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


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 Kondo lattice1. It had remained an unanswered question whether superconductivity would persist on 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 two-dimensional square lattice of Ce atoms (two-dimensional Kondo lattice), which was realized by fabricating epitaxial superlattices2,3 built of alternating layers of heavy-fermion CeCoIn5 (ref. 4) and conventional metal 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-dimensionalization.


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 an anomalously large value of the linear contribution to the specific heat (Sommerfeld coefficient γ1 J mol−1 K−2), 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 systems5,6,7. The superconductivity with d x 2 y 2 pairing symmetry8,9,10,11 which occurs in the proximity of a magnetic instability is a manifestation of magnetic-fluctuation-mediated superconductivity5,6,7,12. A very strong coupling superconductivity, where electron pairs are bound together 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 Δ needed to break the electron pair9. Despite its layered structure, the largely corrugated Fermi surface13, three-dimensional-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 three dimensional rather than two dimensional. Therefore, it is still unclear to what extent the three-dimensional nature is essential for the superconductivity of CeCoIn5.

Recently, a state-of-the-art technique has been developed to reduce the dimensionality of the heavy electrons in a controllable fashion by layer-by-layer epitaxial growth of Ce-based materials. Previously, a series of antiferromagnetic superlattices CeIn3/LaIn3 were successfully grown2, but it remains open whether heavy electrons in a single Ce layer forming a two-dimensional Kondo lattice can be superconducting. Here we fabricate multilayers of CeCoIn5 sandwiched by non-magnetic and non-superconducting metal YbCoIn5(the Yb ion is divalent in closed-shell 4f(14)configuration) forming an (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 (Fig. 1a–c), and distinct lateral satellite peaks in the 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 (Fig. 1e) and atomic force microscopy images (Fig. 1f).

Figure 1: Epitaxial superlattices (n:5) of CeCoIn5(n)/YbCoIn5(5).
figure 1

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. b, The intensity integrated over the horizontal width of the image plotted against vertical position indicates a clear difference between the Ce and Yb layers, showing no discernible atomic interdiffusion between the neighbouring Ce and Yb layers. a (upper right inset), c, The fast Fourier transform (FFT) of the TEM image, which shows clear superspots along the [001] direction (c). d, Cu Kα1 X-ray diffraction patterns for n=1, 2, 3, 4, 5 and 7 superlattices with a typical total thickness of 300 nm show first (red arrows) and second (blue arrow) satellite peaks. The positions of the satellite peaks and their asymmetric heights can be reproduced by the step-model simulations (green lines) ignoring interface and layer-thickness fluctuations29 (see also Supplementary Information for the detailed analysis of the satellite peak intensity). e, Streak patterns of the reflection high-energy electron diffraction image during the growth. f, Typical atomic force microscopy image for n=1 superlattice. The typical surface roughness is within 0.8 nm, comparable to one unit-cell thickness (uct) along the c axis of CeCoIn5.

We investigate the transport properties for the (n:5) superlattices by varying n. The resistivity ρ(T) of the CeCoIn5 thin film (Fig. 2a) reproduces well that of bulk single crystals4. Below 100 K, ρ(T) increases on cooling owing to the Kondo scattering, decreases after showing a peak at around the coherence temperature Tcoh30 K and drops to zero at the superconducting transition. The hump structure of ρ(T) at Tcoh is also observed in the superlattices but becomes less pronounced with decreasing n. The superconducting transition to zero resistance is observed in the superlattices for n≥3 (Fig. 2b). For n=2 and 1, ρ(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, ρ(T) increases and recovers to the value extrapolated above 1 K at 5 T, whereas the reduction of ρ(T) below 1 K remains in the parallel field of 6 T (Fig. 2c). The observed large and anisotropic field response of ρ(T) is typical for layered superconductors, demonstrating superconductivity even in the n=1 superlattice with a two-dimensional square lattice of Ce atoms. The critical temperature Tc determined by the resistive transition gradually decreases with decreasing n (Fig. 2d). The residual resistivity ρ0 of the superlattices is of the same order as ρ0 of single-crystalline film (Fig. 2d) and is much lower than ρ0 of Yb-substituted CeCoIn5 single crystals16.

