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Slicing a Kondo Lattice: The Quest for Exotic Superconductivity in Artificially Engineered Heavy Fer
YUJI MATSUDA
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Slicing a Kondo Lattice: The Quest for Exotic Superconductivity
in Artificially Engineered Heavy Fermion Superlattices

YUJI MATSUDA
DEPARTMENT OF PHYSICS, KYOTO UNIVERSITY

ABSTRACT

Realizing new classes of ground states continues to be at the forefront of condensed matter physics. In rare earth based intermetallic compounds with f electrons —usually called "heavy-fermion" compounds— electron masses are strikingly enhanced due to the electron correlations, and a metallic state with the strongest electron correlation can be achieved. The unconventional superconductivity in heavy fermion compounds has been one of the most fascinating phenomena in condensed matter physics. All of the heavy fermion compounds discovered, until now, have essentially a three dimensional electronic structure. Recently, a state-of-the-art molecular beam epitaxy technique was developed to fabricate superlattices comprised of alternating layers of a heavy fermion compound and conventional metals. In such "Kondo superlattices", two-dimensional confinement of heavy fermions becomes possible. The Kondo superlattices provide a new playground for exploring exotic superconducting states that have not been realized in bulk crystals.

INTRODUCTION

In conventional metals, electrons move freely in a three dimensional (3D) crystal structure. There are two interesting systems that have provided new physical phenomena and new functions, which cannot be realized in conventional systems. First is a 2D system, in which two dimensionalization enhances the quantum effect. Second system is found in strongly correlated electron systems, in which the electrons interact extremely strongly due to the strong Coulomb repulsion, and they move collectively rather than independently. In many exotic superconductors of contemporary interest, superconductivity occurs in the 2D layers. In cuprates, high-Tc superconductivity occurs in the 2D CuO2 plane. In iron pnictides, high-Tc superconductivity occurs in the 2D square lattice of Fe atoms. In these systems, it is generally accepted that the electron correlation effect is important for superconductivity. In fact, in layered 2D metals, interactions decay more slowly and hence are stronger. Consequently, electron correlations are enhanced. At the same time, fluctuations are enhanced and, as a result, the magnetic orders are strongly suppressed.

In ƒ-electron systems such as Ce and U compounds, ƒ-electrons are localized at high temperatures. With decreasing temperature, ƒ-electrons are hybridized with conduction electrons forming the Kondo singlets (Kondo cloud), as illustrated in Fig. 1. At low temperatures, ƒ-electrons become itinerant, forming a narrow band. Within this band, electron masses are strongly enhanced due to the strong electron correlations, sometimes up to nearly 1000 times larger than the free electron mass in Ce systems. Until now, quite a few heavy fermion compounds have been discovered, but these systems essentially have a 3D electronic structure. Given that 2D systems have been shown to display exotic properties, such as enhanced correlation and fluctuations, then the question arises: "Can we reduce the dimensionality of heavy fermion systems?" In this case, new correlated electron systems are expected. This is the subject of our research [1].

Recently, advances in thin-film growth technology have led to the fabrication of artificial 2D structures with controlled atomic-layer thicknesses, providing a unique opportunity to explore novel phenomena in low-dimensional systems with unprecedented control. This approach can produce a novel type of electronic state in 2D heavy fermion systems.

Molecular beam epitaxy

For the epitaxial growth of Ce compounds, we used a state-of-the-art molecular beam epitaxy (MBE) technique, as illustrated in Fig. 2. For Ce deposition, special requirements are necessary. We need an ultrahigh vacuum (~10-9 Pa), high temperature cells that can be heated up to 1400 C, and no active crucibles. We can evaporate four elements simultaneously. The advantage of MBE is that very slow crystal growth, typically 1 nm per minute, is possible. Moreover, by using reflection high energy electron diffraction, we can monitor the surface of the film during the crystal growth. After the growth, the films and superlattices are transferred to a scanning tunneling microscope (STM) chamber, while keeping an ultrahigh vacuum, and in-situ STM observation is performed on the surfaces.

 



Fig. 1: Kondo effect.

Since the crystal growth can be controlled at an atomic layer level, the films are particularly suitable for the STM measurements that require an atomically flat surface. Another important advantage is that since the epitaxial growth occurs in a non-equilibrium condition at temperatures much lower than the temperature used for single crystal growth by a flux method, MBE is suitable for the preparation of systems with homogeneously distributed impurity atoms [2]. This is particularly important in heavy fermion compounds, in which several orders often compete and coexist. Furthermore, owing to the ability to evaporate several atoms simultaneously, the concentration of each element can be controlled precisely.

