Magnetic-field-sensitive charge density waves in the superconductor UTe2.

The intense interest in triplet superconductivity partly stems from theoretical predictions of exotic excitations such as non-Abelian Majorana modes, chiral supercurrents and half-quantum vortices1-4. However, fundamentally new and unexpected states may emerge when triplet superconductivity appears in a strongly correlated system. Here we use scanning tunnelling microscopy to reveal an unusual charge-density-wave (CDW) order in the heavy-fermion triplet superconductor UTe2 (refs. 5-8). Our high-resolution maps reveal a multi-component incommensurate CDW whose intensity gets weaker with increasing field, with the CDW eventually disappearing at the superconducting critical field Hc2. To understand the phenomenology of this unusual CDW, we construct a Ginzburg-Landau theory for a uniform triplet superconductor coexisting with three triplet pair-density-wave states. This theory gives rise to daughter CDWs that would be sensitive to magnetic field owing to their origin in a pair-density-wave state and provides a possible explanation for our data. Our discovery of a CDW state that is sensitive to magnetic fields and strongly intertwined with superconductivity provides important information for understanding the order parameters of UTe2.

Detection of a pair density wave state in UTe2.

Spin-triplet topological superconductors should exhibit many unprecedented electronic properties, including fractionalized electronic states relevant to quantum information processing. Although UTe2 may embody such bulk topological superconductivity1-11, its superconductive order parameter Δ(k) remains unknown12. Many diverse forms for Δ(k) are physically possible12 in such heavy fermion materials13. Moreover, intertwined14,15 density waves of spin (SDW), charge (CDW) and pair (PDW) may interpose, with the latter exhibiting spatially modulating14,15 superconductive order parameter Δ(r), electron-pair density16-19 and pairing energy gap17,20-23. Hence, the newly discovered CDW state24 in UTe2 motivates the prospect that a PDW state may exist in this material24,25. To search for it, we visualize the pairing energy gap with µeV-scale energy resolution using superconductive scanning tunnelling microscopy (STM) tips26-31. We detect three PDWs, each with peak-to-peak gap modulations of around 10 µeV and at incommensurate wavevectors Pi=1,2,3 that are indistinguishable from the wavevectors Qi=1,2,3 of the prevenient24 CDW. Concurrent visualization of the UTe2 superconductive PDWs and the non-superconductive CDWs shows that every Pi:Qi pair exhibits a relative spatial phase δϕ ≈ π. From these observations, and given UTe2 as a spin-triplet superconductor12, this PDW state should be a spin-triplet PDW24,25. Although such states do exist32 in superfluid 3He, for superconductors, they are unprecedented.

Chiral superconductivity in heavy-fermion metal UTe2.

Spin-triplet superconductors are condensates of electron pairs with spin 1 and an odd-parity wavefunction1. An interesting manifestation of triplet pairing is the chiral p-wave state, which is topologically non-trivial and provides a natural platform for realizing Majorana edge modes2,3. However, triplet pairing is rare in solid-state systems and has not been unambiguously identified in any bulk compound so far. Given that pairing is usually mediated by ferromagnetic spin fluctuations, uranium-based heavy-fermion systems containing f-electron elements, which can harbour both strong correlations and magnetism, are considered ideal candidates for realizing spin-triplet superconductivity4. Here we present scanning tunnelling microscopy studies of the recently discovered heavy-fermion superconductor UTe2, which has a superconducting transition temperature of 1.6 kelvin5. We find signatures of coexisting Kondo effect and superconductivity that show competing spatial modulations within one unit cell. Scanning tunnelling spectroscopy at step edges reveals signatures of chiral in-gap states, which have been predicted to exist at the boundaries of topological superconductors. Combined with existing data that indicate triplet pairing in UTe2, the presence of chiral states suggests that UTe2 is a strong candidate for chiral-triplet topological superconductivity.

Probing FeSi, a d-electron topological Kondo insulator candidate, with magnetic field, pressure, and microwaves.