Figure 2: Superconductivity in superlattices (n:5) of CeCoIn5(n)/YbCoIn5(5).
figure 2

a, Temperature dependence of electrical resistivity ρ(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, ρ(T) for n=1 at low temperatures in magnetic field parallel (dotted line) and perpendicular (solid lines) to the a b 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 ρ0 as a function of n is also shown (right axis).

An important question is whether the superconducting electrons in the superlattices are heavy and if so what their dimensionality is. As shown in Figs 2c, 3a and 4a, the parallel and perpendicular (to the layers) upper critical fields, Hc2 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 the Pauli paramagnetic effect, a breaking up of pairs by spin polarization. The zero-temperature value of the orbital upper critical field in perpendicular field reflects the effective electron mass in the plane ma b*, , and is estimated to be 6, 11 and 12 T for n=3, 5 and 7 superlattices from the initial slope of at Tc by the relation . These magnitudes are comparable with or of the same order as (=14 T) in 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 mass17. Moreover, the band-structure calculation for the n=1superlattice shows that the number of f-electrons in each CeCoIn5 layer is very close to unity (Supplementary Information). These facts indicate that the f-electron wavefunctions are essentially confined to Ce layers. The magnetic two-dimensionality is shown by estimating the strength of the Ruderman–Kittel–Kasuya–Yosida 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 (4.568/44.716)31×10−3 of that between neighbouring Ce ions within the same layer (see Supplementary Table S1).

Figure 3: Superconducting anisotropy in superlattices (n:5) of CeCoIn5(n)/YbCoIn5(5).
figure 3

a, Magnetic-field dependence of resistivity for n=3 superlattice at several field angles from to 90° (Ha) (10° step) at T=0.15 K. b, Anisotropy of 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(θ) at several temperatures as a function of field angle θ. Hc2 is determined by the mid-point of the transition except for 1.0 K, where an 80% resistivity criterion has been used. The solid blue and red lines are the fits to the three-dimensional anisotropic mass model represented as Hc2(θ)=Hc2/(sin2θ+γ2cos2θ)1/2 with and Tinkham’s formula for a two-dimensional superconductor, respectively19.

Figure 4: Superconducting phase diagrams of superlattices (n:5) of CeCoIn5(n)/YbCoIn5(5).
figure 4

a, Magnetic-field versus temperature phase diagram of n=3, 5 and 7 superlattices in magnetic field parallel (open symbols) and perpendicular (closed symbols) to the a b plane, compared to the bulk CeCoIn5 data. The mid-point of the transition in ρ(T) (circles) and ρ(H)(squares) has been used to evaluate Hc2(T). b, Superconducting transition temperature, Tc (open triangles), and 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). Note the different scales for parallel (blue) and perpendicular (red) fields.

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 the 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) exceeds , each CeCoIn5 layer acts as a two-dimensional superconductor19. This two-dimensional feature is revealed by the diverging of n=3, 5 and 7 superlattices on approaching Tc (Fig. 3b), in sharp contrast to bulk CeCoIn5 (ref. 20), and by a cusplike angular dependence Hc2(θ) near parallel field for the n=3 superlattice (Fig. 3c), which is qualitatively different from that expected in the three-dimensional anisotropic-mass model but is well fitted by the model in the two-dimensional limit19. On the basis of the above two-dimensional features observed in all electronic, magnetic and superconducting properties, we conclude that the observed heavy-electron superconductivity is mediated most probably by two-dimensional electron-correlation effects.

