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The existence of multiple superconducting phases induced by either pressure or magnetic field is one of the most striking features of superconductivity of UTe$_2$, among the many unusual superconducting properties of this system. Here we report thermodynamic measurements of the superconducting phase diagram combining pressure and magnetic fields up to 30 T. We show that the ambient pressure, high-field, superconducting phase evolves continuously with pressure to join the high-pressure, zero-field superconducting phase. This proves that these two phases are one and the same, and must have the same order parameter., Comment: 5 pages, 5 figure + supplementary material

The electrical resistivity of the unconventional superconductor UTe$_2$ shows very anisotropic behavior in the normal state depending on the current direction. In the present paper we show that the maximum in the resistivity $\rho_c$ for current applied along the $c$ axis at $T^{\rm max}_{\rho_c} \approx 14.75$~K follows the minimum in the thermal expansion $T_\alpha^\star$ along $b$ axis. Under a magnetic field applied along the $b$ axis, $T^{\rm max}_{\rho_c}$ can be tracked up to the critical point of the first order metamagnetic transition, which is located near 6~K and 34.5~T. Surprisingly, at the metamagnetic field $H_m$ the resistivity $\rho_c$ shows a steplike decrease while the resistivities $\rho_a$ and $\rho_b$, for current along the $a$ and $b$ axis, respectively, show a steplike increase. Under hydrostatic pressure $T^{\rm max}_{\rho_c}$ and $H_m$ decrease significantly up to the critical pressure $p_c$ at which superconductivity is suppressed and a long range antiferromagnetic order appears. We show that the phase diagram at different pressures can be scaled by $T^{\rm max}_{\rho_c}$ in field and temperature suggesting that this temperature scale is governing the main interactions in the normal state., Comment: accepted in Phys. Rev. B

The novel spin-triplet superconductor candidate UTe2 was discovered only recently at the end of 2018 and attracted enormous attention. We review key experimental and theoretical progress which has been achieved in different laboratories. UTe2 is a heavy-fermion paramagnet, but right after the discovery of superconductivity it has been expected to be close to a ferromagnetic instability showing many similarities to the U-based ferromagnetic superconductors, URhGe and UCoGe. The competition between different types of magnetic interactions and the duality between the local and itinerant character of the 5f Uranium electrons, as well as the shift of the U valence appear as key parameters in the rich phase diagrams discovered recently under extreme conditions like low temperature, high magnetic field, and pressure. We discuss macroscopic and microscopic experiments at low temperature to clarify the normal phase properties at ambient pressure. Special attention will be given to the occurrence of a metamagnetic transition at Hm = 35 T for a magnetic field applied along the hard magnetic axis b. Adding external pressure leads to strong changes in the magnetic and electronic properties with a direct feedback on superconductivity. Attention will be given on the possible evolution of the Fermi surface as a function of magnetic field and pressure. Superconductivity in UTe2 is extremely rich exhibiting various unconventional behaviors which will be highlighted. It shows an exceptionally huge superconducting upper critical field with a re-entrant behavior under magnetic field and the occurrence of multiple superconducting phases in the temperature field, pressure phase diagram. There is evidence for spin-triplet pairing. The different theoretical approaches will be described. Notably we discuss that UTe2 is a possible example for the realization of a fascinating topological superconductor., Comment: 47 pages, 53 figures, submitted to J. Phys.: Condens. Matter as "Topical Review"

We investigate the spin dynamics in the superconducting phase of UTe$_{2}$ by triple-axis inelastic neutron scattering on a single crystal sample. At the wave-vector $\bf{k_1}$=(0, 0.57, 0), where the normal state antiferromagnetic correlations are peaked, a modification of the excitation spectrum is evidenced, on crossing the superconducting transition, with a reduction of the relaxation rate together with the development of an inelastic peak at $\Omega$ $\approx$ 1 meV. The low dimensional nature and the the $a$-axis polarization of the fluctuations, that characterise the normal state, are essentially maintained below $T_{sc}$. The high ratio $\Omega/k_{B}T_{sc}$ $\approx$ 7.2 contrasts with the most common behaviour in heavy fermion superconductors., Comment: 3 figures, 1 table

