superconductivity inthis material

[111].

15.9 Conclusions

Conventional superconductors such as Pb are

well understood with- in Migdal–Eliashberg the-

ory, which is essentially BCS theory in the strong

electron–phonon coupling limit. The use of proxim-

ity effect tunneling (PETS) methods has allowed the

determination of the electron–phononspectral func-

tion, ˛

F(!), in a number of transition metal ele-

ments (e.g. Nb, V, Ta), alloys and intermetallic com-

pounds. Tunneling spectroscopy measurements on

binary compounds with light elements such as ZrN

have shown that the strong coupling theory also pro-

vides a good description when high frequency opti-

cal phonons (≈60meV)playanimportantroleinthe

pairing.The coupling of electrons to optical phonons

near 40 meV appears to explain T

values up to 30

K in the bismuthate, BKBO, and also describes well

the normal state d.c. resistivity in overdoped sam-

ples. The optical properties of optimal doped BKBO

are not easily understood which might be due to the

nearby CDW phase which develops with even slight

underdoping.

Tunneling measurements on hole-doped, higher

cuprates such as Bi2212, Tl2201 and YBCO have

revealed common, reproducible features including

strong evidence for d-wave gap symmetry and spec-

tral dip/hump features. Since Bi2212 can be doped

over a wide range, tunneling data on this material

have revealed important doping dependent trends.

The energy gap increases monotonically with de-

creasing doping,scaling with the pseudogap temper-

ature, T

∗

. Although not a proof, this trend indicates

that some sort of precursor superconducting state

exists well above T

. Such a state leads to a pseu-

dogap and can explain the non-Fermi-liquid behav-

ior of the quasiparticles in the normal state. How-

ever, tunneling is also providing some evidence for

a weaker, larger scale pseudogap that is about three

times the superconducting gap. This effect may be

causing some of the confusion over the nature and

energy scale of the pseudogap.

15 Tunneling Spectroscopy 865

The doping dependence of the dip feature in

Bi2212 follows that of the resonance spin excitation,

suggestingspinﬂuctuations playanimportant role in

the pairing mechanism. The size and location of the

dip/hump features in Bi2212 are highly reproducible

among various tunneling groups and junctionmeth-

ods. This is in contrast to phonon fine structures

where evidence is sporadic. A similar dip feature is

found in the heavy fermion superconductor UPd

which is also linked to a feature that develops in the

spin excitation spectrum below T

. This common-

ality is striking and suggests that in both cases, su-

perconductivity is generating a magnetic exciton, a

purely electronic phenomenon. This boson is poten-

tially mediating the pairing as well.

The electron-doped cuprate NCCO presents new

mysteries. A successful inversion of tunneling data

in this material showed that electron phonon cou-

pling adequately describes the superconductivity.

However,more recentmeasurementsindicate d-wave

pairing symmetry, similar to that found on hole-

doped cuprates with much higher T

.Incontrast

to hole-doped cuprates, both electron–phonon and

electron–electron interactions may be in competi-

tion in this cuprate.

The large ratios of energy gap to T

in the organic

superconductors is a mystery that might have been

resolved by advancements in the field of cuprate

superconductivity.This large ratio is reminiscent of

that found in Bi2212, especially in the underdoped

region. The fact that the organics display many other

similarities to cuprates,including a layered structure

and similar phase diagram (including antiferromag-

netism), suggests there is an important linkage. It is

possible that high-T

cuprates, organics and some

heavy fermion superconductors might all share a

common pairing interaction that is magnetic in ori-

gin.

Acknowledgements

The author would liketo thank K.E.Gray and the Ma-

terials Science Division of Argonne National Labo-

ratoryfor supportinga sabbaticalleave appointment

during which much of the manuscript was prepared

and written, and also H. Schmidt and L. Ozyuzer

for help in preparation. The author has benefitted

from the experimental work of former and current

IIT graduate students: Q. Huang, N. Tralshawala, S.

Okur, Z. Yusof, L. Ozyuzer, and H. Schmidt as well

as visiting scientists: June Chen, P. Romano and N.

Miyakawa. Dave Hinks was instrumental in provid-

ing high quality materials for the Argonne tunneling

program and C. Kendziora assisted in the overdop-

ing of Bi2212. Important help in understanding the

theoretical background was received from L. Coffey,

M.Norman,A.Chubukov and B.Janko.Research sup-

port has been received from NSF Science and Tech-

nology Center for Superconductivity and DOE Basic

Energy Sciences.

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