Recently, evidence for a conducting surface state (CSS) below 19 K was reported for the correlated d-electron small gap semiconductor FeSi. In the work reported herein, the CSS and the bulk phase of FeSi were probed via electrical resistivity ρ measurements as a function of temperature T, magnetic field B to 60 T, and pressure P to 7.6 GPa, and by means of a magnetic field-modulated microwave spectroscopy (MFMMS) technique. The properties of FeSi were also compared with those of the Kondo insulator SmB6 to address the question of whether FeSi is a d-electron analogue of an f-electron Kondo insulator and, in addition, a "topological Kondo insulator" (TKI). The overall behavior of the magnetoresistance of FeSi at temperatures above and below the onset temperature TS = 19 K of the CSS is similar to that of SmB6. The two energy gaps, inferred from the ρ(T) data in the semiconducting regime, increase with pressure up to about 7 GPa, followed by a drop which coincides with a sharp suppression of TS. Several studies of ρ(T) under pressure on SmB6 reveal behavior similar to that of FeSi in which the two energy gaps vanish at a critical pressure near the pressure at which TS vanishes, although the energy gaps in SmB6 initially decrease with pressure, whereas in FeSi they increase with pressure. The MFMMS measurements showed a sharp feature at TS ≈ 19 K for FeSi, which could be due to ferromagnetic ordering of the CSS. However, no such feature was observed at TS ≈ 4.5 K for SmB6.

Resonant Ultrasound Spectroscopy for Irregularly Shaped Samples and Its Application to Uranium Ditelluride.

Resonant ultrasound spectroscopy (RUS) is a powerful technique for measuring the full elastic tensor of a given material in a single experiment. Previously, this technique was practically limited to regularly shaped samples such as rectangular parallelepipeds, spheres, and cylinders [W. M. Visscher et al. J. Acoust. Soc. Am. 90, 2154 (1991)JASMAN0001-496610.1121/1.401643]. We demonstrate a new method for determining the elastic moduli of irregularly shaped samples, extending the applicability of RUS to a much larger set of materials. We apply this new approach to the recently discovered unconventional superconductor UTe_{2} and provide its elastic tensor at both 300 and 4 kelvin.

Isoelectronic perturbations to f-d-electron hybridization and the enhancement of hidden order in URu2Si2.

Electrical resistivity measurements were performed on single crystals of URu2-x Os x Si2 up to x = 0.28 under hydrostatic pressure up to P = 2 GPa. As the Os concentration, x, is increased, 1) the lattice expands, creating an effective negative chemical pressure Pch(x); 2) the hidden-order (HO) phase is enhanced and the system is driven toward a large-moment antiferromagnetic (LMAFM) phase; and 3) less external pressure Pc is required to induce the HO→LMAFM phase transition. We compare the behavior of the T(x, P) phase boundary reported here for the URu2-x Os x Si2 system with previous reports of enhanced HO in URu2Si2 upon tuning with P or similarly in URu2-x Fe x Si2 upon tuning with positive Pch(x). It is noteworthy that pressure, Fe substitution, and Os substitution are the only known perturbations that enhance the HO phase and induce the first-order transition to the LMAFM phase in URu2Si2 We present a scenario in which the application of pressure or the isoelectronic substitution of Fe and Os ions for Ru results in an increase in the hybridization of the U-5f-electron and transition metal d-electron states which leads to electronic instability in the paramagnetic phase and the concurrent formation of HO (and LMAFM) in URu2Si2 Calculations in the tight-binding approximation are included to determine the strength of hybridization between the U-5f-electron states and the d-electron states of Ru and its isoelectronic Fe and Os substituents in URu2Si2.

From hidden order to antiferromagnetism: Electronic structure changes in Fe-doped URu2Si2.

In matter, any spontaneous symmetry breaking induces a phase transition characterized by an order parameter, such as the magnetization vector in ferromagnets, or a macroscopic many-electron wave function in superconductors. Phase transitions with unknown order parameter are rare but extremely appealing, as they may lead to novel physics. An emblematic and still unsolved example is the transition of the heavy fermion compound [Formula: see text] (URS) into the so-called hidden-order (HO) phase when the temperature drops below [Formula: see text] K. Here, we show that the interaction between the heavy fermion and the conduction band states near the Fermi level has a key role in the emergence of the HO phase. Using angle-resolved photoemission spectroscopy, we find that while the Fermi surfaces of the HO and of a neighboring antiferromagnetic (AFM) phase of well-defined order parameter have the same topography, they differ in the size of some, but not all, of their electron pockets. Such a nonrigid change of the electronic structure indicates that a change in the interaction strength between states near the Fermi level is a crucial ingredient for the HO to AFM phase transition.

