We show that the recently observed spin resonance modes in heavy-fermion superconductors CeCoIn$_5$ and CeCu$_2$Si$_2$ are magnetic excitons originating from superconducting quasiparticles. The wave vector ${\bf Q}$ of the resonance state leads to a powerful criterion for the symmetry and node positions of the unconventional gap function. The detailed analysis of the superconducting feedback on magnetic excitations reveals that the symmetry of the superconducting gap corresponds to a singlet $d_{x^2-y^2}$ state symmetry in both compounds. In particular this resolves the long-standing ambiguity of the gap symmetry in CeCoIn$_5$. We demonstrate that in both superconductors the resonance peak shows a significant dispersion away from ${\bf Q}$ that should be observed experimentally. Our results suggest a unifying nature of the resonance peaks in the two heavy-fermion superconductors and in layered cuprates.
The order parameter and pairing mechanism for superconductivity in heavy fermion compounds are still poorly understood. Scanning tunneling microscopy and spectroscopy at ultra-low temperatures can yield important information about the superconducting order parameter and the gap structure. Here, we study the first heavy fermion superconductor, CeCu_2Si_2. Our data show the superconducting gap which is not fully formed and exhibits features that point to a multi-gap order parameter. Spatial mapping of the zero bias conductance in magnetic field reveals the vortex lattice, which allows us to uneq…
Low-temperature (T) heat-capacity measurements under hydrostatic pressure of up to p=2.1 GPa have been performed on single-crystalline CeCu2Si2. A broad superconducting (SC) region exists in the T-p phase diagram. In the low-pressure region antiferromagnetic spin fluctuations and in the high-pressure region valence fluctuations had previously been proposed to mediate Cooper pairing. We could identify these two distinct SC regions. We found different thermodynamic properties of the SC phase in both regions, supporting the proposal that different mechanisms might be implied in the formation of s…
We report on a study of thermal Hall conductivity k_xy in the superconducting state of CeCoIn_5. The scaling relation and the density of states of the delocalized quasiparticles, both obtained from k_xy, are consistent with d-wave superconducting symmetry. The onset of superconductivity is accompanied by a steep increase in the thermal Hall angle, pointing to a striking enhancement in the quasiparticle mean free path. This enhancement is drastically suppressed in a very weak magnetic field. These results highlight that CeCoIn_5 is unique among superconductors. A small Fermi energy, a large sup…
Recent observations of two nodeless gaps in superconducting CeCu$_2$Si$_2$ have raised intensive debates on its exact gap symmetry, while a satisfactory theoretical basis is still lacking. Here we propose a phenomenological approach to calculate the superconducting gap functions, taking into consideration both the realistic Fermi surface topology and the intra- and interband quantum critical scatterings. Our calculations yield a nodeless $s^\pm$-wave solution in the presence of strong interband pairing interaction, in good agreement with experiments. This provides a possible basis for understa…
We report effects of La substitution on superconducting state of heavy fermion superconductor CeCoIn5, as seen in transport and magnetization measurements. As opposed to the case of conventional superconductors, pair breaking by nonmagnetic La results in depression of Tc and indicates strong gap anisotropy. Upper critical field Hc2 values decrease with increased La concentration, but the critical field anisotropy, gamma=Hc2(a)/Hc2(c), does not change in the Ce_{1-x}La_xCoIn5 (x=0-0.15). The electronic system is in the clean limit for all values of x.
