# Extremely strong coupling superconductivity in artificial two-dimensional Kondo lattices

**ABSTRACT** When interacting electrons are confined to low-dimensions, the

electron-electron correlation effect is enhanced dramatically, which often

drives the system into exhibiting behaviors that are otherwise highly

improbable. Superconductivity with the strongest electron correlations is

achieved in heavy-fermion compounds, which contain a dense lattice of localized

magnetic moments interacting with a sea of conduction electrons to form a 3D

Kondo lattice. It had remained an unanswered question whether superconductivity

would persist upon effectively reducing the dimensionality of these materials

from three to two. Here we report on the observation of superconductivity in

such an ultimately strongly-correlated system of heavy electrons confined

within a 2D square-lattice of Ce-atoms (2D Kondo lattice), which was realized

by fabricating epitaxial superlattices built of alternating layers of

heavy-fermion CeCoIn5 and conventional metal YbCoIn5. The field-temperature

phase diagram of the superlattices exhibits highly unusual behaviors, including

a striking enhancement of the upper critical field relative to the transition

temperature. This implies that the force holding together the superconducting

electron-pairs takes on an extremely strong coupled nature as a result of

two-dimensionalization.

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**ABSTRACT:**Motivated by the remarkable experimental realizations of $f$-electron superlattices, e.g. CeIn$_3$/LaIn$_3$- and CeCoIn$_5$/YbCoIn$_5$- superlattices, we analyze the formation of heavy electrons in layered $f$-electron superlattices by means of the dynamical mean field theory. We show that the spectral function exhibits formation of heavy electrons in the entire system below a temperature scale $T_0$. However, in terms of transport, two different coherence temperatures $T_x$ and $T_z$ are identified in the in-plane- and the out-of-plane-resistivity, respectively. Remarkably, we find $T_z < T_x \sim T_0$ due to scatterings between different reduced Brillouin zones. The existence of these two distinct energy scales implies a crossover in the dimensionality of the heavy electrons between two and three dimensions as temperature or layer geometry is tuned. This dimensional crossover would be responsible for the characteristic behaviors in the magnetic and superconducting properties observed in the experiments.Physical Review B 02/2014; 88(23). · 3.66 Impact Factor - SourceAvailable from: de.arxiv.orgM Shimozawa, S K Goh, R Endo, R Kobayashi, T Watashige, Y Mizukami, H Ikeda, H Shishido, Y Yanase, T Terashima, T Shibauchi, Y Matsuda[Show abstract] [Hide abstract]

**ABSTRACT:**By using a molecular beam epitaxy technique, we fabricate a new type of superconducting superlattices with controlled atomic layer thicknesses of alternating blocks between the heavy-fermion superconductor CeCoIn5, which exhibits a strong Pauli pair-breaking effect, and nonmagnetic metal YbCoIn5. The introduction of the thickness modulation of YbCoIn5 block layers breaks the inversion symmetry centered at the superconducting block of CeCoIn5. This configuration leads to dramatic changes in the temperature and angular dependence of the upper critical field, which can be understood by considering the effect of the Rashba spin-orbit interaction arising from the inversion symmetry breaking and the associated weakening of the Pauli pair-breaking effect. Since the degree of thickness modulation is a design feature of this type of superlattices, the Rashba interaction and the nature of pair breaking are largely tunable in these modulated superlattices with strong spin-orbit coupling.Physical Review Letters 04/2014; 112(15):156404. · 7.73 Impact Factor - SourceAvailable from: Yuki Nagai[Show abstract] [Hide abstract]