A review of UTe2at high magnetic fields.

Uranium ditelluride (UTe2) is recognized as a host material to unconventional spin-triplet superconductivity, but it also exhibits a wealth of additional unusual behavior at high magnetic fields. One of the most prominent signatures of the unconventional superconductivity is a large and anisotropic upper critical field that exceeds the paramagnetic limit. This superconductivity survives to 35 T and is bounded by a discontinuous magnetic transition, which itself is also field-direction-dependent. A different, reentrant superconducting phase emerges only on the high-field side of the magnetic transition, in a range of angles between the crystallographicbandcaxes. This review discusses the current state of knowledge of these high-field phases, the high-field behavior of the heavy fermion normal state, and other phases that are stabilized by applied pressure.

Revealing a 3D Fermi Surface Pocket and Electron-Hole Tunneling in UTe_{2} with Quantum Oscillations.

Spin triplet superconductor UTe_{2} is widely believed to host a quasi-two-dimensional Fermi surface, revealed by first-principles calculations, photoemission, and quantum oscillation measurements. An outstanding question still remains as to the existence of a three-dimensional Fermi surface pocket, which is crucial for our understanding of the exotic superconducting and topological properties of UTe_{2}. This 3D Fermi surface pocket appears in various theoretical models with different physics origins, but has not been unambiguously detected in experiment. Here for the first time we provide concrete evidence for a relatively isotropic, small Fermi surface pocket of UTe_{2} via quantum oscillation measurements. In addition, we observed high frequency quantum oscillations corresponding to electron-hole tunneling between adjacent electron and hole pockets. The coexistence of 2D and 3D Fermi surface pockets, as well as the breakdown orbits, provide a test bed for theoretical models and aid the realization of a unified understanding of the superconducting state of UTe_{2} from the first-principles approach.

From antiferromagnetic and hidden order to Pauli paramagnetism in UM 2Si2 compounds with 5f electron duality.

Using inelastic X-ray scattering beyond the dipole limit and hard X-ray photoelectron spectroscopy we establish the dual nature of the U [Formula: see text] electrons in U[Formula: see text] (M = Pd, Ni, Ru, Fe), regardless of their degree of delocalization. We have observed that the compounds have in common a local atomic-like state that is well described by the U [Formula: see text] configuration with the [Formula: see text] and [Formula: see text] quasi-doublet symmetry. The amount of the U 5[Formula: see text] configuration, however, varies considerably across the U[Formula: see text] series, indicating an increase of U 5f itineracy in going from M = Pd to Ni to Ru and to the Fe compound. The identified electronic states explain the formation of the very large ordered magnetic moments in [Formula: see text] and [Formula: see text], the availability of orbital degrees of freedom needed for the hidden order in [Formula: see text] to occur, as well as the appearance of Pauli paramagnetism in [Formula: see text] A unified and systematic picture of the U[Formula: see text] compounds may now be drawn, thereby providing suggestions for additional experiments to induce hidden order and/or superconductivity in U compounds with the tetragonal body-centered [Formula: see text] structure.

Effect of the Interlayer Ordering on the Fermi Surface of Kagome Superconductor CsV_{3}Sb_{5} Revealed by Quantum Oscillations.

The connection between unconventional superconductivity and charge density waves (CDWs) has intrigued the condensed matter community and found much interest in the recently discovered superconducting Kagome family of AV_{3}Sb_{5} (A=K, Cs, Rb). X-ray diffraction and Raman spectroscopy measurements established that the CDW order in CsV_{3}Sb_{5} comprises of a 2×2×4 structure with stacking of layers in a star-of-David (SD) and inverse-star-of-David (ISD) pattern along the c-axis direction. Such interlayer ordering will induce a vast normalization of the electronic ground state; however, it has not been observed in Fermi surface measurements. Here we report quantum oscillations of CsV_{3}Sb_{5} using tunnel diode oscillator frequency measurements. We observed a large number of frequencies, many of which were not reported. The number of frequencies cannot be explained by DFT calculations when only SD or ISD distortion is considered. Instead, our results are consistent with calculations when interlayer ordering is taken into account, providing strong evidence that the CDW phase of CsV_{3}Sb_{5} has complicated structure distortion which in turn has dramatic effects on the Fermi surface properties.