Inelastic-neutron-scattering measurements were performed on a single crystal of the heavy-fermion paramagnet UTe$_2$ above its superconducting temperature. We confirm the presence of antiferromagnetic fluctuations with the incommensurate wavevector $\mathbf{k}_1=(0,0.57,0)$. A quasielastic signal is found, whose momentum-transfer dependence is compatible with fluctuations of magnetic moments $\mu\parallel\mathbf{a}$, with a sine-wave modulation of wavevector $\mathbf{k}_1$ and in-phase moments on the nearest U atoms. Low dimensionality of the magnetic fluctuations, consequence of the ladder structure, is indicated by weak correlations along the direction $\mathbf{c}$. These fluctuations saturate below the temperature $T_1^*\simeq15$~K, in possible relation with anomalies observed in thermodynamic, electrical-transport and nuclear-magnetic-resonance measurements. The absence or weakness of ferromagnetic fluctuations, in our data collected at temperatures down to 2.1 K and energy transfers from 0.6 to 7.5 meV, is emphasized. These results constitute constraints for models of magnetically-mediated superconductivity in UTe$_2$., Comment: 6 pages, 4 figures, + Supplementary Materials (6 pages, 6 figures)

We investigate ytterbium gallium garnet Yb$_{3}$Ga$_{5}$O$_{12}$ in the paramagnetic phase above the supposed magnetic transition at $T_{\lambda} \approx 54$ mK. Our study combines susceptibility and specific heat measurements with neutron scattering experiments and theoretical calculations. Below 500 mK, the elastic neutron response is strongly peaked in the momentum space. Along with that the inelastic spectrum develops flat excitation modes. In magnetic field, the lowest energy branch follows a Zeeman shift in accordance with the field-dependent specific heat data. An intermediate state with spin canting away from the field direction is evidenced in small magnetic fields. In the field of 2 T, the total magnetization almost saturates and the measured excitation spectrum is well reproduced by the spin-wave calculations taking into account solely the dipole-dipole interactions. The small positive Curie-Weiss temperature derived from the susceptibility measurements is also accounted for by the dipole spin model. Altogether, our results suggest that Yb$_{3}$Ga$_{5}$O$_{12}$ is a quantum dipolar magnet., Comment: 12 pages, 10 figures

We report on low temperature susceptibility and magnetization measurements made on single crystals of the recently discovered heavy-fermion superconductor UTe$_2$ and compare the results with the two ambient pressure ferromagnetic superconductors URhGe and UCoGe. Hysteresis curves in the superconducting phase show a familiar diamond shape superimposed on a large paramagnetic background. The Meissner state was measured by zero field cooling in small fields of a few Oe as well as ac susceptibility measurements in small fields and resulted in 100\% shielding, with a sharp transition. However the field cooling Meissner-Ochsenfeld effect (expulsion of flux) was negligible in fields greater than just a few Oe, but becomes nearly 30\% of the perfect diamagnetic signal when the field was reduced to 0.01~Oe. The critical current due to flux pinning was studied by ac susceptibility techniques. Over the range in fields and temperature of this study, no signature of a ferromagnetic transition could be discerned. The lower critical field $H_{\rm c1}$ has been measured along the three crystalographic axes, and surprisingly, the anisotropy of $H_{\rm c1}$ contradicts that of the upper critical field. We discuss this discrepancy and show that it may provide additional support for a magnetic field-dependent pairing mediated by ferromagnetic fluctuations in UTe$_2$., Comment: 5 pages, 4 figures, supplemental material included, to appear in Phys. Rev B (Letter)

Multiple superconducting order parameters are extremely rare. Here we show that a very small pressure can induce this phenomenon in the recently discovered heavy fermion superconductor UTe2. This nearly ferromagnetic system shows several intriguing phenomena, including an extraordinary reinforcement of superconductivity in very strong magnetic fields. We find that pressure can tune the system to a more correlated state and probable magnetic order. The superconducting critical temperature is strongly enhanced, reaching almost 3K, a new record for Ce- and U-based heavy fermion superconductors. Most spectacularly under pressure we find a transition within the superconducting state, putting UTe2 among the very rare systems having multiple superconducting phases. UTe2 under pressure is a treasure trove of several of the most fascinating phenomena in unconventional superconductivity and may well be a keystone in their understanding.