We investigated the magnetic field dependence of the superconducting phase transition in heavy fermion CeCoIn_5 (T_c = 2.3 K) using specific heat, magneto-caloric effect, and thermal expansion measurements. The superconducting transition becomes first order when the magnetic field is oriented along the 001 crystallographic direction with a strength greater that 4.7 T, and transition temperature below T_0 ~ 0.31 T_c. The change from second order at lower fields is reflected in strong sharpening of both specific heat and thermal expansion anomalies associated with the phase transition, a strong …
The thermal conductivity of the heavy-fermion superconductor CeCoIn_5 has been studied in a magnetic field rotating within the 2D planes. A clear fourfold symmetry of the thermal conductivity which is characteristic of a superconducting gap with nodes along the (+-pi,+-pi)-directions is resolved. The thermal conductivity measurement also reveals a first order transition at H_c2, indicating a Pauli limited superconducting state. These results indicate that the symmetry most likely belongs to d_{x^2-y^2}, implying that the anisotropic antiferromagnetic fluctuation is relevant to the superconduct…
In the heavy fermion superconductor CeCoIn5 (Tc=2.3K) the critical field is large, anisotropic and displays hysteresis. The magnitude of the critical-field anisotropy in the a-c plane can be as large as 70 kOe and depends on orientation. Critical field measurements in the (110) plane suggest 2D superconductivity, whereas conventional effective mass anisotropy is observed in the (100) plane. Two distinct field-induced magnetic phases are observed: Ha appears deep in the superconducting phase, while Hb intersects Hc2 at T=1.4 K and extends well above Tc. These observations suggest the possible r…
The heavy-fermion superconductor CeCoIn$_5$ displays an additional transition within its superconducting (SC) state, whose nature is characterized by high-precision studies of the isothermal field dependence of the entropy, derived from combined specific heat and magnetocaloric effect measurements at temperatures $T\geq 100$ mK and fields $H\leq 12$ T aligned parallel, perpendicular and $18^\circ$ off the tetragonal [100] direction. For any of these conditions, we do not observe an additional entropy contribution upon tuning at constant temperature by magnetic field from the homogeneous SC int…
We present a ^{115}In NMR study of the quasi two-dimensional heavy-fermion superconductor CeCoIn_5 believed to host a Fulde-Ferrel-Larkin-Ovchinnkov (FFLO) state. In the vicinity of the upper critical field and with a magnetic field applied parallel to the ab-plane, the NMR spectrum exhibits a dramatic change below T*(H) which well coincides with the position of reported anomalies in specific heat and ultrasound velocity. We argue that our results provide the first microscopic evidence for the occurrence of a spatially modulated superconducting order parameter expected in a FFLO state. The NMR…
In heavy-fermion superconductors, it is widely believed that the superconducting gap function has sign-reversal due to the strong electron correlation. However, recently discovered fully-gapped s-wave superconductivity in CeCu2Si2 has clarified that strong attractive pairing interaction can appear even in heavy-fermion systems. To understand the origin of attractive force, we develop the multipole fluctuation theory by focusing on the inter-multipole many-body interaction called the vertex corrections. By analyzing the periodic Anderson model for CeCu2Si2, we find that hexadecapole fluctuation…
Taking advantage of a novel multiprobe setup we have measured, on a unique sample, the ac-magnetic susceptibility, the resistivity, the ac-specific heat and the thermopower of the superconductor heavy fermion CeCu$_{2}$Si$_{2}$ under pressure up to 5.1 GPa. At the superconducting transition temperature $T_c$, the Meissner signal corresponds to that expected for the sample volume and coincides with the specific heat jump and the resistive transition completion temperatures. Differing from previous observations, here the susceptibility measurements did not reveal any anomaly in the vicinity of t…
The implications of the spin exciton mechanism are exposed in the context of a Spin Density Wave (SDW) instability occurring inside the superconducting phase of a layered heavy electron compound. In this model a magnetic field serves as a tuning parameter bringing the system to the point where the transverse spin correlations are enhanced due to dx2 -y2 -wave superconductivity and induces an instability to a phase with coexisting superconductivity and SDW order. The model considers electrons in a crystal with antiferromagnetic interactions and provides restrictions on the Fermi surface charact…