Two-dimensional confinement of heavy fermions in Kondo superlattices

MBE enables us to produce systems that do not exist in nature. By growing different compounds alternatively, we can fabricate artificial superlattices. If a Ce-compound with an ƒ-electron and a different compound with no ƒ-electrons are evaporated alternatively, artificially engineered heavy fermion superlattices are fabricated. In such superlattices, heavy fermions may be confined within 2D layers. In other words, "Kondo superlattices" are produced [1].

 



Fig. 2: Schematics of combined MBE-STM.



Fig. 3: TEM image of CeIn3(1)/LaIn3(3) superlattice.

The first 2D confinement of heavy fermions has been achieved in Kondo superlattices with alternating layers of antiferromagnetic heavy fermion compound CeIn3 and the conventional metal LaIn3 with no magnetic f electrons grown by MBE on MgF2 substrate [3]. Fig. 3 displays the high resolution cross sectional transmission electron microscope (TEM) image of the superlattice with 1 unit cell thick (UCT) CeIn3 sandwiched between 3 UCT LaIn3. The white bright spots represents the lineup of Ce atoms. In these superlattices, the magnetic order is suppressed by reducing the thickness of the CeIn3 layers. The 2D confinement of heavy fermion also leads to the enhancement of the effective mass and the striking deviation from conventional metallic behavior (non-Fermi liquid behavior), which is associated with the dimensional tuning of the quantum fluctuations.

Heavy fermion CeCoIn5



Fig. 4: Crystal structure of CeCoIn5 and STM topographic image of thin film grown by MBE.

Recently, the superlattices consisting of heavy fermion compound CeCoIn5 have been extensively studied. The crystal structure of CeCoIn5 is illustrated in Fig. 4. CeCoIn5 exhibits superconductivity at 2.3 K, which is the highest transition temperature among the Ce-based heavy fermion systems. CeCoIn5 has attracted extensive interest because of its anomalous normal state transport and superconducting properties, such as non-Fermi liquid behavior, superconductivity in the vicinity of magnetic instability and dx2-y2 wave superconducting pairing symmetry, strong Pauli paramagnetic effect, possible exotic pairing state in a strong magnetic field, and the unusual coexistence of superconductivity and magnetic order. CoCoIn5 shares many of the characteristics of high-Tc cuprates.

 



Fig. 5: TEM image of CeCoIn5(1)/YbCoIn5(5) superlattice.

We fabricate the c axis oriented thin film by MBE on a MgF2 substrate. The residual resistivity of this thin film is comparable to that of high quality bulk single crystals. The resistivity shows T-linear dependence in the normal state, which is a hallmark of non-Fermi liquids, and nuclear quadrupole resonance spectra and nuclear magnetic resonance relaxation rate are essentially unchanged from high quality bulk single crystals. Fig. 4 displays the STM topographic image of a CeCoIn5 thin film [4]. These CeCoIn5 films have very wide, atomically flat terraces. The spatially periodic spots forming the square lattice represents In(1) atoms in CeIn plane and the large bright spots are defects at In(1) sites.

Superconductivity of one unit-cell-thick heavy fermion compound

We fabricated superlattices with alternating layers of c axis oriented CeCoIn5 and YbCoIn5 [5]. Yb is divalent and has a closed 4ƒ shell in YbCoIn5. YbCoIn5 is a conventional nonmagnetic metal. In this superlattice, the CeCoIn5 block layers (BLs) are magnetically decoupled.

This is because in the presence of 5 UCT YbCoIn5 spacers between CeCoIn5, the magnetic interaction (the so-called RKKY interaction) between the adjacent block layers is as small as 0.1 % of that between the neighboring Ce atoms in the same layer.

Fig. 5 displays the high resolution cross sectional TEM image of a superlattice with 1 UCT CeCoIn5 sandwiched between 5 UCT YbCoIn5. The white bright spots represent the lineup of Ce atoms. The integrated intensity of the TEM image clearly picks out CeCoIn5 layers with 1 UCT. Thus a 2D Kondo lattice consisting of a 2D square lattice of Ce atoms is fabricated.

 



Fig. 6: Resistivity of CeCoIn5(n)/YbCoIn5(5) superlattices.