Evidence for a conducting surface ground state in high-quality single crystalline FeSi.

We report anomalous physical properties of high-quality single-crystalline FeSi over a wide temperature range of 1.8-400 K. The electrical resistivity ρ(T) can be described by activated behavior with an energy gap Δ = 57 meV between 150 and 67 K, below which the estimated energy gap is significantly smaller. The magneto-resistivity and Hall coefficient change sign in the vicinity of 67 K, suggesting a change of dominant charge carriers. At ∼19 K, ρ(T) undergoes a cross-over from semiconducting to metallic behavior which is very robust against external magnetic fields. The low-temperature metallic conductivity depends strongly on the width/thickness of the sample. In addition, no indication of a bulk-phase transition or onset of magnetic order is found down to 2 K from specific heat and magnetic susceptibility measurements. The measurements are consistent with one another and point to complex electronic transport behavior that apparently involves a conducting surface state in FeSi at low temperatures, suggesting the possibility that FeSi is a 3D topological insulator.

Low Energy Band Structure and Symmetries of UTe_{2} from Angle-Resolved Photoemission Spectroscopy.

The compound UTe_{2} has recently been shown to realize spin triplet superconductivity from a nonmagnetic normal state. This has sparked intense research activity, including theoretical analyses that suggest the superconducting order parameter to be topologically nontrivial. However, the underlying electronic band structure is a critical factor for these analyses, and remains poorly understood. Here, we present high resolution angle-resolved photoemission measurements covering multiple planes in the 3D Brillouin zone of UTe_{2}, revealing distinct Fermi-level features from two orthogonal quasi-one-dimensional light electron bands and one heavy band. The electronic symmetries are evaluated in comparison with numerical simulations, and the resulting picture is discussed as a platform for unconventional many-body order.

Phase diagram of URu2-x Fe x Si2 in high magnetic fields.

Electrical transport measurements were performed on URu2 - x Fe x Si2 single-crystal specimens in high magnetic fields up to 45 T (DC fields) and 60 T (pulsed fields). We observed a systematic evolution of the critical fields for both the hidden-order (HO) and large-moment antiferromagnetic (LMAFM) phases and established the 3D phase diagram of T-H-x In the HO phase, H/H0 scales with T/T0 and collapses onto a single curve. However, in the LMAFM phase, this single scaling relation is not satisfied. Within a certain range of x values, the HO phase reenters after the LMAFM phase is suppressed by the magnetic field, similar to the behavior observed for URu2Si2 within a certain range of pressures.

Phase diagram and thermal expansion measurements on the system URu2-xFexSi2.

Thermal expansion, electrical resistivity, magnetization, and specific heat measurements were performed on URu2-xFexSi2 single crystals for various values of Fe concentration x in both the hidden-order (HO) and large-moment antiferromagnetic (LMAFM) regions of the phase diagram. Our results show that the paramagnetic (PM) to HO and LMAFM phase transitions are manifested differently in the thermal expansion coefficient. The uniaxial pressure derivatives of the HO/LMAFM transition temperature T0 change dramatically when crossing from the HO to the LMAFM phase. The energy gap also changes consistently when crossing the phase boundary. In addition, for Fe concentrations at xc ≈ 0.1, we observe two features in the thermal expansion upon cooling, one that appears to be associated with the transition from the PM to the HO phase and another one at lower temperature that may be due to the transition from the HO to the LMAFM phase.

A single crystal study of Kagome metals U2Mn3Ge and U2Fe3Ge.

Single crystals of U2Mn3Ge and U2Fe3Ge with a Kagome lattice structure were synthesized using a high-temperature self-flux crystal growth method. The physical properties of these crystals were characterized through measurements of resistivity, magnetism, and specific heat. U2Fe3Ge exhibits ferromagnetic ground state and anomalous Hall effect, and U2Mn3Ge demonstrates a complex magnetic structure. Both compounds exhibit large Sommerfeld coefficient, indicating coexistence of heavy Fermion behaviour with magnetism. Our results suggest that this U2TM3Ge (TM = Mn, Fe, Co) family is a promising platform to investigate the interplay of magnetism, Kondo physics and the Kagome lattice.