We present very low temperature scanning tunneling microscopy (STM) experiments on single crystalline samples of the superconductor $\beta$-Bi$_2$Pd. We find a single fully isotropic superconducting gap. However, the magnetic field dependence of the intervortex density of states is higher than the one expected in a single gap superconductor, and the hexagonal vortex lattice is locked to the square atomic lattice. Such increase in the intervortex density of states and vortex lattice locking have been found in superconductors with multiple superconducting gaps and anisotropic Fermi surfaces. We compare the upper critical field $H_{c2}(T)$ obtained in our sample with previous measurements and explain available data within multiband supercondutivity. We propose that $\beta$-Bi$_2$Pd is a single gap multiband superconductor. We anticipate that single gap multiband superconductivity can occur in other compounds with complex Fermi surfaces., Comment: 8 pages, 7 figures

The thermal conductivity of YbRh2Si2 has been measured down to very low temperatures under field in the basal plane. An additional channel for heat transport appears below 30 mK, both in the antiferromagnetic and paramagnetic states, respectively below and above the critical field suppressing the magnetic order. This excludes antiferromagnetic magnons as the origin of this additional contribution to thermal conductivity. Moreover, this low temperature contribution prevails a definite conclusion on the validity or violation of the Wiedemann-Franz law at the field-induced quantum critical point. At high temperature in the paramagnetic state, the thermal conductivity is sensitive to ferromagnetic fluctuations, previously observed by NMR or neutron scattering and required for the occurrence of the sharp electronic spin resonance fracture., Comment: 11 pages + Supplementary Materials

The ferromagnetic superconductor UCoGe has been investigated by high field X-ray magnetic circular dichroism (XMCD) at the U-M$_{4,5}$ and Co/Ge-K edges. The analysis of the branching ratio and XMCD at the U-M$_{4,5}$ edges reveals that the U-5$f$ electrons count is close to 3. The orbital ($\sim0.70\,\mu_B$) and spin ($\sim-0.30\,\mu_B$) moments of U at 2.1K and 17T (H//c) have been determined. Their ratio ($\sim-2.3$) suggests a significant delocalization of the 5$f$ electron states. The similar field dependences of the local U/Co and the macroscopic magnetization indicate that the Co moment is induced by the U moment. The XMCD at the Co/Ge-K edges reveal the presence of small Co-4$p$ and Ge-4$p$ orbital moments parallel to the macroscopic magnetization. In addition, the Co-3$d$ moment is estimated to be at most of the order of 0.1$\mu_B$ at 17T. Our results rule out the possibility of an unusual polarisability of the U and Co moments as well as their antiparallel coupling. We conclude that the magnetism which mediates the superconductivity in UCoGe is driven by U., Comment: 4 figures + supplementary material

Thermal conductivity measurements in the superconducting state of the ferromagnet UCoGe were performed at very low temperatures and under magnetic field on samples of different qualities and with the heat current along the three crystallographic axis. This allows to disentangle intrinsic and extrinsic effects, confirm the situation of multigap superconductivity and shed new light on the situation expected or claimed for the gap in these ferromagnetic superconductors, like evidences of absence of "partially gapped" Fermi surfaces., Comment: 6 pages, 5 figures. To be appeared in Physical Review Rapid Communication

New thermoelectric power (TEP) measurements on prototype heavy-fermion compounds close to magnetic quantum criticality are presented. The highly sensitive technique of TEP is an unique tool to reveal Fermi surface instabilities, referred here as Lifshitz transitions. The first focus is on the Ising CeRu2Si2 series. Doping CeRu2Si2 with Rh produces a decoupling between the first order metamagnetic transition and the pseudo-metamagnetism observed in the pure compound. Comparison is made with the case of YbRh2Si2 which is often considered as the archetype of local quantum criticality by contrast to CeRu2Si2, taken as an example of spin-density wave criticality. Up to now for ferromagnetic materials showing ferromagnetic wings, no simple case appears where the Fermi surface is preserved between the ferromagnetic and paramagnetic phases. An open issue is the consequence of Lifshitz transitions on superconductivity in these multiband systems., Comment: invited paper to SCES 2014 conference

