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Local and global effects of quantum

impurities on the quasi particle

tunneling spectra of p-type and n-

type cuprate superconductors

Nai-Chang Yeh, Ching-Tzu Chen, Richard P. Vasquez,

Chang Uk Jung, J. Y. Kim, et al.

Nai-Chang Yeh, Ching-Tzu Chen, Richard P. Vasquez, Chang Uk Jung, J. Y.

Kim, Min-Seok Park, Heon-Jung Kim, Sung-Ik Lee, K. Yoshida, Setsuko

Tajima, "Local and global effects of quantum impurities on the quasi particle

tunneling spectra of p-type and n-type cuprate superconductors," Proc. SPIE

4811, Superconducting and Related Oxides: Physics and Nanoengineering V,

(7 November 2002); doi: 10.1117/12.452324

Event: International Symposium on Optical Science and Technology, 2002,

Seattle, WA, United States

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Local and global effects of quantum impurities on the quasiparticle

tunneling spectra of p-type and n-type cuprate superconductors

N.-C. Yeh

,C.-T.Chen

,R.P.Vasquez

,C.U.Jung

,J.Y.Kim

M. S. Park

,H.J.Kim

,S.I.Lee

, K. Yoshida

, and S. Tajima

Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA

Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA

Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Korea

Superconductivity Research Laboratory, International Superconductivity Technology Center,

Tokyo 135-0062, Japan

ABSTRACT

We report scanning tunneling spectroscopic studies of the effects of quantum impurities on cuprate superconductors. The

samples include p-type YBa

−δ

single crystals with spinless impurities of Zn

and Mg

((Zn,Mg)-YBCO) and n-

type infinite-layer system Sr

0.9

0.1

CuO

with 1% magnetic Ni

- or 1% non-magnetic Zn

-impurities that substitute the

in the CuO

plane. The local effects of spinless impurities on the quasiparticles spectra of (Zn,Mg)-YBCO are

analogous to those of Zn-substituted Bi

CaCu

8+x

, and the global effect is manifested by the suppression of the

pairing potential

∆

and of the spin excitation energy. In contrast, spectroscopic studies of Sr

0.9

0.1

CuO

reveal

momentum-independent spectra and superconducting gap

∆

, with (2

∆

)~7for

=43Kandnopseudogapabove

. The global response of Sr

0.9

0.1

CuO

to quantum impurities is similar to that of

-wave superconductors, being

insensitive to small concentrations of spinless impurities (Zn) while showing rapid degradation in

with increasing

magnetic impurities (Ni). Moreover, the spectra of the Ni-substituted Sr

0.9

0.1

CuO

reveal strong electron-hole

asymmetry and long-range impurity effects, in contrast to the localized impurity effects in the p-type cuprates, and the

introduction of Zn yield no reduction in either

∆

. The physical implications of these findings are discussed.

Keywords:

scanning tunneling spectroscopy (STS), cuprate superconductors, pairing symmetry, quantum impurities,

Kondo effect.

1. INTRODUCTION

Magnetic quantum impurities are known to suppress conventional superconductivity, and the detailed effects have been

a topic of great research interest over the years

1-6

. In contrast, non-magnetic impurities in the dilute limit appear to inflict

negligible effects on conventional superconductivity, as explained by the Anderson theory for dirty superconductors

However, recent findings of strong effects of spinless quantum impurities on the hole-doped (p-type) cuprate

superconductors

8--22

have rekindled active investigation on the effects of quantum impurities on superconductivity. In

particular, theoretical studies have suggested that the effects of quantum impurities depend on the pairing symmetry and

the existence of magnetic correlation in cuprate superconductors

23--31

. For instance, Fermionic nodal quasiparticles in the

cuprates with either

-y

or (

-y

) pairing symmetry can interact strongly with the quantum impurities in the CuO

planes and incur significant suppression of superconductivity regardless of the spin configuration of the impurity

23--27

This phenomenon is in contrast to the insensitivity to spinless impurities in conventional

-wave superconductors

Moreover, the spatial evolution of the quasiparticle spectra near quantum impurities would differ significantly if a small

component of complex order parameter existed in the cuprate. For instance, should the pairing symmetry contain a

complex component such as (

-y

+id

) that broke the time-reversal (

) symmetry, the quasiparticle spectrum at a

spinless impurity site would reveal two resonant scattering peaks at energies of equal magnitude but opposite signs in the

electron-like and hole-like quasiparticle branches

. In contrast, for either

-y

or (

-y

) pairing symmetry

20--22,32--35

only one resonant scattering peak at the impurity site is expected

23,25--27

. In addition, the existence of nearest-neighbor

antiferromagnetic Cu

-Cu

correlation in the superconducting state of the cuprates can result in an unusual Kondo-like