Fig. 6 depicts the temperature dependence of the resistivity of superlattices with alternating layers of n UCT CeCoIn5 and 5 UCT YbCoIn5 [5]. Sharp superconducting transitions with zero resistivity can be seen for all systems down to n=3. By contrast, for n=2 and 1, resistivity decreases below ~1 K but does not reach zero at the lowest temperature of our measurement. However, when the magnetic field is applied perpendicular to the layers for n=1, resistivity increases and recovers to the value extrapolated above 1 K at 5 T, whereas the reduction of resistivity below 1 K remains in the parallel field of 6 T. Such large and anisotropic field response of resistivity is typical for layered superconductors, demonstrating superconductivity in 1 UCT CeCoIn5.

Important questions are whether the superconducting electrons in the superlattices are heavy and, if so, what their dimensionality is. To answer these questions, we focus on the measurements of the upper critical field (Hc2) in CeCoIn5/YbCoIn5 superlattices. The upper critical field near Tc in perpendicular field is determined by the effective mass. The initial slope of the upper critical field near Tc of the superlattices are comparable to the value for the bulk, indicating that the electrons in the superlattices are really heavy. Moreover, the ratio of Hc2 of parallel to perpendicular fields diverges with approaching Tc. This indicates the quenching of the orbital motion of superconducting electrons perpendicular to the layers, which is a typical behavior of 2D superconductivity. These measurements provide direct evidence that heavy ƒ-electrons form Cooper pairs in the superlattices.

The superconducting order parameters of the CeCoIn5 BLs are expected to be weakly coupled to each other by the proximity effect through the normal-metal YbCoIn5 BLs. However, the proximity effect is negligible because the large Fermi velocity mismatch across the interface between CeCoIn5 and YbCoIn5 BLs leads to the huge suppression of the transmission probability of electron currents. CeCoIn5 BL with atomic layer thickness is comparable to or less than the perpendicular coherence length (size of Cooper pair) ~3-4 nm for CeCoIn5; each CeCoIn5 BL effectively acts as a 2D superconductor. On the basis of these results, we conclude that 2D heavy fermion superconductivity is realized in CeCoIn5(n)/YbCoIn5(5) superlattices with n = 3, 5, and 7.

Inversion symmetry breaking

Spin-orbit interaction is an interaction of an electron's spin with its motion, which entangles the spin and orbital degrees of freedom of the electrons. Recently, spin-orbit interaction has aroused great interest when the mirror symmetry is violated with respect to the lattice plane. This is because such an inversion symmetry breaking (ISB) can dramatically affect the electronic properties, giving rise to a number of novel phenomena in various fields of contemporary condensed matter physics, such as spintronics, topological matter, and exotic superconductivity. In superconductors, the inversion symmetry imposes an important constraint on the pairing states. In the presence of inversion symmetry, Cooper pairs are classified into spin-singlet and triplet states. On the other hand, in the absence of inversion symmetry, an asymmetric potential gradient yields a spin-orbit interaction that gives rise to a parity-violated superconductivity, which exhibits unique properties such as the admixture of spin-singlet and triplet states, unusual paramagnetic and electromagnetic response, and topological superconducting states. For instance, asymmetry of the potential in the direction perpendicular to the 2D plane induces the so-called Rashba spin-orbit interaction, which splits the Fermi surface into two sheets with different spin structures. The spin direction is tilted into the plane, rotating clockwise on one sheet and anticlockwise on the other (see Fig. 7). When the Rashba splitting exceeds the superconducting gap energy, the superconducting state is dramatically modified.

 



Fig. 7: Local inversion symmetry breaking and Rashba type spin splitting.

It has been pointed out that the cooperative effect of the strong electron correlation and strong spin-orbit interaction gives rise to exotic electronic states. Although strongly correlated heavy fermion superconductors with broken inversion symmetry have been reported, the superconductivity often coexists with magnetic order in these compounds. Moreover, the magnitude of the Rashba spin-orbit interaction is hard to control, as it is determined by the crystal structure. Recently, the Rashba effect is a topic of growing interest in 2D superconductivity on the surface of the substrate and at the interface between two different materials, which necessarily have broken inversion symmetry. In some of these systems the Rashba-type spin-orbit interaction is tunable and enables the possibility of achieving exotic states such as topological superconducting states. However, in the 2D systems discovered up to now, superconductivity emerges from weakly correlated electron states. Thus, in the superconductors with strong Rashba spin-orbit interaction, the role of strong electron-electron interaction has remained largely unexplored due to the lack of suitable material systems.

The spin-orbit interaction in Ce-based compounds is generally significant because of heavy elements. Recent experiments revealed that the Rashba spin-orbit interaction plays an essential role for the superconductivity in Kondo superlattices.