We present measurements of the superconducting critical temperature Tc and upper critical field Hc2 as a function of pressure in the transition metal dichalcogenide 2H-NbS2 up to 20 GPa. We observe that Tc increases smoothly from 6K at ambient pressure to about 8.9K at 20GPa. This range of increase is comparable to the one found previously in 2H-NbSe2. The temperature dependence of the upper critical field Hc2(T) of 2H-NbS2 varies considerably when increasing the pressure. At low pressures, Hc2(0) decreases, and at higher pressures both Tc and Hc2(0) increase simultaneously. This points out that there are pressure induced changes of the Fermi surface, which we analyze in terms of a simplified two band approach., Comment: 5 pages, 5 figures

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 (\lambda_a), the penetration depth anisotropy (\gamma=\lambda_c/\lambda_a) and the temperature dependence of 1/\lambda_i^2 (i=a,c) were studied in single crystals. A strong decrease of \lambda_a with pressure was observed, while \gamma and \lambda_i^2(0)/\lambda_i^2(T) are pressure independent. A linear relationship between 1/\lambda_a^2(270 mK) and Tc was also found. The large decrease of \lambda_a with pressure is the signature of an increase of the number of superconducting quasiparticles by a factor of about 2., Comment: 5 pages, 6 figures. To appear in PRL

The thermal conductivity measurements have been performed on the heavy-fermion compound YbRh2Si2 down to 0.04 K and under magnetic fields through a quantum critical point (QCP) at Bc = 0.66 T || c-axis. In the limit as T -> 0, we find that the Wiedemann-Franz law is satisfied within experimental error at the QCP despite the destruction of the standard signature of Fermi liquid. Our results place strong constraints on models that attempt to describe the nature of unconventional quantum criticality of YbRh2Si2., Comment: 5 pages, 4 figures

We demonstrate that the vortex state in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase may be very different depending on the field orientation relative to the crystalline axes. We calculate numerically the upper critical field near the tricritical point taking into account the modulation of the order parameter along the magnetic field as well as the higher Landau levels. For s-wave superconductors with the anisotropy described by an elliptical Fermi surface we propose a general scheme of the analysis of the angular dependence of upper critical field at all temperatures on the basis of the exact solution for the order parameter. Our results show that the transitions (with tilting magnetic field) between different types of mixed states may be a salient feature of the FFLO phase. Moreover we discuss the reasons for the first-order phase transition into the FFLO state in the case of CeCoIn5 compound., Comment: 7 figures

The thermoelectric coefficients have been measured on the Yb-based heavy fermion compounds beta-YbAlB4 and YbRh2Si2 down to a very low temperature. We observe a striking difference in the behavior of the Seebeck coefficient, S in the vicinity of the Quantum Critical Point (QCP) in the two systems. As the critical field is approached, S/T enhances in beta-YbAlB4 but is drastically reduced in YbRh2Si2. While in the former system, the ratio of thermopower-to-specific heat remains constant, it drastically drops near the QCP in YbRh2Si2. In both systems, on the other hand, the Nernst coefficient shows a diverging behavior near the QCP. The results provide a new window to the way various energy scales of the system behave and eventually vanish near a QCP.

We report on tunneling spectroscopy measurements using a Scanning Tunneling Microscope (STM) on the spin triplet superconductor Sr2RuO4. We find a negligible density of states close to the Fermi level and a fully opened gap with a value of $\Delta$=0.28 meV, which disappears at T$_c$ = 1.5 K. $\Delta$ is close to the result expected from weak coupling BCS theory ($\Delta_0$=1.76kBT$_c$ = 0.229 meV). Odd parity superconductivity is associated with a fully isotropic gap without nodes over a significant part of the Fermi surface.