We present In NMR measurements in a novel thermodynamic phase of CeCoIn5 in high magnetic field, where exotic superconductivity coexists with the incommensurate spin-density wave order. We show that the NMR spectra in this phase provide direct evidence for the emergence of the spatially distributed normal quasiparticle regions. The quantitative analysis for the field evolution of the paramagnetic magnetization and newly-emerged low-energy quasiparticle density of states is consistent with the nodal plane formation, which is characterized by an order parameter in the Fulde-Ferrell-Larkin-Ovchin…
We investigated the effect of electron and hole doping on the high-field low-temperature superconducting state in CeCoIn$_5$ by measuring specific heat of CeCo(In$_{\rm 1-x}$M$_{\rm x}$)$_5$ with M=Sn, Cd and Hg and $x$ up to 0.33% at temperatures down to 0.1\,K and fields up to 14\,T. Although both Cd- and Hg-doping (hole-doping) suppresses the zero-field $T_c$ monotonically, $H_{c2}$ increases with small amounts of doping and has a maximum around $x$=0.2% (M=Cd). On the other hand, with Sn-doping (electron-doping) both zero-field $T_c$ and $H_{c2}$ decrease monotonically. The critical temper…
We present nuclear magnetic resonance (NMR) measurements on the three distinct In sites of CeCoIn$_5$ with magnetic field applied in the [100] direction. We identify the microscopic nature of the long range magnetic order (LRO) stabilized at low temperatures in fields above 10.2 T while still in the superconducting (SC) state. We infer that the ordered moment is oriented along the $\hat c$-axis and map its field evolution. The study of the field dependence of the NMR shift for the different In sites indicates that the LRO likely coexists with a modulated SC phase, possibly that predicted by Fu…
We have performed $^{63}$Cu nuclear magnetic resonance/nuclear quadrupole resonance measurements to investigate the magnetic and superconducting (SC) properties on a "superconductivity dominant" ($S$-type) single crystal of CeCu$_2$Si$_2$. Although the development of antiferromagnetic (AFM) fluctuations down to 1~K indicated that the AFM criticality was close, Korringa behavior was observed below 0.8~K, and no magnetic anomaly was observed above $T_{\rm c} \sim$ 0.6 K. These behaviors were expected in $S$-type CeCu$_2$Si$_2$. The temperature dependence of the nuclear spin-lattice relaxation ra…
We report high magnetic field linear magnetostriction experiments on CeCoIn$_5$ single crystals. Two features are remarkable: (i) a sharp discontinuity in all the crystallographic axes associated with the upper superconducting critical field $B_{c2}$ that becomes less pronounced as the temperature increases; (ii) a distinctive second order-like feature observed only along the c-axis in the high field (10 T $ \lesssim B \leq B_{c2}$) low temperature ($T \lesssim$ 0.35 K) region. This second order transition is observed only when the magnetic field lies within 20$^o$ of the ab-planes and there i…
Multiband superconductivity with dominant two-gap features are recently proposed to challenge the earlier accepted nodal $d$-wave pairing in the first unconventional superconductor CeCu$_{2}$Si$_{2}$. Here we obtain multiband Fermi-surface topology of CeCu$_{2}$Si$_{2}$ via first-principles calculations, and study the problem within an effective two hybridization band model including detailed band-structure. Within T-matrix approximation, our calculations reveal that different pairing candidates could yield qualitatively distinct features characterised by impurity-induced bound states. Except …
We report $^{115}$In nuclear magnetic resonance (NMR) measurements of the heavy-fermion superconductor CeCoIn$_5$ in the vicinity of the superconducting critical field $H_{c2}$ for a magnetic field applied perpendicular to the $\hat c$-axis. A possible inhomogeneous superconducting state, Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), is stabilized in this part of the phase diagram. In 11 T applied magnetic field, we observe clear signatures of the two phase transitions: the higher temperature one to the homogeneous superconducting state and the lower temperature phase transition to a FFLO state. It …
Quantum criticality in the normal and superconducting state of the heavy-fermion metal CeCoIn$_5$ is studied by measurements of the magnetic Grüneisen ratio, $Γ_H$, and specific heat in different field orientations and temperatures down to 50 mK. Universal temperature over magnetic field scaling of $Γ_H$ in the normal state indicates a hidden quantum critical point at zero field. Within the superconducting state the quasiparticle entropy at constant temperature increases upon reducing the field towards zero, providing additional evidence for zero-field quantum criticality.