**ABSTRACT:**Impurity effects are probes for revealing an unconventional property in superconductivity. We study the effects of nonmagnetic impurities in a two-dimensional (2D) topological superconductor with s-wave pairing, Rashba spin–orbit coupling, and the Zeeman term. Using a self-consistent T-matrix approach, we calculate the phenomenological formula for the Thouless–Kohmoto–Nightingale–Nijs (TKNN) invariant in interacting systems, as well as the density of states, at different magnetic fields. This quantity weakly depends on the magnetic field, when a spectral gap opens. In contrast, it changes markedly when in-gap states occur. Furthermore, in the latter case, we find that Anderson’s theorem (robustness of s-wave superconductivity against nonmagnetic impurities) breaks down. We discuss the origin of this breakdown from the viewpoints of both unconventional superconductivity and the TKNN invariant.Journal of the Physical Society of Japan 08/2014; 83:094722. · 1.48 Impact Factor

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Extremely Strong Coupling Superconductivity in

Artificial Two-dimensional Kondo Lattices

Y. Mizukami1, H. Shishido1+

D. Watanabe1, M.Yamashita1, H. Ikeda1, T. Terashima2, H. Kontani3, and Y. Matsuda1*

1Department of Physics, Kyoto University, Kyoto 606-8502, Japan

2Research Center for Low Temperature and Materials Sciences, Kyoto University,

Kyoto 606-8501, Japan

3Department of Physics, Nagoya University, Furo-cho, Nagoya 464-8602, Japan

+Present address: Department of Physics and Electronics, Osaka Prefecture University, Sakai, Osaka 599-8531,

Japan

*matsuda@scphys.kyoto-u.ac.jp

When interacting electrons are confined to

low-dimensions, the electron-electron correlation effect is

enhanced dramatically, which often drives the system

into exhibiting behaviours that are otherwise highly

improbable. Superconductivity with the strongest

electron correlations is achieved in heavy-fermion

compounds, which contain a dense lattice of localized

magnetic moments interacting with a sea of conduction

electrons to form a three-dimensional (3D) Kondo

lattice1. It had remained an unanswered question

whether superconductivity would persist upon

effectively reducing the dimensionality of these materials

from three to two. Here we report on the observation of

superconductivity in such an ultimately

strongly-correlated system of heavy electrons confined

within a 2D square-lattice of Ce-atoms (2D Kondo

lattice), which was realized by fabricating epitaxial

superlattices2,3 built of alternating layers of

heavy-fermion CeCoIn5

YbCoIn5. The field-temperature phase diagram of the

superlattices exhibits highly unusual behaviours,

including a striking enhancement of the upper critical

field relative to the transition temperature. This implies

that the force holding together the superconducting

electron-pairs takes on an extremely strong coupled

nature as a result of two-dimensionalisation.

The layered heavy-fermion compound CeCoIn5 has the

highest superconducting transition temperature (Tc=2.3 K)

among rare-earth-based heavy-fermion materials4. Its

electronic properties are characterized by anomalously large

value of the linear contribution to the specific heat

(Sommerfeld coefficient ~1 J/mol K2) indicating heavy

effective masses of the 4f electrons which contribute greatly

to the Fermi surface. The tetragonal CeCoIn5 crystal

structure is built from alternating layers of CeIn3 and CoIn2

stacked along the [001] direction. This compound possesses

several key features for understanding the unconventional

superconductivity in strongly correlated systems5-7. The

superconductivity with dx2-y2 pairing symmetry8-11 which

occurs in the proximity of a magnetic instability is a

manifestation of magnetic fluctuations mediated

superconductivity5-7,12. A very strong coupling

superconductivity, where electron-pairs are bound together

, T. Shibauchi1, M. Shimozawa1, S. Yasumoto1,

4 and conventional metal

by strong forces, is revealed by a large specific heat jump4 at

Tc representing a steep drop of the entropy below Tc, and a

large superconducting energy gap needed to break the

electron-pair9. Despite its layered structure, the largely

corrugated Fermi surface13, 3D-like antiferromagnetic

fluctuations in the normal state14, and small anisotropy of

upper critical field15, all indicate that the electronic, magnetic

and superconducting properties are essentially 3D rather

than 2D. Therefore it is still unclear to which extent the 3D

nature is essential for the superconductivity of CeCoIn5.