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Physics and Nanoengineering V, edited by Ivan Bozovic and Davor Pavuna

182

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behavior near a spinless impurity

28--30

due to an induced spin-1/2 (

= 1/2) moment when one of the Cu

ions is

substituted with a spinless ion such as Zn

,Mg

,Al

and Li

8--22

Indeed, the Kondo-like behavior associated with

isolated spinless impurities in p-type cuprates has been confirmed from the nuclear magnetic resonance (NMR)

8,9,17

and

the inelastic neutron scattering (INS) experiments

14,15

, and the spinless impurities are found to have more significant

effects on broadening the NMR linewidth, damping the collective magnetic excitations and reducing the superfluid

density than magnetic impurities such as Ni

with

=1.

8--22

On the other hand, both types of impurities exhibit similar

effects on suppressing superconducting transition temperature (

), increasing the microwave surface resistance in the

superconducting state and increasing the normal state resistivity.

8--22

The overall stronger suppression of

superconductivity due to spinless impurities in

-wave cuprates has been attributed to the slower spatial relaxation of

spin polarization near the spinless impurities than that near the

= 1 impurities, the latter being partially screened by the

surrounding antiferromagnetically coupled Cu

spins

30,31

. The detailed spatial evolution of the quasiparticle tunneling

spectra near these quantum impurities in the cuprates can further provide useful insights into the pairing state of the

cuprates, and has recently been investigated in impurity-substituted Bi

CaCu

and YBa

systems using the

low-temperature scanning tunneling microscopy (STM) techniques

18--22

. While in principle both the potential scattering

and the Kondo effect contribute to the quasiparticle spectra near spinless impurities, which of the two scenarios may be

dominating cannot be conclusively determined from existing data, because direct probing of the quasiparticle spectra

near the quantum impurities using scanning tunneling spectroscopy (STS) involves not only the density of states in the

CuO

planes of the cuprates but also the tunneling matrix. The latter depends on the atomic nature of the surface layer

and the exact path of the tunneling electrons, which is generally difficult to determine.

It is interesting to note that most research activities to date have been focused on the effects of quantum impurities in p-

type cuprate superconductors

8--31

. Few reports associated with similar investigation on the n-type cuprates have been

available until recently.

36,37

Given that the cuprate superconductors do not exhibit particle-hole symmetry and cannot be

described by a simple one-band Hubbard model, it is essential to compare the effects of quantum impurities on the n-

type cuprates with those on the p-type in order to achieve better understanding of the underlying pairing mechanism. For

instance, the inapplicability of the one-band Hubbard model can be realized from the consideration of spin fluctuations

in cuprate superconductors. In the p-type cuprates, holes are known to reside in the oxygen

-orbital of the CuO

planes,

which induces ferromagnetic coupling for the hole-linked Cu

spins thereby causing strong spin fluctuations in the

antiferromagnetic host.

38,39

In contrast, excess electrons in the n-type cuprates reside in the copper

-orbital of the CuO

planes, yielding spinless Cu

-ions that dilute the background antiferromagnetism rather than causing severe spin

fluctuations.

This example suggests the necessity of investigating both the p-type and n-type cuprates in order to

identify universal features that are truly responsible for the occurrence of high-temperature superconductivity.

In this work, we report our recent scanning tunneling spectroscopic (STS) studies of optimally

doped p-type and n-type

cuprates with various quantum impurities, and compare our findings with other related experimental results. These

investigations reveal that the response of cuprates to quantum impurities is indeed sensitive to the pairing symmetry and

the type of the dopant, and that the only common features among all cuprates appear to be strong electronic correlation

and background antiferromagnetism in the superconducting state.

2. QUANTUM IMPURITIES IN P-TYPE CUPRATE SUPERCONDUCTORS

2.1 General consideration of the effects of quantum impurities on

-wave superconductors

Experimental evidence to date has established that the p-type cuprates exhibit either pure

-y

pairing symmetry in

samples with tetragonal crystalline symmetry or (

-y

) pairing symmetry in those with orthorhombic crystalline

symmetry in the superconducting state.

20--22,32--35

The consequence of such pairing symmetries is that these cuprates are

gapless along the (

±π

) directions, hence substantial low-energy excitations in the form of nodal quasiparticles even at

low temperatures. On the other hand, NMR experiments have clearly demonstrated that non-magnetic impurities that

substituted the Cu-ions in the CuO

planes can induce local

= 1/2 moments on the neighboring Cu ions.