In usual superconductors the carriers form Cooper pairs that have zero total momentum meaning that the superfluid density is homogeneous. We know for decades that it is a priori possible to observe at high fields the Fulde-Ferrel-Larkin-Ovchinikov (FFLO) state in which the superfluid density exhibits a field dependent modulation. The search for such inhomogeneous condensates in materials is the subject of tremendous excitement especially after the discovery of a promising high-field superconducting (HFSC) phase in CeCoIn$_5$. However, subsequent neutron and NMR experiments contradicted the FFL…
We show results on the vortex core dissipation through current-voltage measurements under applied pressure and magnetic field in the superconducting phase of CeCoIn$_5$. We find that as soon as the system becomes superconducting, the vortex core resistivity increases sharply as the temperature and magnetic field decrease. The sharp increase in flux flow resistivity is due to quasiparticle scattering on critical antiferromagnetic fluctuations. The strength of magnetic fluctuations below the superconducting transition suggests that magnetism is complimentary to superconductivity and therefore mu…
We measure the ac susceptibility of single-crystal CeCoIn5 in dc field parallel to the c axis and find further evidence for a high-field phase transition within the superconducting phase in this orientation. We apply up to 2.3 kbar uniaxial pressure along the c axis and discuss the pressure dependence of the high-field phase. We also report the behavior of Hc2 under uniaxial pressure for field along c.
The origin of unconventional superconductivity, including high-temperature and heavy-fermion superconductivity, is still a matter of controversy. Spin excitations instead of phonons are thought to be responsible for the formation of Cooper pairs. Using inelastic neutron scattering, we present the first in-depth study of the magnetic excitation spectrum in momentum and energy space in the superconducting and the normal states of CeCu2Si2. A clear spin excitation gap is observed in the superconducting state. We determine a lowering of the magnetic exchange energy in the superconducting state, in…
In exotic superconductors including high-$T_c$ copper-oxides, the interactions mediating electron Cooper-pairing are widely considered to have a magnetic rather than the conventional electron-phonon origin. Interest in such exotic pairing was initiated by the 1979 discovery of heavy-fermion superconductivity in CeCu$_2$Si$_2$, which exhibits strong antiferromagnetic fluctuations. A hallmark of unconventional pairing by anisotropic repulsive interactions is that the superconducting energy gap changes sign as a function of the electron momentum, often leading to nodes where the gap goes to zero.…
The high field superconducting state in CeCoIn5 has been studied by transverse field muon spin rotation measurements with an applied field parallel to the crystallographic c-axis close to the upper critical field Hc2 = 4.97 T. At magnetic fields >= 4.8 T the muon Knight shift is enhanced and the superconducting transition changes from second order towards first order as predicted for Pauli-limited superconductors. The field and temperature dependence of the transverse muon spin relaxation rate sigma reveal paramagnetic spin fluctuations in the field regime from 2 T < H < 4.8 T. In the normal s…
We report a systematic study of high magnetic field specific heat and resistivity in single crystals of CeCoIn_5 for the field oriented in the basal plane (H//ab) of this tetragonal heavy fermion superconductor. We observe a divergent electronic specific heat as well as an enhanced A coefficient of the T^{2} law in resistivity at the lowest temperatures, as the field approaches the upper critical field of the superconducting transition. Together with the results for field along the tetragonal axis (H//c), the emergent picture is that of a magnetic field tuned quantum critical point which exist…
The study of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state has been of considerable recent interest. Below the temperature $T^*$ which is believed to be the transition temperature ($T$) to the FFLO phase in CeCoIn$_5$, K. Kakuyanagi et al. (Phys. Rev. Lett. 94, 047602 (2005)) reported a composite NMR spectrum with a tiny component observed at frequencies corresponding to the normal state signal. The results were interpreted as evidence for the emergence of an FFLO state. This result is inconsistent with two other NMR studies of V. F. Mitrovi{ć} et al. (Phys. Rev. Lett. 97, 117002 (2006)) a…
The appearance of spin-density-wave (SDW) magnetic order in the low-temperature and high-field corner of the superconducting phase diagram of CeCoIn$_5$ is unique among unconventional superconductors. The nature of this magnetic $Q$ phase is a matter of current debate. Here, we present the thermal conductivity of CeCoIn$_5$ in a rotating magnetic field, which reveals the presence of an additional order inside the $Q$ phase that is intimately intertwined with the superconducting $d$-wave and SDW orders. A discontinuous change of the thermal conductivity within the $Q$ phase, when the magnetic f…
