Session E27: Heavy Fermion Superconductors

Tuning the electronic state in CeCu$_{\mathrm{2}}$Si$_{\mathrm{2}}$: Si $\to $ P substitution

The chemical substitution series CeCu$_{\mathrm{2}}$Si$_{\mathrm{2-x}}$Ge$_{\mathrm{x\thinspace }}$hosts two distinct superconducting regions that are accessed under applied pressure. The first of these surrounds an antiferromagnetic quantum critical point, while the second does not appear to be associated with the zero-temperature collapse a line of phase transitions. It has been speculated that the second superconducting dome encompasses a quantum phase transition that is associated with a Ce 4$f$-electron valence collapse, but this has yet to be established. We report a study of the chemical substitution series CeCu$_{\mathrm{2}}$Si$_{\mathrm{2-}}_{x}$P$_{x}_{\mathrm{\thinspace }}$for $x \le $ 0.2, which may expose a new dimension for investigation of quantum valence transitions. This ligand site tuning strategy has the advantage that it changes the number of s/p electrons without strongly modifying other important variables such as the strength of Coulomb, spin orbit, crystal electric field interactions, and the hybridization between $f$- and conduction electrons. We find that the superconductivity is rapidly suppressed and is replaced by strengthening antiferromagnetism with increasing $x. $An unexpected additional hysteretic phase transition (V) appears at temperatures below the antiferromagnetic ordering temperature for $x\ge $0.13, which shows several characteristics of Ce valence physics. We will discuss this $T-x$ phase diagram and consider implications for understanding the proposed valence instability region of CeCu$_{\mathrm{2}}$Si$_{\mathrm{2-x}}$Ge$_{\mathrm{x}}$ alloys at high pressure.   

Evidence for fully-gapped superconductivity in heavy-fermion CeCu$_2$Si$_2$

The discovery of superconductivity in heavy-fermion CeCu$_2$Si$_2$ in 1979 has opened a new playground for unconventional superconductivity in strongly-correlated systems. However, even in this archetypal heavy-fermion superconductor, the symmetry and the structure of the superconducting gap, which are intimately related to the paring mechanism, are still elusive. Here, to investigate the low-energy quasiparticle excitations in the superconducting state of CeCu$_2$Si$_2$ ($T_c=0.6$~K), we performed specific heat, thermal conductivity, and penetration depth measurements down to 60~mK. We found that specific heat and penetration depth exhibit exponential $T$-dependence at low $T$. Moreover, thermal conductivity has no residual $T$-linear term and shows little $H$-dependence. These behavior are in marked contrast to nodal superconductors. From the data taken with different experimental configurations, the detailed superconducting gap structure will be discussed.   

Thermal expansion and magnetostriction under extreme conditions of an archetypal heavy fermion system.

Several dilatometry techniques [1] have been developed and used for low temperature and high magnetic field measurements, but do not permit the use of high pressures. Following the experimental development of R.Daou[2], we successfully coupled Fiber Bragg Gratings (FBG) with pressure cells enabling us to map the magnetic field-pressure-temperature phase space of various systems. FBG measurements permit us to achieve a resolution of $\Delta $L/L$\approx $3.10$-$7 making it a very sensitive technique. Piston-cylinder cells developed at the NHMFL permit us to reach a pressure of 3 GPa, and their compact size allows them to be used in highly constrained sample volume, giving us the ability to do high pressure dilatometry studies in pulsed and dc high magnetic field facility at temperatures as low as 25 mK. Along with the setup we will present our results on the high pressure, high magnetic field dilatometry of CeCu2Ge2. $\backslash \backslash $[4pt] [1] Schmiedeshoff, G., Review of Scientifc Instruments, 77(12) (2006)$\backslash \backslash $[0pt] [2] Daou, R., Review of Scientific Instruments, 81(3) (2010)   

Optical Kerr Measurements of PrOs$_{\mathrm{4}}$Sb$_{\mathrm{12}}$

By probing the symmetries of a superconducting order parameter, it is possible to gain insight into the microscopic physics underlying superconductivity. This approach is especially important for unconventional superconductors, such as heavy fermion materials, where the pairing mechanisms are poorly understood. Time reversal symmetry breaking plays a large role in many heavy fermion systems, due to their strong magnetic interactions; however, TRS is an especially difficult symmetry to probe. Using a zero-loop-area Sagnac interferometer, we measure the polar Kerr effect in materials and thus extract information about TRSB via the optical conductivity. We present measurements of the polar Kerr effect in the multi-phase heavy fermion material PrOs4Sb12, and discuss applications to other materials.   