A fascinating issue is how the two-dimensionalization changes the pairing nature. The fact that estimated from the initial slope of at Tc well exceeds the actual value at low temperatures indicates the predominant Pauli paramagnetic pair-breaking effect even in perpendicular field. Therefore, Hc2(θ) at low temperatures is dominated by the Pauli effect in any field direction. This is reinforced by the result that the cusplike behaviour of Hc2(θ)becomes less pronounced well below Tc (Fig. 3c), which is the opposite trend to the Hc2(θ) behaviour of conventional multilayer systems21. In fact, the Pauli-limited upper critical field Hc2Pauli given by

where g is the gyromagnetic ratio determined by the Ce crystalline electric field levels, varies smoothly with field direction, consistent with Hc2(θ) of the present superlattices at low temperatures. Figure 4a shows the HT phase diagram of the superlattices. What is remarkable is that, with decreasing n, Tc decreases rapidly from the bulk value, whereas 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 Δ) against n reduction indicates that the superconducting pairing interaction is hardly affected by two-dimensionalization. This provides strong evidence that the superconductivity in bulk CeCoIn5 is mainly mediated by two-dimensional spin-fluctuations as in the superlattices with two-dimensional magnetic structure, although the neutron spin resonance mode in bulk CeCoIn5 is observed in the three-dimensional (π,π,π) position below Tc (ref. 10).

In sharp contrast to Hc2, the thickness reduction dramatically enhances Hc2/Tc from the bulk value (Fig. 4b). A comparison to the pressure-dependence results22, which represent the increased three-dimensionality, reveals a Tcdome and a general trend of enhanced Hc2/Tc with reduced dimensionality. Through the relation of equation (1), this trend immediately implies a remarkable enhancement of Δ/Tc by two-dimensionalization. (As the anisotropy of Hc2 at low temperatures does not depend on n, as shown in Fig. 3b, we assume that the g-value of the superlattices deviates little from the bulk value.) We note that the enhanced impurity scatterings cannot be primary origins of the Tc reduction, as these effects do not significantly enhance the Δ/Tc ratio in d-wave superconductors23. This is supported by no discernible interdiffusion by TEM results and a ρ0of superlattices of the same order as ρ0 of the bulk CeCoIn5. The reduction of Tc may be caused by the reduction of density of states in the superlattices, but this scenario is also unlikely because the density-of-states reduction usually reduces the pairing interaction, which results in the reduction of Δ.

Using the reported value of 2Δ/kBTc=6 in the bulk single crystal9, 2Δ/kBTc for the n=5 superlattice is estimated to exceed 10, which is significantly enhanced from the weak-couplingBardeen–Cooper–Schrieffer value of 2Δ/kBTc=3.54. It has been suggested theoretically that d-wave pairing mediated by antiferromagnetic fluctuations in two dimensions can be much stronger than that in three dimensions24,25,26. The striking enhancement of 2Δ/kBTcassociated with the reduction of Tc, a situation resembling that of underdoped high- Tc cuprates, implies that there seem to be further mechanisms, such as two-dimensional phase fluctuations27 and a 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 two-dimensional Kondo lattice and in the two-dimensional 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 new superconducting system and its interface.

Methods summary

CeCoIn5/YbCoIn5 superlattices are grown by the molecular beam epitaxy technique. The pressure of the molecular beam epitaxy chamber was kept at 10−7 Pa during the deposition. The (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 molecular beam epitaxy 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 30–60 times. The deposition rate was monitored by a quartz oscillating monitor and the typical deposition rate was 0.01–0.02 nm s−1.


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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 the Japan Society for the Promotion of Science and the Ministry of Education, Culture, Sports, Science and Technology (MEXT) and by a Grant-in-Aid for the Global COE program ‘The Next Generation of Physics, Spun from Universality and Emergence’ from MEXT.

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The first two authors contributed equally to this work. Y. Matsuda and T.S. planned the experiments, analysed the data and wrote the paper. Y. Mizukami, H.S. and T.T. fabricated the superlattices. M.S., S.Y., D.W. and M.Y. contributed to the measurements. H.I. carried out the band-structure calculation and H.K. analysed the data. All authors critically reviewed the paper.

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Correspondence to Y. Matsuda.

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Mizukami, Y., Shishido, H., Shibauchi, T. et al. Extremely strong-coupling superconductivity in artificial two-dimensional Kondo lattices. Nature Phys 7, 849–853 (2011).

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