According to [M.A. Tanatar et al., Phys. Rev. Lett. 95, 067002 (2005)], in a multi-band d-wave superconductor CeCoIn5 electrons remain partially uncondensed. Interactions must induce superconducting order on all Fermi surfaces. We calculate specific heat and thermal conductivity in a two band model in presence of defects. Superconductivity originates on one Fermi surface, inducing a smaller gap on the other. Impurities diminish the induced gap and increase the density of states, restoring rapidly the Wiedemann-Franz law for this Fermi surface. Our calculations are in agreement with experiment.
We report ^{115}In nuclear magnetic resonance (NMR) measurements in the heavy-fermion superconductor CeCoIn_5 as a function of temperature in different magnetic fields applied parallel to the $(\hat a, \hat b)$ plane. The measurements probe a part of the phase diagram in the vicinity of the superconducting critical field H_{c2} where a possible inhomogeneous superconducting state, Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), is stabilized. We have identified clear NMR signatures of two phase transitions occurring in this part of the phase diagram. The first order phase transitions are characterized…
Motivated by recent experimental progress in high-resolution scanning tunneling microscopy (STM) techniques, we propose to investigate the local quasiparticle density of states around a unitary impurity in the heavy fermion superconductor CeCoIn$_{5}$. Based on the T-matrix approach we obtain a sharp nearly zero-energy resonance state (ZERS) in the strong impurity potential scattering localized around the impurity, and find qualitative differences in the spatial pattern of the tunneling conductance modulated by the nodal structure of the superconducting gap. These unique features may be used a…
We present NMR data in the normal and superconducting states of CeCoIn$_5$ for fields close to $H_{\rm c2}(0)=11.8$ T in the $ab$ plane. Recent experiments identified a first-order transition from the normal to superconducting state for $H> 10.5$ T, and a new thermodynamic phase below 290 mK within the superconducting state. We find that the Knight shifts of the In(1), In(2) and the Co are discontinuous across the first-order transition and the magnetic linewidths increase dramatically. The broadening differs for the three sites, unlike the expectation for an Abrikosov vortex lattice, and sugg…
Magnetization measurements were performed on CeCoIn_5 at temperature down to 30 mK with the magnetic field applied in three different orientations: parallel, near parallel ($\sim$ 10$^{0}$ rotated) and perpendicular to the ab-plane. For these three orientations we have observed crossover features in the torque/magnetization traces at fields just below $H_{c2}$, giving further evidence for the formation of a high field Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) superconducting state in CeCoIn_5 for $H \parallel ab$-plane and newly indicates that the FFLO state persists for out-of-plane field orient…
We demonstrate that the electronic bandstructure extracted from quasi-particle interference spectroscopy [Nat. Phys. 9, 468 (2013)] and the theoretically computed form of the superconducting gaps [Proc. Nat. Acad. Sci. 111, 11663 (2014)] can be used to understand the $dI/dV$ lineshape measured in the normal and superconducting state of CeCoIn$_5$ [Nat. Phys. 9, 474 92103)]. In particular, the $dI/dV$ lineshape, and the spatial structure of defect-induced impurity states, reflects the existence of multiple superconducting gaps of $d_{x^2-y^2}$-symmetry. These results strongly support a recently…
Magnetic fluctuations is the leading candidate for pairing in cuprate, iron-based and heavy fermion superconductors. This view is challenged by the recent discovery of nodeless superconductivity in CeCu$_2$Si$_2$, and calls for a detailed understanding of the corresponding magnetic fluctuations. Here, we mapped out the magnetic excitations in \ys{superconducting (S-type)} CeCu$_2$Si$_2$ using inelastic neutron scattering, finding a strongly asymmetric dispersion for $E\lesssim1.5$~meV, which at higher energies evolve into broad columnar magnetic excitations that extend to $E\gtrsim 5$ meV. Whi…
The evolution of the magnetic excitation spectrum of the unconventional superconductor CeCoIn$_{5}$ was studied by inelastic neutron scattering as a function of magnetic field applied in the [1, -1, 0] direction. The spin resonance characteristic of the superconducting states was observed up to about $H_{c2}$/2 : it is still centered at (1/2, 1/2, 1/2) when the magnetic field increases while its characteristic energy decreases and its lineshape substantially broadens.