9,17

Moreover,

magnetic impurities such as Ni

with

= 1 naturally exhibit excess magnetic moments

despite the antiferromagnetic

background with

= 1/2 moments. These effective excess magnetic moments in the cuprate are expected to interact with

the elementary excitations of the host, with particularly strong interaction with the existing nodal quasiparticles. Due to

the complexity of many-body interactions in the strongly correlated electronic system, theoretical consideration for the

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effect of quantum impurities has been limited to perturbative and one-band approximation, without self-consistently

solving for the spatially varying pairing potential due to the presence of impurities.

23--30

Moreover, the interaction among

impurities has been neglected. Thus, the Hamiltonian

is approximated by

BCS

imp

,where

BCS

is the

-wave

BCS Hamiltonian that contains the normal (diagonal) one-band single-particle eigen-energy and anomalous (off-

diagonal)

-y

-wave pairing potential

∆

(

∆

cos

being the angle relative to the anti-node of the order parameter

in the momentum space) of the unperturbed host, and

imp

pot

mag

denotes the impurity perturbation due to both

the localized potential scattering term

pot

∑

0σ

†

0σ

;

: the on-site Coulomb scattering potential) and the Kondo-

like magnetic exchange interaction term

mag

∑

•

) between the spins of the conduction carriers on the

sites

(

) and those of the localized magnetic moments (

Assuming the aforementioned model Hamiltonian, one can obtain the quasiparticle spectra due to impurities by using the

Green's function derived from

. If one further neglects the contributions from the tunneling matrix, one obtain in the

pure potential scattering limit a resonant energy at

Ω

on the impurity site that satisfies the following relation

23,24

Ω/∆

≈

[(

)

cot

ln(

cot

)],

(1)

where

is the impurity-induced phase shift in the quasiparticle wavefunction. Generally

→

(

/2) in the strong

potential scattering (unitary) limit. On the other hand, in the case of magnetic impurities with both contributions from

pot

and

mag

, one expects two spin-polarized impurity states at energies

Ω

1,2

, which are given by

Ω

1,2

/∆

=1/[

(

)

ln|

(

)

|],

(2)

where

is the density of states at the Fermi level and

≡

•

implies that magnetic impurities are isolated and

equivalent at all sites. We remark that the assumption of non-interacting impurities is only valid in the limit of dilute

impurities and strong screening due to conducting carriers.

2.2 STS studies of (Zn,Mg)-YBCO

We have performed STS studies on an optimally doped YBa

(YBCO) single crystal with 0.26% Zn and 0.4%

Mg substituted into the Cu sites in the CuO

planes, hereafter denoted as (Zn,Mg)-YBCO. The superconducting

transition temperature of the sample is

= 82.0 K, which is substantially lower than that of the pure optimally doped

YBCO with

= 93.0 K. Additional STS studies on pure YBCO single crystals with different hole doping levels have

also been performed for comparison with the impurity-substituted sample.

20--22

The quasiparticle tunneling spectra were

taken with a low-temperature STM, and measurements on the (Zn,Mg)-YBCO have been concentrated on c-axis

quasiparticle tunneling, while STS studies on other pure YBCO samples have been made along different crystalline axes,

as reported elsewhere.

20--22,34,35

The measurements were taken at 4.2 K with a tunneling tip made of Pt(85%)-Ir(15%).

The voltage resolution at 4.2 K was ~ 1 meV, and the sample surface was prepared using a chemical etching process

detailed before.

20--22,34,35

This process has been shown to yield reproducible and high-quality surface, as verified by both

XPS and our extensive STS studies.

20--22,34,35

The spectroscopic information obtained from the studies of (Zn,Mg)-YBCO is illustrated in Figure 1 and summarized as

follows. For STM tip significantly far away from any impurities, the tunneling spectra were similar to the typical c-axis

quasiparticle tunneling spectra in pure YBCO, as shown in the upper panel of Figure 1(a). However, we note that the

global superconducting energy gap

∆

was suppressed to (25

2) meV from the value

∆

=(29

1) meV in pure YBCO.

20--22

Moreover, the energy

dip

associated with the "dip-hump" satellite features had also shifted substantially relative to

that in pure YBCO. We note that the dip-hump feature has been attributed to effects of quasiparticle damping by the

background many-body excitations such as spin fluctuations

42,43

or phonons

, and the resonant energy of the many-body

excitation may be empirically given by |

Ω

res

|=|

dip

−

∆

|. We find that the magnitude of

Ω

res

in the (Zn,Mg)-YBCO

sample decreased significantly to (7

1) meV from that in the pure YBCO where |

Ω

res

|=(17

1) meV. This drastic

decrease in

Ω

res

with the very small impurity concentration in our (Zn,Mg)-YBCO has clearly ruled out phonons as the

relevant many-body excitations to the satellite features. We can therefore associate the

dip

satellite feature with the

presence of spin fluctuations in YBCO, and can also conclude that the presence of spinless impurities suppresses the Cu

spin fluctuations in the optimally doped

-wave cuprates.