Recently the state-of-the-art technique has been developed

to reduce the dimensionality of the heavy electrons in a

controllable fashion by the layer-by-layer epitaxial growth of

Ce-based materials. Previously a series of antiferromagnetic

superlattices CeIn3/LaIn3 have been successfully grown2, but

it remains open whether heavy electrons in a single Ce-layer

forming a 2D Kondo lattice can be superconducting. Here

we fabricate multilayers of CeCoIn5 sandwiched by

nonmagnetic and nonsuperconducting metal YbCoIn5

(Yb-ion is divalent in closed-shell 4f(14) configuration)

forming (n:m) c-axis oriented superlattice structure, where n

and m are the number of layers of CeCoIn5 and YbCoIn5 in a

unit cell, respectively. Small lattice mismatch between

CeCoIn5 and YbCoIn5 offers a possibility of providing an

ideal heterostructure. The high resolution cross-sectional

transmission-electron-microscope (TEM) results (Figs. 1a-c),

and distinct lateral satellite peaks in X-ray diffraction pattern

(Fig. 1d) demonstrate the continuous and evenly spaced

CeCoIn5 layers with no discernible interdiffusion even for

n=1 cases (see Supplementary Fig. S1 for quantitative

analysis of interdiffusion by X-ray). The epitaxial growth

of each layer with atomic flatness is shown by the streak

patterns of the reflection-high-energy-electron-diffraction

(RHEED) (Fig.1e) and atomic-force-microscopy (AFM)

image (Fig. 1f). We investigate the transport properties for

the (n:5) superlattices by varying n. The resistivity of

CeCoIn5 thin film (Fig. 2a) reproduces well that of bulk

single crystals4; Below ~100 K (T) increases upon cooling

due to the Kondo scattering, decreases after showing a peak

at around the coherence temperature Tcoh~30 K, and drops to

zero at the superconducting transition. The hump structure of

(T) at ~Tcoh is also observed in the superlattices but

becomes less pronounced with decreasing n. The

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Figure 1 | Epitaxial superlattices (n:5) of CeCoIn5(n)/YbCoIn5(5). a, High-resolution cross sectional TEM image of n=1

superlattice. The bright dot arrays are identified as the Ce layers and the less bright dots are Yb atoms, which is consistent with

the designed superlattice structure in the left panel. The intensity integrated over the horizontal width of the image plotted

against vertical position (b) indicates clear difference between the Ce and Yb layers, showing no discernible atomic

interdiffusion between the neighboring Ce and Yb layers. Upper right inset is the fast Fourier transform (FFT) of the TEM

image, which shows clear superspots along the [001] direction (c). d, Cu-K1 x-ray diffraction patterns for n=1, 2, 3, 4, 5, and 7

superlattices with typical total thickness of 300 nm show first (red arrows) and second (blue arrow) satellite peaks. The position

of the satellite peaks and their asymmetric heights can be reproduced by the step-model simulations (green lines) neglecting

interface and layer-thickness fluctuations29 (see also Supplementary Information for the detailed analysis of the satellite peak

intensity). e, Streak patterns of the RHEED image during the growth. f, Typical AFM image for n=1 superlattice. Typical

surface roughness is within 0.8 nm, comparable to one unit-cell-thickness along the c axis of CeCoIn5.

superconducting transition to zero resistance is observed in

the superlattices for n?3 (Fig. 2b). For n=2 and 1, (T)

decreases below ~1 K, but it does not reach zero. However,

when the magnetic field is applied perpendicular to the

layers for n=1, (T) increases and recovers to the value

extrapolated above 1 K at 5 T, while the reduction of (T)

below 1 K remains in the parallel field of 6 T (Fig. 2c). The

observed large and anisotropic field response of (T) is

typical for layered superconductors, demonstrating the

superconductivity even in n=1 superlattice with 2D square

lattice of Ce-atoms. The critical temperature Tc determined

by the resistive transition gradually decreases with

decreasing n (Fig. 2d). The residual resistivity 0 of the

superlattices is in the same order as 0 of single-crystalline

film (Fig. 2d) and is much lower than 0 of Yb-substituted

CeCoIn5 single crystals16. An important question is whether

the superconducting electrons in the superlattices are heavy

and if so what is their dimensionality. As displayed in Figs.