By using a molecular beam epitaxy technique, we fabricate a new type of superconducting superlattices with controlled atomic layer thicknesses of alternating blocks between heavy fermion superconductor CeCoIn_5, which exhibits a strong Pauli pair-breaking effect, and nonmagnetic metal YbCoIn_5. The introduction of the thickness modulation of YbCoIn_5 block layers breaks the inversion symmetry centered at the superconducting block of CeCoIn_5. This configuration leads to dramatic changes in the temperature and angular dependence of the upper critical field, which can be understood by considerin…
Unconventional superconductivity and magnetism are intertwined on a microscopic level in a wide class of materials, including high-$T_c$ cuprates, iron pnictides, and heavy-fermion compounds. A new approach to this most fundamental and hotly debated subject focuses on the role of interactions between superconducting electrons and bosonic fluctuations at the interface between adjacent layers in heterostructures. A recent state-of-the-art molecular-beam-epitaxy technique has enabled us to fabricate superlattices consisting of different heavy-fermion compounds with atomic thickness. These Kondo s…
To identify the microscopic mechanism of heavy-fermion Cooper pairing is an unresolved challenge in quantum matter studies; it may also relate closely to finding the pairing mechanism of high temperature superconductivity. Magnetically mediated Cooper pairing has long been the conjectured basis of heavy-fermion superconductivity but no direct verification of this hypothesis was achievable. Here, we use a novel approach based on precision measurements of the heavy-fermion band structure using quasiparticle interference (QPI) imaging, to reveal quantitatively the momentum-space (k-space) structu…
In the tetragonal heavy fermion system CeCoIn5 the unconventional superconducting state is probed by means of muon spin rotation. The pressure dependence (0-1 GPa) of the basal-plane magnetic penetration depth (λ_a), the penetration depth anisotropy (γ=λ_c/λ_a) and the temperature dependence of 1/λ_i^2 (i=a,c) were studied in single crystals. A strong decrease of λ_a with pressure was observed, while γand λ_i^2(0)/λ_i^2(T) are pressure independent. A linear relationship between 1/λ_a^2(270 mK) and Tc was also found. The large decrease of λ_a with pressure is the signature of an increase of the…
A superconducting quantum interference device (SQUID) was prepared on a micron-sized single crystal using a selected growth domain of a thin film of $CeCoIn_5$ grown by molecular beam epitaxy. SQUID voltage oscillations of good quality were obtained as well as interference effects stemming from the individual Josephson microbridges. The transport characteristics in the superconducting state exhibited several peculiarities which we ascribe to the periodic motion of vortices in the microbridges. The temperature dependence of the Josephson critical current shows good correspondence to the Ambegao…