 

Fig. 8: Schematics of two types of superconducting Kondo superlattices. Left shows ABAB' -type: 5-UCT CeCoIn5 BLs are sandwiched by 8- and 2-UCT YbCoIn5 layers, (n:m:n:m') = (5:8:5:2). Right shows ABC-type: Tricolor superlattice consisting of 5-UCT CeCoIn5, 5-UCT YbCoIn5, and 5-UCT YbRhIn5, (n:m:l)=(5:5:5). All layers, including the middle CeCoIn5 layer (gray plane), are not mirror planes. .

Local inversion symmetry breaking at the interface of heavy fermions and normal metals

In the CeCoIn5/YbCoIn5 superlattices, the inversion symmetry is locally broken at the top and the bottom CeCoIn5 layers in the immediate proximity of the YbCoIn5 BLs, as illustrated in Fig. 7. With the reduction of n, the fraction of noncentrosymmetric interface layers increases rapidly. The importance of local ISB for the superconducting state has been emphasized experimentally through the anomalous temperature and angular dependencies of Hc2, which can be interpreted as a strong suppression of the Pauli pair-breaking effect [6]. Site-selective NMR spectroscopy experiments have also indicated that the local ISB affects the magnetic properties [7], leading to the suppression of antiferromagnetic fluctuations near the interface [8]. Thus, the interfacial effect becomes a key element for understanding the electronic state in the CeCoIn5/YbCoIn5 superlattices.

Controlling the inversion symmetry breaking

It has been proposed theoretically that Rashba spin orbit interaction leads to a wide variety of exotic superconducting states. One of our primary interests is to develop a scheme to control the degree of ISB through the appropriate design of Kondo superlattices. For this purpose, two types of superlattices (ABAB'-, and ABC-type superlattices) were fabricated as illustrated in Fig. 8.

The ABAB'-type superlattice is a modulated superlattice consisting of n-UCT CeCoIn5 sandwiched by m- and m'-UCT YbCoIn5 or YbRhIn5, denoted as an (n:m:n:m') superlattice. In this superlattice, inversion symmetry is disrupted in all of Ce planes through the thickness modulation of the YbCoIn5 BLs, in addition to the local ISB [9]. The asymmetric potential gradient associated with the YbCoIn5 BL thickness modulation is oriented in the opposite direction in the neighboring CeCoIn5 BLs, as shown by the orange (medium) arrows in Fig. 8. We note that mirror planes are present in YbCoIn5 BLs even in the ABAB'-type superlattice; however, we focus mainly on ISB in the Ce-planes. We expect that the degree of this "block layer ISB" can be enhanced with increasing |m-m'|, which represents the degree of thickness modulation of YbCoIn5 BLs.

The ABC-type superlattice is a tricolor superlattice composed of n-UCT CeCoIn5, m-UCT YbCoIn5, and l-UCT YbRhIn5, forming an (n:m:l) c-axis-oriented superlattice structure [10]. In this case, we find immediately that inversion symmetry is globally broken along the c-axis, as well as the local ISB. The asymmetric potential gradient is associated with global ISB. We anticipate that the degree of this "global" ISB can be tuned by changing the ratio between the thickness of YbCoIn5 and that of YbRhIn5, m/l.

We have succeeded in fabricating both types of superlattices and have shown that the degree of the ISB is controllable, which offers the prospect of achieving fascinating superconducting states.

Quest for exotic superconductivity in Kondo superlattices

The distinct features of CeCoIn5 are
(1) d-wave superconductivity,
(2) strong Pauli paramagnetic effect and
(3) strong spin-orbit interaction.

In the presence of ISB, (3) gives rise to strong Rashba spin orbit interaction. Several kinds of exotic superconducting states, which are difficult to be realized in bulk systems, have been proposed in the Kondo superlattices containing CeCoIn5 layers. Controlling the local ISB is important because it has been proposed that the combination of (1) (2) and (3) leads to several exotic superconducting states.

(a) Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state
Property (2) is important for the formation of FFLO state, in which a new pairing state (k↑, -k + q↓) with finite q is realized. Two dimensionality generally favors FFLO states. Therefore, 2D Kondo superlattices made of CeCoIn5 are good candidates for realizing the FFLO state [11].

(b) Helical and stripe superconducting state
In a non-centrosymmetric superconductor in a magnetic field parallel to the 2D plane, the shift of the Fermi surface with the Rashba spin-orbit interaction by the external magnetic field leads to an exotic superconducting state, in which the phase of the superconducting order parameter is modulated as Δ(r)=Δ0eiqr in the helical superconducting state and Δ(r)=Δ1eiqr2e-iqr in the stripe state. A possible observation of such states has been recently reported in YbRhIn5/CeCoIn5/YbCoIn5 tricolor superlattices [10].