20--22

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On the other hand, detailed studies on the surface of (Zn,Mg)-YBCO also revealed apparent impurity scattering spectra

that could be associated with two types of impurities, with maximum scattering intensity occurring at either

Ω

−

meV or

Ω

~4meV.

20--22

By identifying the location of a maximum scattering intensity to the position of either a Zn or

Mg impurity, we found that the intensity of the resonant scattering peak decreased rapidly within approximately one

Fermi wavelength along the Cu-O bonding direction, as shown in the lower panels of Figures 1(a) and 1(b), while the

coherence peaks associated with the superconducting gap were significantly suppressed, and the degree of suppression

was asymmetric between the electron-like and hole-like branches. Moreover, with the STM tip moving away from the

impurity site, the resonant scattering peak appeared to alternate between energies of the same magnitude and opposite

signs, as exemplified in the upper panel of Figure 1(b). Such spatial variations are expected for both Kondo-like and

charge-like impurities. However, some of these spatially varying spectra near impurities also revealed slow temporal

variations over long times (about ~ 10

s), which would have been more consistent with the Kondo effect. Finally, the

impurity effects on the variations in the quasiparticle spectra appeared to have completely diminished at approximately

two coherence lengths (~ 3 nm) away from the impurity, as shown in lower panel of Figure 1(b).

Figure 1

Normalized c-axis differential conductance (

dI/dV

) versus bias voltage (

) quasiparticle tunneling spectra of the (Zn,Mg)-

YBCO single crystal near impurity sites at 4.2 K.

(a)

Upper panel

: A representative impurity scattering spectrum with a resonant peak

Ω

−

10 meV and a typical spectrum away from impurities. Lower panel

: Spatial variation of the impurity-induced resonant peak

intensity.

(b)

Upper panel

: Representative spectra revealing spatial variations in the quasiparticle spectra along the Cu-O bonding

direction from an impurity with a maximum scattering at

Ω

4 meV. We note the alternating resonant peak energies between

meV and

−

4 meV and the particle-hole asymmetry in the degrees of suppression of the superconducting coherence peaks. Lower

panel

: Spatial variation of the impurity-induced resonant peak intensity, showing alternating peak intensities at energies + 4 meV and

−

4 meV with distance from an impurity.

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Independent of the dominating interaction of the impurity with quasiparticles, the resonant energy at

Ω

−

10 meV can

be associated with a weaker impurity than that at

Ω

~ 4 meV. This attribution can be verified by considering the

following two extreme limits. If we assume pure potential scattering, we obtain a phase shift

0.38

associated with

Ω

and

0.43

associated with

Ω

by using Eq. (1), and the latter is clearly associated with a stronger scattering

potential

. On the other hand, if we assume pure Kondo scattering effects, the resonant peak energy would be

comparable to the corresponding Kondo temperature

29,30

and the latter decreases with increasing exchange interaction.

Hence, the impurity associated with the energy

Ω

would correspond to stronger magnetic exchange interaction with the

quasiparticles. Considering that Mg

-ions is likely to cause stronger structural distortion in the CuO

planes than Zn

we may tentatively assign

Ω

to Zn-impurities and

Ω

to Mg-impurities. This issue can be verified in the future by

studying purely Zn-substituted YBCO and Mg-substituted YBCO.

Table 1

Summary of the effects of spinless quantum impurities on the superconductivity of YBa

and Bi

CaCu

18,20-22

Properties

YBa

CaCu

(Ref. 18)

Resonant scattering energy

Ω

=−

10 meV

Ω

−

1.5 meV

at the impurity site

Ω

4meV

Phase shift due to potential

∼

0.38

δ∼

0.45

scattering

∼

0.43

Spectral recovery length (

−1

)

−1

∼

3.0 nm (empirical)

−1

∼

1.5 nm (empirical)

∼

2.5 nm (theoretical)

Global effect on the maximum

∆

decreases from (30

1) meV

unknown due to nanoscale spectral

-wave energy gap

∆

to (25

2) meV.

variations.

Global effect on the spin

Ω

res

decreases from 16 ~ 18 meV

unknown due to nanoscale spectral

resonant energy

Ω

res

to 8 ~ 10 meV.

variations.

Global effect on

decreases from ~ 93 K

decreases from ~ 87 K

to~82K.

to~84K.

General remarks

weaker & longer-range impurity

non-interacting impurities

effects

→

stronger impurity correlation?

nearly in the unitary limit.

both potential scattering and Kondo

more consistent with potential

effect appear to be relevant.

scattering.

-symmetry is preserved.