The electrical resistivity rho(T) of single crystalline CeCu_5Au under pressure was measured in the temperature range 30mK<T<300K. Pressure suppresses the antiferromagnetic order (T_N=2.35K at ambient pressure) and drives the system into a non-magnetic heavy-fermion state above P_c=4.1(3)GPa. The electrical resistivity shows a deviation from a T^2 dependence of a Fermi-liquid in the pressure range 1.8GPa<=P<=5.15GPa. The rho(T)-curves can be compared with those of CeCu_{6-x}Au_x at different Au concentrations. Just before the long-range magnetic order vanishes, a possibly superconducting phase…
A key aspect of unconventional pairing by the antiferromagnetic spin-fluctuation mechanism is that the superconducting energy gap must have opposite sign on different parts of the Fermi surface. Recent observations of non-nodal gap structure in the heavy-fermion superconductor CeCu$_2$Si$_2$ were then very surprising, given that this material has long been considered a prototypical example of a superconductor where the Cooper pairing is magnetically mediated. Here we present a study of the effect of controlled point defects, introduced by electron irradiation, on the temperature-dependent magn…
Thermal conductivity and specific heat were measured in the superconducting state of the heavy fermion material Ce_{1-x}La_{x}CoIn_{5}. With increasing impurity concentration x, the suppression of T_{c} is accompanied by the increase in the residual electronic specific heat expected of a d-wave superconductor, but it occurs in parallel with a decrease in residual electronic thermal conductivity. This contrasting behavior reveals the presence of uncondensed electrons coexisting with nodal quasiparticles. An extreme multiband scenario is proposed, with a d-wave superconducting gap on the heavy-e…
Understanding the origin of superconductivity in strongly correlated electron systems continues to be at the forefront of unsolved problems in all of physics. Among the heavy f-electron systems, CeCoIn5 is one of the most fascinating, as it shares many of the characteristics of correlated d-electron high-Tc cuprate and pnictide superconductors, including the competition between antiferromagnetism and superconductivity. While there has been evidence for unconventional pairing in this compound, high-resolution spectroscopic measurements of the superconducting state have been lacking. Previously,…
Beside the spin density wave (SDW) order inside the superconducting phase in $\mathrm{CeCoIn_5}$ at high magnetic fields, recent neutron scattering measurements have found Bragg peaks in $5\%$ Nd doped $\mathrm{CeCoIn_5}$ at low fields. The intensity of Bragg peaks in low fields is suppressed by increasing field. Based on the phenomenological and microscopic modeling, we show that for the Pauli limited $d$-wave superconductors in the vicinity of SDW instability relevant for $\mathrm{CeCoIn_5}$, magnetic impurities locally induce droplets of SDW order. Because of the strong anisotropy in the mo…
Field-angle dependent specific heat measurement has been done on the heavy-fermion superconductor CeCoIn5 down to ~ 0.29 K, in a magnetic field rotating in the tetragonal c-plane. A clear fourfold angular oscillation is observed in the specific heat with the minima (maxima) occurring along the [100] ([110]) directions. Oscillation persists down to low fields H << Hc2, thus directly proving the existence of gap nodes. The results indicate that the superconducting gap symmetry is most probably of dxy type.