2c, 3a and 4a, the parallel and perpendicular (to the layers)

upper critical field, ???|| and ???, of the superlattices at

low temperature are significantly larger than those in

conventional superconductors with similar Tc. The magnetic

field destroys the superconductivity in two distinct ways, the

orbital pair-breaking effect (vortex formation) and Pauli

paramagnetic effect, a breaking up of pair by

spin-polarization. The zero-temperature value of the orbital

upper critical field in perpendicular field ???

the effective electron mass in the plane ???

???

superlattices from the initial slope of ??? at Tc by the

relation, ???

are comparable or in the same order of ???

bulk single crystal, providing strong evidence for the

superconducting ``heavy'' electrons in the superlattices. We

stress that even a slight deviation of the f-electron number

from unity leads to a serious reduction of the heavy electron

????0? reflects

∗, ???

????0? ∝

∗?, and is estimated to be 6, 11, 12 T for n=3, 5, and 7

????0?=0.69Tc (-d???/dT)Tc. These magnitudes

????0? (=14 T) in

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Figure 2 | Superconductivity in superlattices (n:5)

of CeCoIn5(n)/YbCoIn5(5).

dependence of electrical resistivity (T) for n=1, 2, 3, 5,

7, and 9, compared with those of 300-nm-thick

CeCoIn5 and YbCoIn5 single-crystalline thin films. b,

Low-temperature part of the same data as in a. c, (T)

for n=1 at low temperatures in magnetic field parallel

(dotted line) and perpendicular (solid lines) to the ab

plane. d, Superconducting transition temperature as a

function of n (left axis). The circles are the mid points

of the resistive transition and the bars indicate the

onset and zero-resistivity temperatures. The residual

resistivity 0 as a function of n is also shown (right

axis).

mass17. Moreover the band structure calculation for n=1

superlattice shows the number of f-electrons in each

CeCoIn5 layer is very close to unity (Supplementary

Information). These indicate that the f-electron wave

functions are essentially confined to Ce-layers. The magnetic

two-dimensionality is shown by estimating the strength of

Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, an

intersite magnetic exchange interaction between the

localized f-moments, which decays with the distance as 1/r3.

This interaction between the Ce-ions in different layers of

(n:5) superlattices reduces to less than 1/200 of that between

neighboring Ce-ions within the same layer.

The superconducting order parameters in the CeCoIn5

layers of the superlattices are expected to be coupled

weakly by the proximity effect through the normal metal

YbCoIn5 layers. The proximity induced superconductivity in

YbCoIn5 layers is expected to be very fragile and destroyed

when a weak field is applied18. If the thickness of CeCoIn5

layer is comparable to the perpendicular coherence length

(~2.1 nm for CeCoIn5) and the separation of

superconducting layers (~3.7 nm for (n:5) superlattices)

a, Temperature

Figure 3 | Superconducting anisotropy in superlattices

(n:5) of CeCoIn5(n)/YbCoIn5(5). a, Magnetic-field

dependence of the resistivity for n=3 superlattice at several

field angles from ab) to 90 deg (H//c) (10 deg step)

at T=0.1 K. b, Anisotropy of Hc2, Hc2||/Hc2, as a function of

reduced temperature T/Tc for n=3, 5, and 7 superlattices and

for the bulk CeCoIn5. c, Upper critical field Hc2() at

several temperatures as a function of field angle . Hc2 is

determined by the mid-point of the transition except for 1.0

K, where a 80% resistivity criterion has been used. The solid

blue and red lines are the fits to the 3D anisotropic mass

model represented as Hc2() = Hc2||/(sin2+2cos2)1/2 with =

Hc2||/Hc2and Tinkham's formula | Hc2() cos/ Hc2|+{Hc2()

sin/ Hc2||}2=1 for a 2D superconductor, respectively19.