Superconducting gap symmetry in Pr$_{\mathrm{1-x}}$Ce$_{\mathrm{x}}$Pt$_{\mathrm{4}}$Ge$_{\mathrm{12}}$ studied through specific heat and resistivity measurements

We present results of a systematic study of polycrystalline samples of Pr$_{\mathrm{1-x}}$Ce$_{\mathrm{x}}$Pt$_{\mathrm{4}}$Ge$_{\mathrm{12}}$ (0 $\le $ x $\le $ 0.2) through low-temperature specific heat and electrical resistivity measurements, which allow us to explore the nature of the superconducting gap symmetry and its evolution with Ce concentration x. As reported earlier, Ce substitution on the Pr site suppresses monotonically the superconducting (SC) transition temperature T$_{\mathrm{c}}$: a small Ce concentration of x $=$ 0.14 suppresses T$_{\mathrm{c}}$ from 7.8 K in the parent compound to 0.6 K. This study points toward a two-band SC gap scenario for the parent compound, in which the larger gap is nodeless, whereas the smaller gap is nodal. While the larger gap remains nodeless irrespective of the amount of Ce substitution, a rather dramatic effect of Ce substitution is seen in the evolution of the smaller gap: a small amount of Ce substitution (x \textless 0.04) increases the value of this gap, while for x \textgreater 0.04, the data suggest that the nodal character of this gap disappears and both SC order parameters become nodeless. We will discuss our findings in the context of other resent results on this series of filled skutterudite compounds.   

Heavy fermion superconductivity under strong orbital fluctuations in PrV$_2$Al$_{20}$

Novel quantum phases formed in the vicinity of a magnetic quantum critical point (QCP) have been studied extensively in 4$f$ based intermetallics. On the other hand, it is an interesting open question what types of ground state emerges in the vicinity of a QCP of orbital orderings if the $f$ electrons' orbital degrees of freedom strongly hybridize with conduction electrons. In order to study this, it is important to choose a material with purely orbital degrees of freedom in the ground state. In addition, the material should be clean and the hybridization should be large. Recent our studies have revealed that Pr$T_2$Al$_{20}$ ($T$ = Ti, V) are ideal systems. Both systems have the nonmagnetic cubic $\Gamma _3$ crystal electric field doublet. In addition, the hybridization is strong as is evident in many physical properties. We found that both exhibit heavy fermion superconductivity inside the multipole ordering phases. Especially, in the case of PrV$_2$Al$_{20}$, the effective mass is highly enhanced ($m*/m_0\sim$ 140) even at ambient pressure, revealing even stronger hybridization. This observation indicates the first realization of the novel superconductivity arising from the orbital fluctuation of the $f$ electrons at ambient pressure, suggesting a proximity to an orbital QCP.   

Superconducting Pairing Correlations near a Kondo-destruction Quantum Critical Point in Cluster Impurity Models

Heavy fermion metals represent a canonical system to study superconductivity driven by quantum criticality. We are particularly motivated by the properties of CeRhIn$_{5}$, which shows the characteristic features of a Kondo destruction quantum critical point (QCP) in its normal state, and has one of the highest $T_c$'s among the heavy fermion superconductors. As a first step to study this problem within a cluster-EDMFT approach [1], we analyze a four-site Anderson impurity model with the antiferromagnetic spin component of the cluster coupled to a sub-Ohmic bosonic bath. We find a QCP that belongs to the same universality class as the single-site Bose-Fermi Anderson model. Together with previous work on a two-site model [2], our result suggests that the Kondo destruction QCP is robust as cluster size increases. More importantly, we are able to calculate the d-wave pairing susceptibility, which we find to be enhanced near the QCP. Using this model as the effective cluster model of the periodic Anderson model, we are also able to study the superconducting pairing near the Kondo-destruction QCP of the lattice model; preliminary results will be presented. [1] J. H. Pixley, A. Cai, Q. Si, Phys. Rev. B 91, 125127 [2] J. H. Pixley, L. Deng, K. Ingersent, Q. Si, Phys. Rev. B 91, 201109   

