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.
We present a detailed analysis of the upper critical field for CeCoIn5 under high pressure. We show that, consistently with other measurements, this system shows a decoupling between maximum of the superconducting transition temperature Tc and maximum pairing strength. This puts forward CeCoIn5 as an important paradigm for this class of unconventional, strongly correlated superconductors.
Measurements of specific heat and electrical resistivity in magnetic fields up to 9 T along [001] and temperatures down to 50 mK of Sn-substituted CeCoIn5 are reported. The maximal -ln(T) divergence of the specific heat at the upper critical field H_{c2} down to the lowest temperature characteristic of non-Fermi liquid systems at the quantum critical point (QCP), the universal scaling of the Sommerfeld coefficient, and agreement of the data with spin-fluctuation theory, provide strong evidence for quantum criticality at H_{c2} for all x < 0.12 in CeCoIn5-xSnx. These results indicate the "accid…
We report resistivity measurements in the normal state of CeCoIn5 down to 40 mK and simultaneously in magnetic fields up to 9 T in the [001] crystallographic direction and under pressures up to 1.3 GPa. At ambient pressure the data are consistent with a field tuned quantum critical point coincident with the superconducting upper critical field H_{c2}, as observed previously. We find that with increasing pressure the quantum critical point moves inside the superconducting dome to lower fields. Thus, we can rule out that superconductivity is directly responsible for the non-Fermi liquid behavior…
Electrical resistivity measurements on a single crystal of the heavy-fermion superconductor CeCoIn_5 at pressures to 4.2 GPa reveal a strong crossover in transport properties near P^* \approx 1.6 GPa, where T_c is a maximum. The temperature-pressure phase diagram constructed from these data provides a natural connection to cuprate physics, including the possible existence of a pseudogap.
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.
We have made the first complete measurements of the London penetration depth $λ(T)$ of CeCoIn5, a quantum-critical metal where superconductivity arises from a non-Fermi-liquid normal state. Using a novel tunnel diode oscillator designed to avoid spurious contributions to $λ(T)$, we have established the existence of intrinsic and anomalous power-law behaviour at low temperature. A systematic analysis raises the possibility that the unusual observations are due to an extension of quantum criticality into the superconducting state.
The low-temperature thermal expansion of CeCoIn5 single crystals measured parallel and perpendicular to magnetic fields B oriented along the c axis yields the volume thermal-expansion coefficient $β$. Considerable deviations of $β(T)$ from Fermi-liquid behavior occur already within the superconducting region of the (B, T) phase diagram and become maximal at the upper critical field $B^0_{c2}$. However, $β(T)$ and the Grüneisen parameter $Γ$ are incompatible with a quantum critical point (QCP) at $B^0_{c2}$, but allow for a QCP shielded by superconductivity and extending to negative pressures f…
The resistivity of CeCoIn_5 was measured down to 20 mK in magnetic fields of up to 16 T. With increasing field, we observe a suppression of the non-Fermi liquid behavior, rho~T, and the development of a Fermi liquid state, with its characteristic rho=rho_0+AT^2 dependence. The field dependence of the T^2 coefficient shows critical behavior with an exponent of ~4/3. This is evidence for a new field-induced quantum critical point, occuring in this case at a critical field which coincides with the superconducting upper critical field H_c2.
We present a study of thermoelectric coefficients in CeCoIn_5 down to 0.1 K and up to 16 T in order to probe the thermoelectric signatures of quantum criticality. In the vicinity of the field-induced quantum critical point, the Nernst coefficient nu exhibits a dramatic enhancement without saturation down to lowest measured temperature. The dimensionless ratio of Seebeck coefficient to electronic specific heat shows a minimum at a temperature close to threshold of the quasiparticle formation. Close to T_c(H), in the vortex-liquid state, the Nernst coefficient behaves anomalously in puzzling con…
The presence of a quantum critical point separating two distinct zero-temperature phases is thought to underlie the `strange' metal state of many high-temperature superconductors. The nature of this quantum critical point, as well as a description of the resulting strange metal, are central open problems in condensed matter physics. In large part, the controversy stems from the lack of a clear broken symmetry to characterize the critical phase transition, and this challenge is no clearer than in the example of the unconventional superconductor CeCoIn$_5$. Through Hall effect and Fermi surface …
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 normal-state Hall effect and magnetoresisitance (MR) have been measured in the quasi-2D heavy fermion superconductor CeCoIn_5. In the non-Fermi liquid region where the reistivity rho_xx exhibits an almost perfect T-linear dependence, the Hall angle varies as cot theta_H propto T^2 and the MR displays a strong violation of Kohler's rule. We demonstrate a novel relation between the MR and the Hall conductivity, Delta rho_xx/rho_xx propto (sigma_xy rho_xx)^2. These results bear a striking resemblance to the normal-state properties of high-T_c cuprates, indicating universal transport propertie…
The resistivity of the heavy-fermion superconductor CeCoIn5 was measured as a function of temperature, down to 25 mK and in magnetic fields of up to 16 T applied perpendicular to the basal plane. With increasing field, we observe a suppression of the non-Fermi liquid behavior, rho ~ T, and the development of a Fermi liquid state, with its characteristic rho = rho_0 + AT^2 dependence. The field dependence of the T^2 coefficient shows critical behavior with an exponent of 1.37. This is evidence for a field-induced quantum critical point (QCP), occuring at a critical field which coincides, within…
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.