exceeds , each CeCoIn5 layer acts as a 2D

superconductor19. This 2D feature is revealed by diverging

Hc2||/Hc2 of n=3, 5 and 7 superlattices with approaching Tc

(Fig. 3b) in sharp contrast to bulk CeCoIn5

cusp-like angular dependence Hc2() near parallel field for

n=3 superlattice (Fig. 3c), which is qualitatively different

from that expected in the 3D anisotropic-mass-model but is

well fitted by the model in 2D limit19. Based on the above

2D features observed in all electronic, magnetic and

superconducting properties, we conclude that the observed

heavy-electron superconductivity is mediated most likely by

2D electron correlation effects. A fascinating issue is how the

two-dimensionalisation changes the pairing nature. The fact

that ???

well exceeds the actual ??? at low temperatures indicates

the predominant Pauli paramagnetic pair-breaking effect

even in perpendicular field. Therefore Hc2 at low

temperatures is dominated by the Pauli effect in any field

directions. This is reinforced by the result that the cusplike

behaviour of Hc2 becomes less pronounced well below Tc

(Fig. 3c), which is the opposite trend to Hc2 behaviour of

the conventional multilayer systems21. In fact

Pauli-limited upper critical field ???

???

20, and by a

???(0) estimated from the initial slope of Hc2(T) at Tc

??????given by

?????√2g

where g is the gyromagnetic ratio determined by the Ce

crystalline electric field levels, varies smoothly with field

direction, consistent with Hc2 of the present superlattices

at low temperatures. Figure 4a displays the H-T phase

diagram of the superlattices. What is remarkable is that with

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Figure 4 | Superconducting phase diagrams of superlattices (n:5) of CeCoIn5(n)/YbCoIn5(5). a, Magnetic field vs.

temperature phase diagram of n=3, 5, and 7 superlattices in magnetic field parallel (open symbols) and perpendicular (closed

symbols) to the ab plane compared with the bulk CeCoIn5 data. The mid-point of the transition in the (T) (circles) and (H)

(squares) has been used to evaluate Hc2(T). b, Superconducting transition temperature, Tc (open triangles), the reduced critical

fields Hc2/Tc in parallel (filled blue circles) and perpendicular (filled red squares) fields as a function of dimensionality

parameter 1/n (right panel). The pressure dependence of these quantities28 is also shown for comparison (left panel).

decreasing n, Tc decreases rapidly from the bulk value, while

Hc2 does not exhibit such a reduction for both field directions.

In fact, at low temperatures, Hc2|| of n=5 and 7 is even larger

than that of the bulk. This robustness of Hc2 (and hence of

against n-reduction indicates that the superconducting

pairing-interaction is hardly affected by

two-dimensionalisation. This provides strong evidence that

the superconductivity in bulk CeCoIn5 is mainly mediated

by 2D spin-fluctuations, although neutron spin resonance

mode is observed at 3D () position below Tc

In sharp contrast to Hc2, the thickness reduction

dramatically enhances Hc2/Tc from the bulk value (Fig. 4b).

A comparison with the pressure dependence results22, which

represent the increased three dimensionality, reveals a Tc

dome and a general trend of enhanced Hc2/Tc with reduced

dimensionality. Through the relation of Eq. (1), this trend

immediately implies a remarkable enhancement of /Tc by

two-dimensionalisation. We note that the enhanced impurity

scattering cannot be primary origins of the Tc reduction, as

these effects do not significantly enhance the /Tc ratio in

d-wave superconductors23. This is supported by no

discernible interdiffusion by TEM results and 0 of

superlattices in the same order as 0 of the bulk CeCoIn5.