Visualization of Ce atoms and surface-induced magnetism in CeCoIn$_{5}$

CeCoIn$_{5}$ is known as a heavy fermion compound naturally born at the quantum critical point having an unconventional d-wave superconducting phase at low temperatures. Recently, several STM works on a cleaved surface of this compound reported visualization of emerging heavy fermion bands and consistency of the bulk superconducting properties reported previously. However, reported STM images in those works only visualized In atoms on the Ce-In plane even though the Ce-In plane contains Ce and In atoms. By performing precise low-temperature STM measurements on CeCoIn$_{5}$, we successfully visualize Ce atoms on the Ce-In plane and, in addition, surface-induced staggered dumbblell-shaped order on the Co plane. This ordered structure locally has C$_{2v}$ symmetry but retaining C$_{4}$ symmetry. This structure coexists with the superconductivity, and is robust against temperatures (\textgreater T$_{c})$ and an external magnetic field (\textgreater H$_{c2})$. In the talk, we will discuss the origin of the peculiar ordered structure based on our experimental observations together with first principles calculations.   

Mapping Dimensionality and Directionality of Electronic Behavior in CeCoIn$_{\mathrm{5}}$: the Normal State

Materials made from alternating layers of different constituents can exhibit dramatic variability in their electronic properties depending on which layer is probed. This is evident in the heavy fermion compound CeCoIn$_{\mathrm{5}}$, where scanning tunneling microscopy (STM) has revealed preferential coupling to either light or heavy electron states depending on the surface termination. Here we report STM measurements of CeCoIn$_{\mathrm{5}}$ cleaved perpendicular to its basal plane that clearly shows the quasi-two-dimensional nature of the electronic behavior on a single (100) surface. We observe atomic scale modulation of tunneling into the light and heavy electron bands in the $c$-axis direction, with no variation visible along the basal planes in the $b$-axis direction. In addition, conductance maps reveal preferential scattering along the two-dimensional basal planes. Our measurements highlight the reduced effective dimensionality of electronic states in CeCoIn$_{\mathrm{5}}$, and underscore the potential insight that can be gained by imaging layered materials perpendicular to their $c$-axis.   

Mapping Dimensionality and Directionality of Electronic Behavior in CeCoIn$_{5}$: the Superconducting State

Unconventional superconductors often exhibit anisotropic physical properties that arise from the directional dependence of their order parameters. A prime example is CeCoIn$_{5}$, a heavy fermion $d$-wave superconductor with a rich low-temperature phase diagram consisting of competing and coexisting magnetic and superconducting orders. Here we present dilution refrigerator scanning tunneling microscopy of CeCoIn$_{5}$ cleaved perpendicular to its basal plane. We study superconductivity on the (100) surface, whose normal vector points along the antinode of the superconducting energy gap. The gap magnitude is similar to that observed in the basal plane, with a key difference: it does not exhibit any suppression near step edges. Application of a magnetic field along the [100] direction leads to the formation of anisotropic vortices, and the vortex lattice undergoes a transition at high field before the superconducting state gives way to a pseudogap phase. Our measurements illustrate the directional dependence of the superconducting properties in CeCoIn$_{5}$, and more generally, demonstrate the utility of imaging $d$-wave superconductors along their nodal and antinodal directions.   

Zero-field magnetism in Nd-doped CeRhIn5 under pressure

Unconventional superconductivity is often found in heavy fermion compounds close to a magnetic instability. Although magnetism and superconductivity may coexist when $T_{N} > T_{c}$, evidence for magnetism is usually suddenly lost when $T_{N} < T_{c}$. Here we study the heavy-fermion compound Ce$_{0.95}$Nd$_{0.05}$RhIn$_{5}$ under pressure by means of electrical resistivity and AC calorimetry measurements. Our results show that, even at zero applied magnetic field, Nd substitution unveils a hidden magnetic instability below the superconducting dome. We examine the similarities and differences between our results and those on Nd-doped CeCoIn$_{5}$ as well as pure CeRhIn$_{5}$ under applied field and pressure. We discuss our results in light of recent calculations that include $d$-wave superconductivity and underlying magnetic correlations.   