The main properties and the type of the field-tuned quantum critical point in the heavy-fermion metal CeCoIn$_5$ arisen upon applying magnetic fields $B$ are considered within the scenario based on the fermion condensation quantum phase transition. We analyze the behavior of the effective mass, resistivity, specific heat, charge and heat transport as functions of applied magnetic fields $B$ and show that in the Landau Fermi liquid regime these quantities demonstrate the critical behavior which is scaled by the critical behavior of the effective mass. We show that in the high-field non-Fermi li…
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…
This paper demonstrates the anisotropic response of quantum critical fluctuations with respect to the direction of the magnetic field $B$ in Ni-doped CeCoIn$_5$ by measuring the magnetization $M$ and specific heat $C$. The results show that $M/B$ at $B=0.1\ {\rm T}$ for both the tetragonal $c$ and $a$ directions exhibits $T^{-η}$ dependencies, and that $C/T$ at $B=0$ follows a $-\ln T$ function, which are the characteristics of non-Fermi-liquid (NFL) behaviors. For $B\,||\,c$, both the $M/B\propto T^{-η}$ and $C/T \propto -\ln T$ dependencies change into nearly temperature-constant behaviors b…
Employing the elemental sensitivity of x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD), we study the valence and magnetic order in the heavy fermion superconductor CeCoIn$_5$. We probe spin population of the f-electrons in Ce and d-electrons in Co as a function of temperature (down to 0.1 K) and magnetic field (up to 6 T). From the XAS we find a pronounced contribution of Ce$^{4+}$ component at low temperature and a clear temperature dependence of the Ce valence below 5 K, suggesting enhanced valence fluctuations, an indication for the presence of a nearby quan…
The nature of quantum criticality in CeCoIn$_5$ is studied by low-temperature thermal expansion $α(T)$. At the field-induced quantum critical point at H=5 T a crossover scale $T^\star\approx 0.3$ K is observed, separating $α(T)/T\propto T^{-1}$ from a weaker $T^{-1/2}$ divergence. We ascribe this change to a crossover in the dimensionality of the critical fluctuations which may be coupled to a change from unconventional to conventional quantum criticality. Disorder, whose effect on quantum criticality is studied in CeCoIn$_{5-x}$Sn$_x$ ($0\leq x\leq 0.18$), shifts $T^\star$ towards higher temp…
We have performed de Haas-van Alphen (dHvA) measurements of the heavy-fermion superconductor CeCoIn$_5$ down to 2 mK above the upper critical field. We find that the dHvA amplitudes show an anomalous suppression, concomitantly with a shift of the dHvA frequency, below the transition temperature $T_{\rm n}=20$ mK. We suggest that the change is owing to magnetic breakdown caused by a field-induced antiferromagnetic (AFM) state emerging below $T_{\rm n}$, revealing the origin of the field-induced quantum critical point (QCP) in CeCoIn$_5$. The field dependence of $T_{\rm n}$ is found to be very w…
We report measurements of the pressure-dependent superconducting transition temperature $T_c$ and electrical resistivity of the heavy-fermion compound CeCoIn$_5$. Pressure moves CeCoIn$_5$ away from its proximity to a quantum-critical point at atmospheric pressure. Experimental results are qualitatively consistent with theoretical predictions for strong-coupled, d-wave superconductivity in an anisotropic 3D superconductor.