The reduction of Tc may be caused by the reduction of

density-of-states (DOS) in the superlattices, but this scenario

is also unlikely because the DOS reduction usually reduces

the pairing interaction, which results in the reduction of

Using the reported value of 2/kBTc=6 in the bulk single

crystal9, 2/kBTc for the n=5 superlattice is estimated to

exceed 10, which is significantly enhanced from the

weak-coupling BCS value of 2/kBTc=3.54. It has been

suggested theoretically that d-wave pairing mediated by

10.

antiferromagnetic fluctuations in two-dimension can be

much stronger than that in three-dimension24-26. The striking

enhancement of 2/kBTc associated with the reduction of Tc,

a situation resemblant to underdoped high-Tc cuprates,

implies that there appear to be additional mechanisms, such

as 2D phase-fluctuations27 and strong pair-breaking effect

due to inelastic scattering28. Further investigation,

particularly probing electronic and magnetic excitations in

the normal and superconducting states, is likely to bridge the

physics of highly unusual correlated electrons in the 2D

Kondo lattice and in the 2D CuO2 planes of cuprates. The

fabrication in a wide variety of nanometric superlattices also

opens up a possibility of nanomanipulation of

heavy-electrons, providing a unique opportunity to produce

a novel superconducting system and its interface.

Method. CeCoIn5/YbCoIn5 superlattices are grown by

the molecular-beam-epitaxy (MBE) technique. The pressure

of the MBE chamber was kept at 10-7 Pa during the

deposition. (001) surface of MgF2 with rutile structure

(a=0.462 nm, c=0.305 nm) was used as a substrate. The

substrate temperature was kept at 550˚C during the

deposition. Atomic-layer-by-layer MBE provides for

digital control of layer thickness, which we measure by

counting the number of unit cells2. Each metal element was

evaporated from individually controlled Knudsen-cells.

15-unit-cell-thick (uct) YbCoIn5 was grown after CeIn3 (28

nm) was grown on the (001) surface of substrate MgF2 as a

buffer layer. Then n-uct CeCoIn5 layers and m-uct YbCoIn5

(typically m=5) were grown alternately, typically repeated

for 30-60 times. The deposition rate was monitored by a

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quartz oscillating monitor and the typical deposition rate was

0.01-0.02 nm/s.

Acknowledgments. We acknowledge discussions with R.

Arita, A.V. Chubukov, M. J. Graf, P.A. Lee, N.P. Ong, S.A.

Kivelson, T. Takimoto, and I. Vekhter. This work was

supported by KAKENHI from JSPS and MEXT and by

Grant-in-Aid for the Global COE program ``The Next

Generation of Physics, Spun from Universality and

Emergence" from MEXT.

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SUPPLEMENTARY INFORMATION

Extremely Strong Coupling Superconductivity in Artificial

Two-dimensional Kondo Lattices

X-ray diffraction (XRD) analysis

Figure S1 shows the XRD satellite peak near the (004) peak for (1:5)

superlattice and the results of our simulation with various interdiffusion ratio. The

intensity I is calculated from the Laue function G and crystal structure factor F:

I = |F|2G.

The crystal structure factor of the superlattice can be described as

FF

where FCe and FYb are the crystal structure factors of CeCoIn5 and YbCoIn5,

respectively. To estimate the Ce/Yb interdiffusion quantitatively, we assume that the

interdiffuion occurs only at the CeCoIn5/YbCoIn5 interface layers (diffusion ratio p),

ignoring the interdiffusion in the next layers. (The step model used in Fig. 1c

corresponds to p=0.) Then FCe and FYb of the superlattice (1:5) having l unit blocks

perpendicular to the film plane are given by

) 1 (exp)2 exp(2

YbYb CeCeInIn

zpczcpiqff

,

YbCe

F

1 (

) 1 () 1 () exp

)1 (exp)1 (

YbYb CeCe

YbCeCoYbCeCe

z pczcp

pc

cpiqf pffpF

1 (

1

1

1

1

1

)1 (

2

)1 (

2

exp

22

exp)2exp(2

22

exp

22

2

4

2

2exp)exp

YbYbCeCe YbYbCeCeInIn

YbCeCoYbCe

YbCeYbCeYb

zc

p

zc

p

zc

p

zc

p

iqff

c

p

c

p

iqff

p

f

p

c

p

c

p

iqpffpF

,1exp)exp()exp(2)exp(

22

12exp

3

1

YbYbYbInInYbCoYb

j

YbCe

zziqc

ffiqc

ff

c

p

jc

p

iq

where

sin2

q

.