A thorough characterization of many samples of the filled skutterudite compound PrOs4Sb12 is provided. We find that the double superconducting transition in the specific heat Tc1~1.89K and Tc2~1.72K tends to appear in samples with a large residual resistivity ratio, large specific heat jump at the superconducting transition and with the highest absolute value of the specific heat above Tc1. However, we present evidence which casts doubt on the intrinsic nature of the double superconducting transition. The ratio of the two specific heat jumps \Delta C(Tc1)/\Delta C(Tc2) shows a wide range of values on crystals from different batches but also within the same batch. This ratio was strongly reduced by polishing a sample down to 120um. Remarkably, three samples exhibit a single sharp transition of ~15mK in width at Tc~1.7K. The normalized specific heat jump (C-Cnormal)/Cnormal at Tc of two of them is higher than ~32% so larger than the sum of the two specific heat jumps when a double transition exists. As an evidence of better quality, the slope in the transition is at least two time steeper. We discuss the origins of the double transition; in particular we consider, based on X-ray diffraction results, a scenario involving Pr-vacancies. The superconducting phase diagram under magnetic field of a sample with a single transition is fitted with a two-band model taking into account the good values for the gap as deduced from thermal conductivity measurements., Comment: 10 pages, 9 figures, 2 tables, submitted to Physical review B

We report measurements of the temperature dependence of both in-plane and out-of-plane penetration depths ($\lambda_a$ and $\lambda_c$ respectively) in 2\textit{H}-NbSe$_2$. Measurements were made with a radio-frequency tunnel diode oscillator circuit at temperatures down to 100 mK. Analysis of the anisotropic superfluid density shows that a reduced energy gap is located on one or more of the quasi-two-dimensional Nb Fermi surface sheets rather than on the Se sheet, in contrast to some previous reports. This result suggests that the gap structure is not simply related to the weak electron-phonon coupling on the Se sheet and is therefore important for microscopic models of anisotropic superconductivity in this compound., Comment: 4 pages, Revtex

The interplay of magnetism and unconventional superconductivity (d singlet wave or p triplet wave) in strongly correlated electronic system (SCES) is discussed with recent examples found in heavy fermion compounds. A short presentation is given on the formation of the heavy quasiparticle with the two sources of a local and intersite enhancement for the effective mass. Two cases of the coexistence or repulsion of antiferromagnetism and superconductivity are given with CeIn3 and CeCoIn5. A spectacular example is the emergence of superconductivity in relatively strong itinerant ferromagnets UGe2 and URhGe. The impact of heavy fermion matter among other SCES as organic conductor or high Tc oxide is briefly pointed out., Comment: 22pages, 15 figures

The pressure dependence of the critical temperature $T_c$ and upper critical field $H_{c2}(T)$ has been measured up to 19 GPa in the layered superconducting material 2H-NbSe$_2$. Relating the behavior of $H_{c2}(T)$ to Fermi surface parameters, we find that the electron phonon coupling of the 2D Nb 4d derived bands shows a peak at 5 GPa when the charge density wave (CDW) order is suppressed. On the other hand, $T_c(P)$ shows a bell shaped curve with a maximum at 10.5 GPa, well above the pressure for the suppression of the CDW order. Changes in the band structure produce this shift in the maximum of $T_c(P)$, demonstrating that 2H-NbSe$_2$ shows important differences with respect to other compounds where $T_c$ has a maximum in the temperature-density phase diagram shaped by the suppression of another, non-superconducting, ground state., Comment: 5 pages, 4 figures. Small changes in discussion. Typos corrected

We present measurements of H$_{c2}(T)$ under pressure in MgB$_2$ and in YNi$_2$B$_2$C. The changes in the shape of H$_{c2}(T)$ are interpreted within current models and show the evolution of the main Fermi surface velocities $v_F$ and electron-phonon coupling parameters $\lambda$ with pressure. In MgB$_2$ the electron-phonon coupling strength of the nearly two dimensional $\sigma$ band, responsible for the high critical temperature, is more affected by pressure than the $\pi$ band coupling, and the hole doping of the $\sigma$ band decreases. In YNi$_2$B$_2$C, the peculiar positive curvature of H$_{c2}(T)$ is weakened by pressure., Comment: 5 pages, 5 figures