The heavy-electron superconductor CeCoIn$_5$ exhibits a puzzling precursor state above its superconducting critical temperature at $T_c$ = 2.3 K. The thermopower and Nernst signal are anomalous. Below 15 K, the entropy current of the electrons undergoes a steep decrease reaching $\sim$0 at $T_c$. Concurrently, the off-diagonal thermoelectric current $α_{xy}$ is enhanced. The delicate sensitivity of the zero-entropy state to field implies phase coherence over large distances. The prominent anomalies in the thermoelectric current contrast with the relatively weak effects in the resistivity and m…
We report an {\it in-situ} scanning tunneling microscopy study of atomically thin films of CeCoIn$_5$, a $d$-wave heavy-fermion superconductor. Both hybridization and superconducting gaps are observed even in monolayer CeCoIn$_5$, providing direct evidence of superconductivity of heavy quasiparticles mediated by purely two-dimensional bosonic excitations. In these atomically thin films, $T_c$ is suppressed to nearly half of the bulk, but is similar to CeCoIn$_5$/YbCoIn$_5$ superlattices containing CeCoIn$_5$ layers with the same thickness as the thin films. Remarkably, the out-of-plane upper c…
The superconducting order parameter of the first heavy-fermion superconductor CeCu2Si2 is currently under debate. A key ingredient to understand its superconductivity and physical properties is the quasiparticle dispersion and Fermi surface, which remains elusive experimentally. Here we present measurements from angle-resolved photoemission spectroscopy. Our results emphasize the key role played by the Ce 4f electrons for the low-temperature Fermi surface, highlighting a band-dependent conduction-f electron hybridization. In particular, we find a very heavy quasi-two-dimensional electron band …
Since the progress in the fabrication techniques of thin-films of exotic materials such as strongly correlated heavy-fermion compounds, microscopic studies of the magnetic and electronic properties inside the films have been needed. Herein, we report the first observation of 115In nuclear quadrupole resonance (NQR) in an epitaxial film of the heavy-fermion superconductor CeCoIn5, for which the microscopic field gradient within the unit cell as well as magnetic and superconducting properties at zero field are evaluated. We find that the nuclear spin-lattice relaxation rate in the film is in exc…
We study the anomalously large specific heat jump and its systematic change with pressure in CeCoIn$_5$ superconductor. Starting with the general free energy functional of the superconductor for a coupled electron boson system, we derived the analytic result of the specific heat jump of the strong coupling superconductivity occurring in the coupled electron boson system. Then using the two component spin-fermion model we calculate the specific heat coefficient $C(T)/T$ both for the normal and superconducting states and show a good agreement with the experiment of CeCoIn$_5$. Our result also cl…
We theoretically study the effect of a nonmagnetic impurity in heavy fermion superconductor CeCoIn$_{5}$ within a realistic band model and the T-matrix approximation approach. By considering two known possible pairing symmetry candidates $d_{x^{2}-y^{2}}$ and $d_{xy}$, we find that although both total density of states exhibit a similar V-shaped gaplike feature, only the $d_{x^{2}-y^{2}}$-wave pairing symmetry gives rise to robust intragap impurity resonance states reflected by the resonance peaks near the Fermi energy in the local density of states. These features can be readily probed by sca…
Electronic structure and the shape of the Fermi surface are known to be of fundamental importance for the superconducting instability in real materials. We demonstrate that such an instability may be explored by static Cooper pair susceptibility renormalized by pairing interaction and present an efficient method of its evaluation using Wannier orbitals derived from ab initio calculation. As an example, this approach is used to search for an unconventional superconducting phase of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type in a heavy-fermion compound CeCoIn$_5$ and an iron-based supercond…
We have investigated the effect of Yb substitution on the Pauli limited, heavy fermion superconductor, CeCoIn$_5$. Yb acts as a non-magnetic divalent substituent for Ce throughout the entire doping range, equivalent to hole doping on the rare earth site. We found that the upper critical field in (Ce,Yb)CoIn$_5$ is Pauli limited, yet the reduced (H,T) phase diagram is insensitive to disorder, as expected in the purely orbitally limited case. We use the Pauli limiting field, the superconducting condensation energy and the electronic specific heat coefficient to determine the Wilson ratio ($R_{W}…
We report a highly unusual angular variation of the upper critical field (H_c2) in epitaxial superlattices CeCoIn_5(n)/YbCoIn_5(5), formed by alternating layers of n and a 5 unit-cell thick heavy-fermion superconductor CeCoIn_5 with a strong Pauli effect and normal metal YbCoIn_5, respectively. For the n=3 superlattice, H_{c2}(θ) changes smoothly as a function of the field angle θ. However, close to the superconducting transition temperature, H_{c2}(θ) exhibits a cusp near the parallel field (θ=0 deg). This cusp behavior disappears for n=4 and 5 superlattices. This sudden disappearance suggest…