Here is the wave length of the X-ray, is the diffraction angle, fCe, fYb, fCo and fIn are

the atomic form factors for Ce, Yb, Co and In, respectively, and cCe, cYb are the c-axis

lattice constants of CeCoIn5 and YbCoIn5, respectively. In the equation of FYb, 1st , 2nd

and 3rd lines correspond to the YbCoIn5 layers at the interfaces (2nd and 6th layers of the

(1:5) superlattice) involving Ce/La interdiffusion with a ratio p/2, 4th and 5th lines

correspond to 3 pure YbCoIn5 layers. The Laue function G for the superlattice (n:m)

having l unit blocks is written as

Page 7

7

2

sin

sin

YbCe

YbCe

mcncq

mc ncql

G

.

To compare with the XRD data, we further use the Gaussian distribution function for

calculating I(2) to account for the instrumental resolution of 0.18 deg. The height of

the satellite peaks normalized by the main (004) peak can be reproduced well by

assuming no interdiffusion between Ce and Yb atoms near the interfaces (p=0). A 10 %

interdiffusion makes the peak height discernibly lower.

Combining the TEM, and XRD analyses, we conclude that the superlattice

structures are realized in an epitaxial form without noticeable interdiffusions.

Supplementary Figure S1. XRD satellite peaks (black dots) around (004) main peak in

the (1:5) superlattice with 60 unit blocks. The satellite peaks are compared with our

simulations assuming that 0 (red solid line), 10 (orange), 20 (green) and 30 % (blue) of

Ce atoms at the interfaces are replaced with Yb. We used c-axis lattice constants of

0.75513 nm for CeCoIn5 and 0.7433 nm for YbCoIn5.

Electronic band structure of the superlattice

We investigate the electronic band structure in the (1:5) superlattice based on the ab

initio density functional theory. The band structure calculations for LnCoIn5 (Ln=Ce, La,

and Yb) and for the superlattice have been performed by using the relativistic

full-potential (linearized) augmented plane-wave (FLAPW) + local orbitals method as

implemented in the WIEN2k packageS1. The crystallographical parameters used in the

calculations are summarized in Table S1.

Figures S2(a)-(h) display the energy dispersion, Ek, along the high-symmetry line. In

the Yb case, the almost dispersion-less bands between 0 and -2 eV come from the 4f

electrons, which do not cross the Fermi level (Fig. S2(c)). This indicates that the 4f

electrons do not participate in the conduction, which is consistent with the absence of

Kondo behavior in the transport properties in YbCoIn5. In contrast, the 4f bands extend

to the Fermi level in the Ce case (Fig. S2(a)), in which the Kondo effect is clearly

observed. This difference between Yb and Ce is reinforced by the calculations of partial

Page 8

8

charges in the atomic spheres (Table S2). In the case of Ce, the number of 4f electrons

inside the Muffin-tin sphere is estimated as 0.95 in the FLAPW calculations. This

number is very close to exact unity, as we expect some protrusion (~5%) outside the

sphere. In YbCoIn5, we should also consider that the obtained number of 13.45 for f

electrons is actually close to 14, which is in the closed-shell configuration. (In fact we

verified this fact by an additional calculation of the 4f open-core treatment.) In the

superlattice, we found that these occupation numbers of f orbitals in each layer are

essentially unchanged from the parent materials. This indicates that mobile 4f electrons

are confined only in the Ce layers.