Breakdown of the scaling relation of anomalous Hall effect in Kondo lattice ferromagnet USbTe.

The interaction between strong correlation and Berry curvature is an open territory of in the field of quantum materials. Here we report large anomalous Hall conductivity in a Kondo lattice ferromagnet USbTe which is dominated by intrinsic Berry curvature at low temperatures. However, the Berry curvature induced anomalous Hall effect does not follow the scaling relation derived from Fermi liquid theory. The onset of the Berry curvature contribution coincides with the Kondo coherent temperature. Combined with ARPES measurement and DMFT calculations, this strongly indicates that Berry curvature is hosted by the flat bands induced by Kondo hybridization at the Fermi level. Our results demonstrate that the Kondo coherence of the flat bands has a dramatic influence on the low temperature physical properties associated with the Berry curvature, calling for new theories of scaling relations of anomalous Hall effect to account for the interaction between strong correlation and Berry curvature.

An unusual chemoselective hydrogenation of quinoline compounds using supported gold catalysts.

The pursuit of modern sustainable chemistry has stimulated the development of innovative catalytic processes that enable chemical transformations to be performed under mild and clean conditions with high efficiency. Herein, we report that gold nanoparticles supported on TiO(2) catalyze the chemoselective hydrogenation of functionalized quinolines with H(2) under mild reaction conditions. Our results point toward an unexpected role for quinolines in gold-mediated hydrogenation reactions, namely that of promoter; this is in stark contrast to what prevails in the traditional noble metal Pd-, Pt-, and Ru-based catalyst systems, in which quinolines and their derivatives typically act as poisons. As a result of the remarkable promotional effect of quinoline molecules to H(2) activation over supported gold, the transformation can proceed smoothly under very mild conditions (even at temperatures as low as 25 °C). Of practical significance is that various synthetically useful functional groups including halogens, ketone, and olefin remain intact during the hydrogenation of quinolines. Moreover, the protocol also shows promise for the regiospecific hydrogenation of the heterocyclic ring of a variety of other biologically important heteroaromatic nitrogen compounds, such as isoquinoline, acridine, and 7,8-benzoquinoline, in a facile manner. Apart from its importance in catalytic hydrogenation, we believe that this intriguing self-promoted effect by reactant molecules may have fundamental implications for the broad field of gold catalysis and form the basis for development of new catalytic procedures for other key transformations.

Comparison of Two Different Synthesis Methods of Single Crystals of Superconducting Uranium Ditelluride.

Single crystal specimens of the actinide compound uranium ditelluride, UTe2, are of great importance to the study and characterization of its dramatic unconventional superconductivity, believed to entail spin-triplet electron pairing. A variety in the superconducting properties of UTe2 reported in the literature indicates that discrepancies between synthesis methods yield crystals with different superconducting properties, including the absence of superconductivity entirely. This protocol describes a process to synthesize crystals that exhibit superconductivity via chemical vapor transport, which has consistently exhibited a superconducting critical temperature of 1.6 K and a double transition indicative of a multi-component order parameter. This is compared to a second protocol that is used to synthesize crystals via the molten metal flux growth technique, which produces samples that are not bulk superconductors. Differences in the crystal properties are revealed through a comparison of structural, chemical, and electronic property measurements, showing that the most dramatic disparity occurs in the low-temperature electrical resistance of the samples.

Anomalous normal fluid response in a chiral superconductor UTe2.

Chiral superconductors have been proposed as one pathway to realize Majorana normal fluid at its boundary. However, the long-sought 2D and 3D chiral superconductors with edge and surface Majorana normal fluid are yet to be conclusively found. Here, we report evidence for a chiral spin-triplet pairing state of UTe2 with surface normal fluid response. The microwave surface impedance of the UTe2 crystal was measured and converted to complex conductivity, which is sensitive to both normal and superfluid responses. The anomalous residual normal fluid conductivity supports the presence of a significant normal fluid response. The superfluid conductivity follows the temperature behavior predicted for an axial spin-triplet state, which is further narrowed down to a chiral spin-triplet state with evidence of broken time-reversal symmetry. Further analysis excludes trivial origins for the observed normal fluid response. Our findings suggest that UTe2 can be a new platform to study exotic topological excitations in higher dimension.