(c) Pair density wave
In the presence of local ISB, a pair density wave state, in which the superconducting gap changes the sign at the top and the bottom CeCoIn5 layer, has been proposed.

(d) Topological superconducting state
The search for topological superconductors is one of the most urgent contemporary problems in condensed matter systems. Topological superconductors are characterized by a full superconducting gap in the bulk and topologically protected gapless surface (or edge) states. The availability of the tricolor Kondo superlattices provides a new playground for exploring exotic superconducting states, topological crystalline superconductivity, and Majorana fermion excitations, in strongly correlated electron systems.

SUMMARY

We have fabricated heavy fermion thin films for the first time by using a state-of-the-art MBE technique. The in-site STM observation reveals the wide area of atomically flat terraces. We have also designed and fabricated a Kondo superlattice, which is a novel type of superlattice in which strongly correlated heavy fermion compounds CeIn3, CeCoIn5 and CeRhIn5 with atomic layer thickness are sandwiched by nonmagnetic metals. In these Kondo superlattices, 2D confinement of heavy fermions is achieved. In particular, we demonstrate that 1UCT CeCoIn5 exhibits superconductivity. It is revealed that the two dimensionality and Rashba spin-orbit interaction lead to profound changes in the superconducting properties of CeCoIn5 with atomic layer thickness. In particular, local ISB at the interface plays an important role even when the inversion symmetry is globally preserved. By fabricating modulated and tricolor Kondo superlattices, the magnitude of the Rashba spin orbit interaction incorporated into the 2D CeCoIn5 BLs is largely controllable.

Bulk heavy fermion compounds host an abundance of fascinating superconducting properties. The present Kondo superlattices offer the prospect of achieving even more fascinating pairing states than bulk systems. Therefore, the availability of the Kondo superlattices provides a new opportunity for exploring exotic superconducting states, such as helical and stripe superconducting states, a pair density wave state, complex stripe state, a topological crystalline superconductivity, and Majorana fermion excitations, in strongly correlated electron systems.

Finally, we provide an up-to-date status report concerning Kondo superlattices. Most recently, we successfully fabricated a new type of superlattice (a hybrid superlattice of CeCoIn5 and antiferromagnetic heavy fermion CeRhIn5) [12]. These superlattices exhibit both superconducting and antiferromagnetic transitions. These superlattices offer the potential of further in-depth exploration of the interplay between magnetic fluctuations and superconductivity.

Acknowledgements: This work has been done in collaboration with S.K. Goh, Y. Hanaoka, M. Haze, K. Ishida,
T. Ishii, S. Kasahara, Y. Kasahara, S. Miyake, Y. Mizukami, M. Naritsuka, T. Shibauchi, M. Shimozawa, H. Shishido,
T. Terashima, R. Toda, Y. Tokiwa, and T. Yamanaka.

References

[1] M. Shimozawa, S.K. Goh, T. Shibauchi and Y. Matsuda Rep. Prog. Phys. 79 074503 (2016).
[2] M. Shimozawa et al. Phys. Rev. B 86 144526 (2012).
[3] H. Shishido et al. Science 327 980 (2010).
[4] M. Haze et al. a preprint.
[5] Y. Mizukami et al. Nature Phys. 7 849 (2011).
[6] S. K. Goh et al. Phys. Rev. Lett. 109 157006 (2012).
[7] T. Yamanaka et al. Phys. Rev. B 92, 241105 (2015).
[8] T. Ishii et al. Phys. Rev. Lett. 116 206401 (2016).
[9] M. Shimozawa et al. Phys. Rev. Lett. 112 156404 (2014).
[10] M. Naritsuka et al. a preprint.
[11] Y. Matsuda and H. Shimahara, J.Phys. Soc. Jpn 76 051005 (2007).
[12] M. Naritsuka et al. in preparation.

 

Yuji Matsuda received his PhD in physics from the University of Tokyo (Japan) in 1987 and became a research associate at the Department of Pure and Applied Science, the University of Tokyo. He became an associate professor in 1993 at Hokkaido University (Japan) after spending two years at Princeton University (USA) as a postdoctoral fellow. He moved to the Institute for Solid State Physics, University of Tokyo, as an associate professor in 1997, and became a full professor at Kyoto University (Japan) in 2004. He is a condensed matter experimentalist with interests in electronic and magnetic properties of solids. His current research interests include strongly correlated electron systems, in particular exotic superconductivity, heavy fermion systems, high-Tc superconductors, and quantum spin systems. .