Figures S3(a)-(d) depict the partial density of states (DOS), whose values at the

Fermi level are reported in Table S2. The DOS at the Fermi level in the superlattice is

nearly equal to the total of the DOS in the parent materials, 26.83 ? 8.70 ? 5 ? 70.33

(mJ/mol K2). In addition, the partial DOS of Ce component is also comparable to that in

CeCoIn5.

In Figs. S4(a)-(d), we show the Fermi surface colored by the Fermi velocity,

vkF=|(vx

smaller Fermi velocity, and then larger weight of Ce(4f) component. The Fermi surface

of the superlattice (Fig. S4(d)) is much more two-dimensional than the 3D structure in

the parent materials, which is mostly due to the folding along the c-axis. We note that

the cylindrical bands near the zone center ( point) are hole-like Fermi surface whilst

the bands near the zone corner (M point) are electron-like (see the band dispersions in

Fig. S2(h)). This shape of these sheets suggests a good nesting between these bands,

which would enhance the susceptibility at a Q-vector of (). It is tempting to

suggest that such 2D antiferromagnetic fluctuations are responsible for the observed

strong-coupling 2D superconductivity in the superlattices, which deserves further

studies.

Supplementary Table S1 | All materials studied here have the space group No.123

P4/mmm. Lattice constants in the superlattice CeCoIn5(1)/YbCoIn5(5) are determined

by a=(aCeCoIn5+5aYbCoIn5)/6 and c=cCeCoIn5+5cYbCoIn5, and we keep the relative atomic

positions (Wyckoff positions) in each layer the same as those in the parent materials.

a (Å) c (Å)

CeCoIn5 (S2) 4.612 7.549

LaCoIn5 (S3) 4.634 7.615

YbCoIn5 (S4) 4.559 7.433

(1:5) superlattice 4.568 44.714

Supplementary Table S2 | Occupation number of d and f orbitals inside the Muffin-tin

spheres of Ln and Co atoms and the DOS at the Fermi level. Occupation number in the

superlattice is described as Ce/Yb. Five Yb atoms have almost the same occupation

number. In the last column, values in the parentheses represent the partial DOS of Ce

components.

Ln(f) Ln(d)

CeCoIn5 0.950 0.718

LaCoIn5 0.081 0.646

YbCoIn5 13.45 0.456

(1:5)

superlattice

kF ,vy

kF ,vz

kF)| , where vi

kF = 1/ħ(dEkF/dki

F). The blue parts of Fermi surface have

Wyckoff position z of In(2)

0.305

0.311

0.305

---

Co(d)

7.54

7.55

7.58

7.59

DOS(mJ/mol K2)

26.83 (14.5)

6.81

8.70

69.36 (13.4) 0.986 / 13.48 0.712 / 0.456

Page 9

9

Supplementary Figure S2 | Energy band dispersion along the high-symmetry line in

CeCoIn5 (a), LaCoIn5 (b), YbCoIn5 (c), and the (1:5) superlattice (d). The Fermi level is

indicated by the green line. Lower panels (e-h) are the enlarged figures near the Fermi

level.

Supplementary Figure S3 | DOS in the unit of eV. The partial DOS of Ln ions is

indicated by green dashed lines.

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10

Supplementary Figure S4 | The Fermi surfaces colored by magnitude of the Fermi

velocity. The unit is 106 (m/sec).

SUPPLEMENTARY REFERENCES

S1. Blaha, P., Schwarz, K., Madsen, G. K. H., Kvasnicka, D. & Luitz, J., WIEN2k, An

Augmented Phane Wave + Local Orbitals Program for Calculating Crystal Properties

(Karlheinz Schwarz, Techn. Universitat Wien, Austria, 2001).

S2. Settai, R., J. Phys.: Condens. Matter 13, L627 (2001).

S3. Macaluso, R. T., J. Solid State Chem. 166, 245 (2002).

S4. Zaremba, V. I., Z Anorg. Allg. Chem. 629, 1157 (2003).

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- Available from Hiroaki Ikeda · May 23, 2014
- Available from arxiv.org