The thermal conductivity kappa of the heavy-fermion metal CeCoIn5 was measured in the normal and superconducting states as a function of temperature T and magnetic field H, for a current and field parallel to the [100] direction. Inside the superconducting state, when the field is lower than the upper critical field Hc2, kappa/T is found to increase as T approaches absolute zero, just as in a metal and in contrast to the behavior of all known superconductors. This is due to unpaired electrons on part of the Fermi surface, which dominate the transport above a certain field. The evolution of kap…
We report detailed very low temperature resistivity measurements on the heavy fermion compounds Ce_{1-x}La_{x}CoIn5 (x=0 and x=0.01), with current applied in two crystallographic directions [100] (basal plane) and [001] (perpendicular to the basal plane) under magnetic field applied in the [001] or [011] direction. We found a Fermi liquid (ρ\propto T^{2}) ground state, in all cases, for fields above the superconducting upper critical field. We discuss the possible location of a field induced quantum critical point with respect to Hc2(0), and compare our measurements with the previous reports i…
The Ce compounds CeCoIn$_5$ and CeRhIn$_5$ are ideal model systems to study the competition of antiferromagnetism (AF) and superconductivity (SC). Here we discuss the pressure--temperature and magnetic field phase diagrams of both compounds. In CeRhIn$_5$ the interesting observation is that in zero magnetic field a coexistence AF+SC phase exist inside the AF phase below the critical pressure $p_{\rm c}^\star \approx 2$ GPa. Above $p_{\rm c}^\star$ AF is suppressed in zero field but can be re-induced by applying a magnetic field. The collapse of AF under pressure coincides with the abrupt chang…
The heavy fermion superconductor CeCoIn_5 can be tuned between superconducting and antiferromagnetic ground states by hole doping with Cd. Nuclear magnetic resonance (NMR) data indicate that these two orders coexist microscopically with an ordered moment ~0.7 μ_B. As the ground state evolves, there is no change in the low frequency spin dynamics in the disordered state. These results suggest that the magnetism emerges locally in the vicinity of the Cd dopants.
Temperature dependence of the London penetration depth $λ$ measured in single crystals of CeCoIn$_5$ is interpreted as caused by a strong pair-breaking scattering that makes the superconductivity in this compound gapless. For a gapless d-wave superconductor, we derive $λ=λ_0/\sqrt{1-(T/T_c)^2}$ caused by combined effect of magnetic and non-magnetic scattering in excellent agreement with the data in the full temperature range and with the gapless s-wave case of Abrikosov and Gor'kov. We also obtain the slope of the upper critical field at $T_c$ that compares well with the measured slope.
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…
Magnetic field as a dynamic energy scale in quantum-critical CeCoIn$_5$
Stockholm University（斯德哥尔摩大学）；Institute of Science and Technology Austria（奥地利科学技术研究所）；National High Magnetic Field Laboratory（国家高磁场实验室）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Cornell University（康奈尔大学）
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…
We present the results of out-of-plane electrical transport measurements on the heavy fermion superconductor CeCoIn$_{5}$ at temperatures from 40 mK to 400 K and in magnetic field up to 9 T. For $T <$ 10 K transport measurements show that the zero-field resistivity $ρ_{c}$ changes linearly with temperature and extrapolates nearly to zero at 0 K, indicative of non-Fermi-liquid (nFL) behavior associated with a quantum critical point (QCP). The longitudinal magnetoresistance (LMR) of CeCoIn$_{5}$ for fields applied parallel to the c-axis is negative and scales as $B/(T+T^{*})$ between 50 and 100 …
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 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…
Superconductivity and fractionalized magnetic excitations in CeCoIn5
Oak Ridge National Laboratory（橡树岭国家实验室）；The University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）；Harvard University（哈佛大学）；Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）；Neutron Scattering Division, Oak Ridge National Laboratory（橡树岭国家实验室中子散射部）；Department of Physics, Brookhaven National Laboratory（布鲁海文国家实验室物理系）；University of Edinburgh（爱丁堡大学）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究所计算量子物理中心）；Quantum Condensed Matter Division and Shull-Wollan Center, Oak Ridge National Laboratory（橡树岭国家实验室量子凝聚态物质部和舒尔-沃兰中心）
We measured specific heat and resistivity of heavy fermion CeCoIn5 between the superconducting critical field $H_{c2} = 5 T$ and 9 T, with field in the [001] direction, and at temperatures down to 50mK. At 5T the data show Non Fermi Liquid behavior down to the lowest temperatures. At field above 8T the data exhibit crossover from the Fermi liquid to a Non Fermi Liquid behavior. We analyzed the scaling properties of the specific heat, and compared both resistivity and the specific heat with the predictions of a spin-fluctuation theory. Our analysis leads us to suggest that the NFL behavior is d…