Hybrid heavy-fermion superlattices of CeCoIn$_5$/CeRhIn$_5$

Interplay between superconductivity and magnetism continues to provide central topics in condensed matter physics. Among others, Ce$T$In$_5$ ($T$ = Co, Rh) compounds offer one of the suitable platforms for the study of this important issue --- CeCoIn$_5$ undergoes superconducting transition at $T_c$ = 2.3 K while CeRhIn$_5$ orders antiferromagnetically below $T_N$ = 3.8 K at ambient pressure. An intriguing issue concerns coexistence of superconductivity and antiferromagnetism which could be realized at an artificial interface of different materials, but it is not clear how the two different states are affected each other at the interface. Here, by using atomic layer-by-layer molecular beam epitaxy, we fabricate superconducting-antiferromagnetic hybrid superlattices consisting of alternating layers of CeCoIn$_5$ and CeRhIn$_5$. Transport measurements confirm the presence of both superconducting and antiferromagnetic phases. The coexistence of superconductivity and antiferromagnetism in a hybrid system is discussed based on the proximity effect at the interface.   

Switching of the Spin-Density-Wave in CeCoIn$_5$ probed by Thermal Conductivity

Unconventional superconductor CeCoIn$_5$ orders magnetically in a spin-density-wave (SDW) in the low-temperature and high-field corner of the superconducting phase. Recent neutron scattering experiment revealed that the single-domain SDW's ordering vector Q depends strongly on the direction of the magnetic field, switching sharply as the field is rotated through the anti-nodal direction. This switching may be manifestation of a pair-density-wave (PDW) $p$-wave order parameter, which develops in addition to the well-established $d$-wave order parameter due to the SDW formation. We have investigated the hypersensitivity of the magnetic domain with a thermal conductivity measurement. The heat current (J) was applied along the [110] direction such that the Q vector is either perpendicular or parallel to J, depending on the magnetic field direction. A discontinuous change of the thermal conductivity was observed when the magnetic field is rotated around the [100] direction within $0.2\,^{\circ}$. The thermal conductivity with the Q parallel to the heat current (J$\parallel$Q) is approximately 15\% lager than that with the Q perpendicular to the heat current (J$\perp$Q). This result is consistent with additional gapping of the nodal quasiparticle by the $p$-wave PDW coupled to SDW.   

Entanglement and exotic superfluidity in one-dimensional spin-imbalanced lattices

The exotic coexistence of superfluidity and magnetism has been investigated theoretical and experimentally since decades. Among the several ideas and models to describe exotic superconductors the so-called Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase stands out. In strongly correlated systems at low temperatures the FFLO state might emerges by the presence of external magnetic fields or by internal polarization as produced by spin-imbalanced populations. Although the FFLO papers are in their 50th birthday and state-of-the-art experiments have been addressed this matter, there have been no unequivocal observations of FFLO superconductivity. We investigate the FFLO superfluid regime in one-dimensional fermionic lattices from a quantum information theory perspective: studying the properties of entanglement. We find that entanglement is non-monotonic with the polarization whenever the lattice is predicted to be an exotic superfluid. We thus propose a simple model for the spin-flip channels involved in the process. Our model is found to allow a very good description of exotic superfluids, while beyond the FFLO regime it reveals a breaking pairs avalanche. Our findings are supported by both density functional theory and density matrix renormalization group calculations.   

Microscopic investigation of electronic inhomogeneity induced by substitutions in quantum critical CeCoIn$_{\mathrm{5}}$.

In Cd-doped CeCoIn$_{\mathrm{5}}$ magnetic order can be suppressed by pressure giving rise to a dome of superconductivity surrounding a quantum critical point (QCP). However, the typical non-Fermi liquid (NFL) signatures expected at this QCP are absent. In contrast, in Sn-doped CeRhIn$_{\mathrm{5}}$, pressure also suppresses magnetism giving rise to a dome of superconductivity, but in this case, the NFL signatures ARE observed at the QCP. We presents results using nuclear quadrupole resonance to probe microscopically the response of the prototypical quantum-critical metal CeCoIn$_{\mathrm{5}}$ to substitutions of small amounts of Sn and Cd for In. These substituents induce very different local electronic environments as observed by site dependent spin lattice relaxation rates 1/T$_{\mathrm{1}}$. Cd-doped samples generate a much more inhomogeneous spin environment than observed in Sn-doped samples. This difference naturally explains the presence and absence of NFL signatures at the respective QCPs mentioned above. The effects found here illustrate the need for care in general when interpreting NFL properties determined by macroscopic measurements achieved by chemical substitutions.