2.3 Comparing the Effect of Non-Magnetic Quantum Impurities in YBa

and Bi

CaCu

Next, we compare our findings derived from the (Zn,Mg)-YBCO sample with similar STS studies of a 0.6% Zn-

substituted Bi

CaCu

+δ

(BSCCO).

Generally speaking, the primary features such as the appearance of single

resonant scattering peak and strong suppression of the superconducting coherence peaks at the impurity site, as well as

the rapidly decreasing intensity of the resonant peak with the displacement from the impurity site, are comparable in

both systems. These findings are also consistent with the preservation of time-reversal (

) symmetry in both systems,

suggesting the absence of any discernible complex order parameter in the pairing symmetry. On the other hand, several

differences are noteworthy. First, the strength of impurity scattering appears weaker and longer-ranged in YBCO.

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Second, various phenomena that are more consistent with the Kondo effect, such as alternating resonant peak energies

between +

Ω

and

−

Ω

with the distance from a spinless impurity and temporal variations of the resonant peak, have only

been observed in YBCO. Third, global suppression of the superconducting energy gap and of the collective magnetic

excitation energy has only been revealed in YBCO. Such a difference may be attributed to the fact that pure YBCO

generally exhibits long-range spectral homogeneity, whereas nanoscale spectral variations have been reported in

nominally pure BSCCO samples, yielding difficulties in identifying the global effect of impurity substitutions. The

similarities and differences between the effects of spinless impurities on YBCO and those on BSCCO are summarized

below in Table 1.

3. QUANTUM IMPURITIES IN N-TYPE CUPRATE SUPERCONDUCTORS

As stated in the introduction, most studies of the impurity effects on the cuprate superconductors have focused on the p-

type cuprates. We shall consider in the following the effects of quantum impurities on the simplest form of cuprates,

known as the n-type infinite-layer system. However, it is necessary to first address several issues of general importance

and relevance to all n-type cuprates, particularly in light of various competing orders in the cuprates

38--40

that are

extremely sensitive to the fine tuning of structural variations and doping levels. In this context, it is informative to

compare the structures of the representative p-type and n-type cuprates, as shown below in Figure 2. Generally speaking,

the most significant structural difference between n-type and p-type cuprates is that all p-type cuprates have apical

oxygen associated with the Cu atoms in the CuO

planes, whereas no apical oxygen exists along the c-axis of all n-type

cuprates

. A very important effect of the presence of apical oxygen is that it lifts the energy degeneracy between the

-orbital and the

-r

-orbital, with the former lower in energy for holes. This phenomenon can play an important role

in the determination of the pairing symmetry in various cuprates, as discussed in the following.

Figure 2

Crystalline structures of representative cuprates:

(a)

The n-type infinite-layer system Sr

1-x

CuO

,withLn=La,Gd,and

Sm.

(b)

The one-layer p-type system La

2-x

CuO

(c)

The one-layer n-type system R

2-x

CuO

,withR=Pr,Nd,Sm,Eu;M=Ce,

Th.

3.1 Pairing symmetry in n-type cuprates

The pairing symmetry in the one-layer n-type cuprates has been controversial, with different experiments suggesting

either

-wave or

-y

-wave pairing symmetry

45,46

. Noting that the undoped cuprates are Mott antiferromagnetic

insulators with very large on-site Coulomb repulsion

38-40

and that a large charge reservoir exists between the CuO

planes and the Cu atoms in each CuO

plane of all p-type cuprates are connected to apical oxygen, it seems reasonable

that the pairing symmetry favors

-y

-wave over

-wave in most p-type cuprates so that the on-site Coulomb repulsion

and orbital potential energy can be minimized while maintaining the quasi two dimensionality of the system. On the

other hand, the absence of apical oxygen in the n-type cuprates results in degenerate

-y

and

-r

orbitalsothatthe

benefit of forming

-y

-wave pairing is reduced, although the significantly large separation between consecutive CuO

planes in the one-layer n-type cuprates could still favor a pairing symmetry that preserves the quasi-two dimensionality.

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The exact pairing symmetry in a specific sample may therefore depend sensitively on the subtle balance of various

competing energy scales. Indeed, it has been suggested recently that the pairing symmetry in the one-layer n-type

cuprates can be either

-wave or

-y

-wave, depending on the electron doping level.

This proposed doping

dependence could in fact account for the controversies surrounding the pairing symmetry of the one-layer n-type

cuprates.