We demonstrate a close connection between observed field-induced antiferromagnetic (AFM) order and quantum critical fluctuation (QCF) in the Zn7%-doped heavy-fermion superconductor CeCoIn5. Magnetization, specific heat, and electrical resistivity at low temperatures all show the presence of new field-induced AFM order under the magnetic field B of 5-10 T, whose order parameter is clearly distinguished from the low-field AFM phase observed for B < 5 T and the superconducting phase for B < 3 T. The 4f electronic specific heat divided by the temperature, C_e/T, exhibits -lnT dependence at B~10 T …
The origin of the partial suppression of the electronic density states in the enigmatic pseudogap behavior, which is at the core of understanding high-$T_c$ superconductivity, has been hotly contested as either a hallmark of preformed Cooper pairs or an incipient order of competing interactions nearby. Here, we report the quasi-particle scattering spectroscopy of the quantum critical superconductor CeCoIn$_5$, where a pseudogap with energy $Δ_g$ was manifested as a dip in the differential conductance ($dI/dV$) below the characteristic temperature of $T_g$. When subjected to external pressure, …
Heat and charge transport were used to probe the magnetic field-tuned quantum critical point in the heavy-fermion metal CeCoIn$_5$. A comparison of electrical and thermal resistivities reveals three characteristic energy scales. A Fermi-liquid regime is observed below $T_{FL}$, with both transport coefficients diverging in parallel and $T_{FL}\to 0$ as $H\to H_c$, the critical field. The characteristic temperature of antiferromagnetic spin fluctuations, $T_{SF}$, is tuned to a minimum but {\it finite} value at $H_c$, which coincides with the end of the $T$-linear regime in the electrical resis…
The dynamic conductance of the heavy-fermion superconductor CeCoIn$_5$ is measured by point-contact spectroscopy as a function of temperature from 60 K down to 400 mK. The contact between the gold tip and the single-crystal is shown to be in the Sharvin limit with the enhanced sub-gap conductance arising from Andreev reflection. The zero-bias conductance data are best fit using the extended Blonder-Tinkham-Klapwijk model with a d-wave superconducting order parameter. A fit to the full conductance curve at 400 mK indicates strong coupling ($2Δ(0)/k_\textrm{B}T_\textrm{c} = 4.6$) and quantifies …
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…
Ultrasound velocity measurements of the unconventional superconductor CeCoIn_5 with extremely large Pauli paramagnetic susceptibility reveal an unusual structural transformation of the flux line lattice (FLL) in the vicinity of the upper critical field. The transition field coincides with that at which heat capacity measurements reveal a second order phase transition. The lowering of the sound velocity at the transition is consistent with the collapse of the FLL tilt modulus and a crossover to quasi two-dimensional FLL pinning. These results provide a strong evidence that the high field state …
We investigate the properties of the coexistence phase of itinerant antiferromagnetism and nodal $d$-wave superconductivity (Q-phase) discovered in heavy fermion CeCoIn5 under applied magnetic field. We solve the minimal model that includes $d$-wave superconductivity and underlying magnetic correlations in real space to elucidate the structure of the $Q$-phase in the presence of an externally applied magnetic field. We further focus on the role of magnetic impurities, and show that they nucleate the Q-phase at lower magnetic fields. Our most crucial finding is that, even at zero applied field,…
We present nuclear spin-lattice relaxation rate (1/T1) at the Co site and ac-susceptibility results in the normal and superconducting (SC) states of CeCoIn5 for H || c near the SC upper critical field Hc2 above 0.1 K. At 4.2 T, 1/T1 rapidly decreases below the SC transition temperature, consistent with the previous reports. Although the field dependence of 1/T1T at 0.1 K shows a peak at 5.2 T above Hc2, the temperature dependence of 1/T1T at 5.2 T is independent of temperature below 0.2 K, showing a Fermi-liquid behavior. In addition, we found no NMR-spectrum broadening by the appearance of in…
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 …
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…
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…
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…
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…
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…
We have measured the thermal conductivity of the heavy-fermion superconductor CeCoIn_5 in the vicinity of the upper critical field, with the magnetic field perpendicular to the c axis. Thermal conductivity displays a discontinuous jump at the superconducting phase boundary below critical temperature T_0 ~ 1 K, indicating a change from a second to first order transition and confirming the recent results of specific heat measurements on CeCoIn_5. In addition, the thermal conductivity data as a function of field display a kink at a field H_k below the superconducting critical field, which closely…
In-plane angular dependent resistivity ADR was measured in the non-Fermi liquid regime of CeCoIn$_5$ single crystals at temperatures $T \le 20$ K and in magnetic fields $H$ up to 14 T. Two scaling behaviors were identified in low field region where resistivity shows T-linear dependence, separated by a critical angle $θ_{c}$ which is determined by the anisotropy of CeCoIn$_5$; i.e., ADR depends only on the perpendicular (parallel) field component below (above) $θ_c$. These scaling behaviors and other salient features of ADR are consistent with d-wave density waves.