The pressure-temperature phase diagrams of the heavy fermion antiferromagnet CeRhIn$_5$ and the heavy fermion superconductor CeCoIn$_5$ have been studied under hydrostatic pressure by ac calorimetry and ac susceptibility measurements using diamond anvil cells with argon as pressure medium. In CeRhIn$_5$, the use of a highly hydrostatic pressure transmitting medium allows for a clean simultaneous determination by a bulk probe of the antiferromagnetic and superconducting transitions. We compare our new phase diagram with the previous ones, discuss the nature (first or second order) of the various lines, and the coexistence of antiferromagnetic order and superconductivity. The link between the collaps of the superconducting heat anomaly and the broadening of the antiferromagnetic transition points to an inhomogeneous appearence of superconductivity below $P_c \approx 1.95$ GPa. Homogeneous bulk superconductivity is only observed above this critical pressure. We present a detailed analysis of the influence of pressure inomogeneities on the specific heat anomalies which emphasizes that the observed broadening of the transitions near $P_c$ is connected with the first order transition. For CeCoIn$_5$ we show that the large specific heat anomaly observed at $T_c$ at ambient pressure is suppressed linearly at least up to 3 GPa.

We present new measurements of the specific heat of the heavy fermion superconductor PrOs4Sb12, on a sample which exhibits two sharp distinct anomalies at Tc1= 1.89K and Tc2= 1.72K. They are used to draw a precise magnetic field-temperature superconducting phase diagram of PrOs4Sb12 down to 350 mK. We discuss the superconducting phase diagram of PrOs4Sb12 and its possible relation with an unconventional superconducting order parameter. We give a detailed analysis of Hc2(T), which shows paramagnetic limitation (a support for even parity pairing) and multiband effects.

We present transport and specific heat measurements on high quality single crystals of UPt$_3$ before and after irradiation by high energy electrons. We observe a strong dependence of the critical temperature with the sample thickness. The dramatic effects of the irradiation on the specific heat in the superconducting state can then be simply explained in terms of an inhomogeneous distribution of superconducting transition temperatures. The question of the failure of the "universal limit" in the heat transport of UPt3 is reexamined, and the conditions for a clean experimental test are established., Comment: 6 pages 4 figures. submitted to J Low Temp. Phys

We present scanning tunneling spectroscopy and microscopy measurements at low temperatures in the borocarbide materials RNi2B2C (R=Y, Lu). The characteristic strong coupling structure due to the pairing interaction is unambiguously resolved in the superconducting density of states. It is located at the superconducting gap plus the energy corresponding to a phonon mode identified in previous neutron scattering experiments. These measurements also show that this mode is coupled to the electrons through a highly anisotropic electron-phonon interaction originated by a nesting feature of the Fermi surface. Our experiments, from which we can extract a large electron-phonon coupling parameter lambda (between 0.5 and 0.8), demonstrate that this anisotropic electron-phonon coupling has an essential contribution to the pairing interaction. The tunneling spectra show an anisotropic s-wave superconducting gap function., Comment: 5 pages, 3 figures

We present new measurements about the tunneling conductance in the borocarbide superconductor TmNi$_2$B$_2$C. The results show a very good agreement with weak coupling BCS theory, without any lifetime broadening parameter, over the whole sample surface. We detect no particular change of the tunneling spectroscopy below 1.5K, when both the antiferromagnetic (AF) phase and the superconducting order coexist., Comment: Submitted to Phys. Rev. B, Rapid Communications

We discuss a model based on a field-induced mixture of two odd-parity irreducible representations to explain the unusual features of Hc2(T) in the heavy fermion compound UBe13. We compare its predictions with recent pressure measurements as well as with the most prominent theoretical models which have been proposed up to now., Comment: 19 pages, 4 figures, submitted to J. Low Temp. Phys

We present new measurements of the thermal conductivity of UPt3 down to very low temperatures (16mK) and under magnetic fields (up to 4 T) which cover all the superconducting phases of UPt3. The measurements in zero field are compared with recent theoretical predictions for the thermal conductivity, which is dominated by impurity states at the lowest temperatures studied. The measurements under magnetic field at low temperatures are surprising since they don't show the expected low field square root dependence. The discontinuity of d kappa/dT at Tc changes drastically when passing from the high field low temperature C phase to the low field high temperature A phase : this is related to the change of the symmetry of the superconducting order parameter when crossing the A - C phase transition., Comment: 21 pages, 9 Figures, Latex, to be published in Journal of Low Temperature Physics