45,46

On the other hand, the infinite-layer n-type cuprate Sr

1-x

CuO

(Ln = La, Gd, Sm), known as the simplest form among

all cuprate superconductors,

48-50

has several unique characteristics that differ from other cuprates and may in fact favor

wave pairing. First, in contrast to all other cuprates with a large charge reservoir between the CuO

planes, the infinite-

layer system only contains a metallic monolayer of La(Sr) between consecutive CuO

planes. Second, the c-axis

superconducting coherence length (

~ 0.53 nm) is longer than the c-axis lattice constant (

in contrast to the typical

condition of

<< c

in most other cuprates. Hence, the infinite-layer system is expected to reveal characteristics more

like a three-dimensional superconductor. Third, it is found from the Knight shift experiments

that the carrier density of

the optimally doped Sr

0.9

0.1

CuO

at the Fermi level is significantly smaller than that in typical p-type cuprates, being ~

25% that of optimally doped YBa

. These atypical characteristics of the infinite-layer system are suggestive of a

stronger tendency toward more isotropic pairing symmetry as well as weak screening and strong electronic correlation,

and are therefore worthy of careful investigation.

3.2 Evidence of strongly correlated s-wave superconductivity in pure Sr

0.9

0.1

CuO

Despite the importance of understanding the infinite-layer cuprates, these materials are very difficult to synthesize, and

the lack of single-phased compounds with high volume fraction of superconductivity

48-50

has hampered the research until

a recent breakthrough.

Using high-pressure (~ 4 GPa) and high-temperature (~ 2000

C) annealing conditions, Jung

al.

have been able to routinely achieve single-phased Sr

0.9

0.1

CuO

compounds with nearly ~ 100% superconducting

volume.

With the availability of these high-quality infinite-layer cuprates, it has finally become possible for us to

perform scanning tunneling spectroscopic studies to investigate the quasiparticle tunneling spectra and the pairing

symmetry. Our recent STS studies on the optimally doped Sr

0.9

0.1

CuO

system have revealed a number of curious

phenomena that defy various widely accepted scenarios in p-type cuprate superconductors.

First, the quasiparticle

tunneling spectra and the superconducting energy gap

∆

appear to be momentum-independent, and the ratio of (2

∆

)

~7for

= 43 K is much larger than the BCS ratio (~ 3.5) for weak coupling

-wave superconductors. Moreover, no

discernible satellite features exist in the quasiparticle spectra, in sharp contrast to those of all p-type cuprates, as

exemplified by the thick curve in Figure 3(a) for a representative spectrum taken on the optimally doped Sr

0.9

0.1

CuO

In addition, the superconducting coherence peaks completely vanish above

, suggesting the absence of

pseudogap

38,39,53

, which has also been independently verified by NMR experiments

on similar samples. Combined with

recent confirmation of complete absence of pseudogap phenomena in various one-layer n-type cuprates with different

doping levels

and the lack of universal pairing symmetries in all cuprates, it may be suggested that the pseudogap

phenomena and

-y

-wave pairing symmetry in most p-type cuprates are the consequence of competing orders rather

than the sufficient conditions for cuprate superconductivity. In this context, it seems particularly interesting to

investigate how the infinite-layer cuprates respond to various quantum impurities in the Cu sites.

3.3 Effects of quantum impurities on the infinite-layer system

As discussed in the previous sections, cuprates with

-y

-wave pairing symmetry are strongly affected by both

magnetic and non-magnetic quantum impurities in the CuO

planes. On the other hand, superconductors with

-wave

pairing symmetry are expected to be insensitive to a small concentration of non-magnetic impurities due to the fully

gapped Fermi surface and therefore limited interaction with the low-energy excitations at low temperatures.

It is

therefore natural to further substantiate the unusual finding of

-wave pairing symmetry in the infinite-layer system by

investigating the effect of quantum impurities on its superconductivity. Indeed, our bulk magnetization studies

revealed

that the substitution of spinless Zn-impurities into the Cu sites of Sr

0.9

0.1

CuO

was found to yield no suppression in the

bulk

up to 3% impurities, beyond which the compound became inhomogeneous and phase segregated. On the other

hand, the substitution of magnetic Ni-impurities into the Cu sites of Sr

0.9

0.1

CuO

yielded significant

suppression.

With 1% Ni,

already decreased from 43 K to 32 K; 2% Ni dropped

to below 4 K, and 3% Ni completely suppressed

the bulk superconductivity although the sample was still stoichiometrically homogeneous from x-ray diffraction. Hence,

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the response of the Sr

0.9

0.1

CuO

system to quantum impurities appeared to differ significantly from that of p-type

cuprates

8--22

and was analogous to that of conventional

-wave superconductors

4,6

. In this context, we may apply the

Abrikosov-Gor'kov theory

for magnetic impurities in conventional superconductors to estimate the exchange interaction

energy

between the magnetic impurity and the conduction electrons. Using the relation (

∆

where

denotes

the critical concentration of magnetic impurities for complete suppression of superconductivity and

is the Fermi

energy,

we obtain

≈

0.28 eV if we take the empirical values of

≈

0.03 and

∆≈

13meV,andalsoassumea

reasonable value of

≈

0.2 eV for Sr

0.9

0.1

CuO

. This exchange energy is comparable to but somewhat larger than the

-Cu

antiferromagnetic coupling constant.