Low temperature magnetization M measurements down to 70~mK have been performed through the superconducting upper critical field H_c2 of CeCoIn5 with the field H parallel to the c axis of the tetragonal crystal. The crossing through the upper critical field H_c2(0) is marked by a sign change in the temperature dependence of M(T). A Fermi liquid law of the magnetization is observed in the superconducting phase while in the paramagnetic state above H_c2 a quasi-linear temperature dependence is obeyed. The specific heat below H_c2 is therefor dominated by the increase of γ(H), the linear term of t…
The in-plane electrical resistivity, rho, and thermal conductivity, kappa, of the heavy-fermion superconductor CeIrIn5 were measured down to 40mK in magnetic fields up to 11 T applied along the c axis. For all fields above Hc2=4T of filamentary superconductivity, we find that the ratio of heat and charge conductivities in the T to 0 limit obeys the Wiedemann-Franz law, kappa/T=L0/rho, where L0 = 2.45*10^-8 WOhmK^-2 is the Sommerfeld value of the Lorenz number. The temperature-dependent parts of both the electrical and thermal resistivity,w = T/L0 kappa, follow the functional dependence expecte…
We report penetration depth and resistivity measurements on the heavy fermion superconductor CeCoIn_5 using a self resonant tank circuit based on a tunnel diode oscillator. For magnetic fields applied near parallel to the \emph{ab}-planes and temperatures below 250 mK, two phase transitions were found. The lower field transition, within the superconducting state, is of a second order and we identify it as the transition from the ordinary vortex state to the Fulde, Ferrell, Larkin, Ovchinnikov (FFLO) state. The higher field transition marks the change from the FFLO to the normal state. This hig…
The interplay between magnetism and superconductivity has been a central issue in unconventional superconductors. While the dynamic magnetism could be the source of electron pairing, the static magnetism is generally believed to compete with superconductivity. In this sense, the observation of Q phase, the coupled spin-density wave order and superconductivity, in the heavy-fermion superconductor CeCoIn5 is very puzzling. Whether this Q phase origins from the novel Fulde-Ferrel-Larkin-Ovchinnikov state is under hot debate. Here we report the resistivity and thermal conductivity study of a newly…
We report In-NQR and Co-NMR experiments of CeCoIn$_5$ that undergoes a superconducting transition with a record high $T_{\rm c}$ = 2.3 K to date among heavy-fermion superconductors. At zero magnetic field, an anomalous temperature ($T$) dependence of nuclear spin-lattice relaxation rate $1/T_1$ of $^{115}$In is explained by the relation $1/T_1\propto T\cdotχ_Q(T)^{3/4}$ based on the anisotropic spin-fluctuations model in case of the proximity to an antiferromagnetic (AFM) quantum critical point (QCP). The novel behavior of $1/T_1\sim T^{1/4}$ over a wide $T$ range of $T_{\rm c} < T < 40$ K ari…
We re-analyze Nuclear Magnetic Resonance (NMR) spectra observed at low temperatures and high magnetic fields in the field-induced B-phase of CeCoIn5. The NMR spectra are consistent with incommensurate antiferromagnetic order of the Ce magnetic moments. However, we find that the spectra of the In(2) sites depend critically on the direction of the ordered moments, the ordering wavevector and the symmetry of the hyperfine coupling to the Ce spins. Assuming isotropic hyperfine coupling, the NMR spectra observed for H||[100] are consistent with magnetic order with wavevector Q=pi((1+delta)/a,1/a,1/…
We analyse the combined effect of orbital and Pauli depairing on the superconducting state, and apply the results to the heavy fermion CeCoIn$_5$. We find that: a) standard extrapolation based on the slope of $H_{c2}(T)$ in the vicinity of the transition temperature to T=0 does not always give accurate values of the orbital upper critical field; b) critical value of the Maki parameter, $α$, that determines onset of the first order transition depends on the Fermi surface shape and the symmetry of the gap, and is $α^*\approx 3$ for CeCoIn$_5$; c) the anisotropy of the thermodynamic and transport…
Recent findings of anomalous super-linear scaling of low temperature ($T$) penetration depth (PD) in several nodal superconductors near putative quantum critical points suggest that the low temperature PD can be a useful probe of quantum critical fluctuations in a superconductor. On the other hand, cuprates which are poster child nodal superconductors have not shown any such anomalous scaling of PD, despite growing evidence of quantum critical points. Then it is natural to ask when and how can quantum critical fluctuations cause anomalous scaling of PD? Carrying out the renormalization group c…