Figure 3

Quasiparticle tunneling spectra of the infinite-layer system at 4.2 K.

(a)

Comparison of the spectrum taken on a pure

0.9

0.1

CuO

(thick line) and that on a 1% Ni-substituted Sr

0.9

0.1

CuO

(thin line). The inset illustrates the spectral difference of the

two spectra in the main panel, which corresponds to the

= 1 Ni-impurity contributions.

(b)

Long-range spatial extension of the

impurity spectral contribution is shown over ~ 30 nm. The spatial separation between two consecutive curves was 3 nm, and the

spectra were shifted vertically in the graph for clarity. These spectra appeared to be quite homogeneous over long range within one

grain, although slight spectral variations existed. Two asymmetric bound-state energies in the electron-like and hole-like branches

were visible at |

Ω

∼

5meV.

(c)

Other representative spectral contributions from Ni-impurities in different grains, showing some

variations from grain to grain. The origin for such variations is unknown, and may be related to inhomogeneous Ni concentrations.

Our spectroscopic studies

of 1% Zn-substituted Sr

0.9

0.1

CuO

and 1% Ni-substituted Sr

0.9

0.1

CuO

further

corroborated earlier findings from the bulk magnetization measurements

. That is, the tunneling spectra taken on 1%

Zn-substituted Sr

0.9

0.1

CuO

appeared to be spatially homogeneous, with no suppression in the superconducting gap

value although the quasiparticle lifetime was reduced due to Zn-induced disorder in the sample. In contrast, detailed

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spectroscopic studies on the 1% Ni-substituted Sr

0.9

0.1

CuO

revealed quasiparticle spectra with large electron-hole

asymmetry, as shown by a representative spectrum in Figure 3(a). The spectral difference between the 1% Ni-substituted

0.9

0.1

CuO

and the pure Sr

0.9

0.1

CuO

is shown in the inset of Figure 3(a), which represents the impurity

contribution to an effective bound state, known as the Shiba state in conventional superconductivity. We further notice

that the impurity contribution appeared to extend over a relatively long range, as exemplified in Figure 3(b) where

consecutive tunneling spectra taken at ~ 3 nm apart on the same grain are shown. Studies over many grains consistently

revealed that the Ni-impurities contributed to a bound state at energies

Ω

where the average value over all grains

yielded |

Ω

2) meV. While slight variations can be observed in the impurity-induced bound state from one grain

to another, overall the bound-state spectral contribution appeared to be quite consistent over a long range. This finding is

in sharp contrast to the rapidly vanishing effects of magnetic impurities at approximately one Fermi wavelength away

from an isolated Mn or Gd atom on Nb-superconductor. We attribute the difference to the weak screening effect of the

infinite-layer system, and also to the strong overlap of the Ni-impurity wavefunctions. That is, the average Ni-Ni

separation for 1% Ni-substitution in Sr

0.9

0.1

CuO

~ 1.8 nm in the CuO

planes and ~ 1.6 nm along the c-axis,

whereas the spatial extension (

)

of the impurity wavefunction can estimated using the following formula

1,2,5

∆

− Ω

)

1/2

,(3)

with

being the BCS coherence length at

= 0. Using the anisotropic superconducting coherence lengths

37,51,55

≈

4.8 nm and

≈

0.53 nm, also using |

Ω

≈

5 meV and

∆≈

13 meV, we estimate the in-plane spatial extension of the

impurity wavefunction as

⊥

≈

5.2 nm ~

while the c-axis wavefunction extension is

⊥

≈

0.58 nm ~

0.4 d

.This

simple estimate suggests that there is substantial overlap of impurity wavefunctions. Thus, the effects of 1% Ni

substitution in Sr

0.9

0.1

CuO

should be considered as a Kondo alloy rather than a typical Kondo problem for isolated

magnetic impurities.

Comparing the magnetic impurity effects on the n-type infinite-layer system with the STS studies of Ni-substitution in

thep-typecuprateBi

CaCu

we note that the latter revealed relatively short-range impurity effects and two

bound state energies at

Ω

and

Ω

,where|

Ω

(9.2

1.1) meV and |

Ω

(18.6

0.7) meV. Furthermore, the

potential scattering effects of Ni on Bi

CaCu

appeared to be more significant than the Kondo effect,

whereas in

the Sr

0.9

0.1

CuO

system the potential scattering seemed less relevant, as manifested by the insignificant Zn-impurity

effects on the superconductivity of Sr

0.9

0.1

CuO

. The relatively insignificant potential scattering effect on the infinite-

layer system may be understood in terms of the

-wave pairing that ensures a fully gapped Fermi surface at low

temperatures and therefore insensitivity to the non-magnetic disorder

. In Table 2 we summarize the effects of Ni-

substitutions on the n-type Sr

0.9

0.1

CuO

system and compare them with those on the p-type cuprate Bi

CaCu

Table 2

Comparison of the effects of Ni-impurities on the n-type Sr

0.9

0.1

CuO

andonthep-typeBi

CaCu

Properties

0.9

0.1

CuO

CaCu

(Ref. 19)

Pairing symmetry

-wave

-y

-wave

Impurity bound-state

Ω

2) meV

Ω

(9.2

1.1) meV

energies

Ω

(18.6

0.7) meV

Effective range of

long range

short range

magnetic impurities

(~ 10

nm )

(<~ 3 nm)

Global effect of Ni on the

:0%--43K,1%--32K,

:0%--95K,0.2%--85K

transition temperature

2% --

≤

4 K, 3% -- 0 K.

0.5% -- 83 K.

Cause for the suppression

broken particle-hole symmetry due to

more significant potential scattering than

of superconductivity

collective Kondo effect;

= 0.2 ~ 0.3 eV.

the Kondo effect.

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Finally, we remark on the apparent absence of induced magnetic moments due to Zn-substitution in Sr

0.9

0.1

CuO

,as

opposed to the situation in p-type cuprates.

9,17

By considering the available electronic configurations for the outer

orbitals of the cations in the CuO

plane, it seems feasible that a Zn

substitution in the n-type cuprates tends to localize

of a spinless Cu

-ion to its neighboring site. Thus, no excess magnetic moments are formed due to Zn-substitution in the

n-type cuprates, and the corresponding perturbation to both the spin and orbital degrees of freedom is minimized.

4. SUMMARY

We have investigated the effects of magnetic and non-magnetic quantum impurities on the quasiparticle tunneling

spectra of both p-type and n-type cuprate superconductors. In the case of optimally doped YBa

, we find that the

introduction of spinless impurities such as Zn or Mg results in global suppression of the superconducting energy gap and

the spin fluctuations. Furthermore, the local quasiparticle spectra near impurities reveal interesting spatial variations that

are similar to the findings from the Zn-substituted Bi

CaCu

, although the spinless impurities appear to extend

over longer spatial range and also weaker in the impurity scattering strength in the YBa

system. The occasional

observation of long-time temporal variations in the latter suggests that the Kondo effect induced by the spinless

impurities may be more significant than the potential scattering effect in YBa

. The overall strong response of p-

type cuprates to both the magnetic and non-magnetic impurities can be attributed to the

-y

-wave pairing symmetry

and the existence of background antiferromagnetic correlation. On the other hand, our investigation of the quantum

impurity effects on the simplest cuprate Sr

0.9

0.1

CuO

, known as the n-type infinite-layer system, reveals results that are

in general consistent with

-wave superconductors. That is, both the global

and the local quasiparticle spectra of the

0.9

0.1

CuO

system appear insensitive to spinless impurities such as Zn

while showing significant suppression of

superconductivity with Ni

substitution. However, the magnetic impurities in Sr

0.9

0.1

CuO

manifest substantial

overlap in their wavefunctions, yielding long-range electron-hole asymmetry in the quasiparticle spectra. Such

observation of impurity effects is consistent with our other findings of momentum-independent quasiparticle spectra and

strong electronic correlation in the pure Sr

0.9

0.1

CuO

system. These detailed comparisons between the p-type and n-

type cuprates led us to conclude that various widely accepted characteristics such as the

-y

-wave pairing symmetry,

spin fluctuations and pseudogap phenomena are not truly universal among all cuprates. Rather, they are likely the

consequences of competing orders. The only ubiquitous features among all cuprates appear to be the strong electronic

correlation and the background antiferromagnetic coupling.

ACKNOWLEDGEMENT

The research at Caltech was jointly supported by the NSF Grant No. DMR-0103045 and the Caltech President's Fund.

Part of the research was performed by the Center for Space Microelectronics Technology, Jet Propulsion Laboratory,

Caltech, and was sponsored by NASA. The work at Pohang University was supported by the Ministry of Science and

Technology of Korea through the Creative Research Initiative Program, and the work at SRL/ISTEC in Japan has been

partially supported by NEDO.

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Gor'kov,

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,P.FuldeandR.A.Ferrell,

Phys. Rev.

135

, A550 (1964).

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,M.A.WolfandF.Reif,

Phys. Rev.

137

A557 (1965).

"Spatial variations of the order parameter in superconductors containing a magnetic impurity"

, P. Schlottmann,

Phys. Rev. B

, 1 (1976).

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