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.

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.

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.

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.

Spin jam induced by quantum fluctuations in a frustrated magnet.

Since the discovery of spin glasses in dilute magnetic systems, their study has been largely focused on understanding randomness and defects as the driving mechanism. The same paradigm has also been applied to explain glassy states found in dense frustrated systems. Recently, however, it has been theoretically suggested that different mechanisms, such as quantum fluctuations and topological features, may induce glassy states in defect-free spin systems, far from the conventional dilute limit. Here we report experimental evidence for existence of a glassy state, which we call a spin jam, in the vicinity of the clean limit of a frustrated magnet, which is insensitive to a low concentration of defects. We have studied the effect of impurities on SrCr9pGa12-9pO19 [SCGO(p)], a highly frustrated magnet, in which the magnetic Cr(3+) (s = 3/2) ions form a quasi-2D triangular system of bipyramids. Our experimental data show that as the nonmagnetic Ga(3+) impurity concentration is changed, there are two distinct phases of glassiness: an exotic glassy state, which we call a spin jam, for the high magnetic concentration region (p > 0.8) and a cluster spin glass for lower magnetic concentration (p < 0.8). This observation indicates that a spin jam is a unique vantage point from which the class of glassy states of dense frustrated magnets can be understood.

Pressure-Resistant Intermediate Valence in the Kondo Insulator SmB_{6}.

Resonant x-ray emission spectroscopy was used to determine the pressure dependence of the f-electron occupancy in the Kondo insulator SmB_{6}. Applied pressure reduces the f occupancy, but surprisingly, the material maintains a significant divalent character up to a pressure of at least 35 GPa. Thus, the closure of the resistive activation energy gap and onset of magnetic order are not driven by stabilization of an integer valent state. Over the entire pressure range, the material maintains a remarkably stable intermediate valence that can in principle support a nontrivial band structure.

Spectroscopic Determination of the Atomic f-Electron Symmetry Underlying Hidden Order in URu2Si2.

The low-temperature hidden-order state of URu2Si2 has long been a subject of intense speculation, and is thought to represent an as-yet-undetermined many-body quantum state not realized by other known materials. Here, x-ray absorption spectroscopy and high-resolution resonant inelastic x-ray scattering are used to observe electronic excitation spectra of URu2Si2, as a means to identify the degrees of freedom available to constitute the hidden-order wave function. Excitations are shown to have symmetries that derive from a correlated 5f(2) atomic multiplet basis that is modified by itinerancy. The features, amplitude, and temperature dependence of linear dichroism are in agreement with ground states that closely resemble the doublet Γ5 crystal field state of uranium.

Quantum critical scaling at the edge of Fermi liquid stability in a cuprate superconductor.

In the high-temperature cuprate superconductors, the pervasiveness of anomalous electronic transport properties suggests that violation of conventional Fermi liquid behavior is closely tied to superconductivity. In other classes of unconventional superconductors, atypical transport is well correlated with proximity to a quantum critical point, but the relative importance of quantum criticality in the cuprates remains uncertain. Here, we identify quantum critical scaling in the electron-doped cuprate material La(2-x)Ce(x)CuO(4) with a line of quantum critical points that surrounds the superconducting phase as a function of magnetic field and charge doping. This zero-temperature phase boundary, which delineates a metallic Fermi liquid regime from an extended non-Fermi liquid ground state, closely follows the upper critical field of the overdoped superconducting phase and gives rise to an expanse of distinct non-Fermi liquid behavior at finite temperatures. Together with signatures of two distinct flavors of quantum fluctuations, these facts suggest that quantum criticality plays a significant role in shaping the anomalous properties of the cuprate phase diagram.

Ambipolar surface state thermoelectric power of topological insulator Bi2Se3.

We measure gate-tuned thermoelectric power of mechanically exfoliated Bi2Se3 thin films in the topological insulator regime. The sign of the thermoelectric power changes across the charge neutrality point as the majority carrier type switches from electron to hole, consistent with the ambipolar electric field effect observed in conductivity and Hall effect measurements. Near the charge neutrality point and at low temperatures, the gate-dependent thermoelectric power follows the semiclassical Mott relation using the expected surface state density of states but is larger than expected at high electron doping, possibly reflecting a large density of states in the bulk gap. The thermoelectric power factor shows significant enhancement near the electron-hole puddle carrier density ∼0.5 × 10(12) cm(-2) per surface at all temperatures. Together with the expected reduction of lattice thermal conductivity in low-dimensional structures, the results demonstrate that nanostructuring and Fermi level tuning of three-dimensional topological insulators can be promising routes to realize efficient thermoelectric devices.

Electrostatic coupling between two surfaces of a topological insulator nanodevice.

We report on electronic transport measurements of dual-gated nanodevices of the low-carrier density topological insulator (TI) Bi_{1.5}Sb_{0.5}Te_{1.7}Se_{1.3}. In all devices, the upper and lower surface states are independently tunable to the Dirac point by the top and bottom gate electrodes. In thin devices, electric fields are found to penetrate through the bulk, indicating finite capacitive coupling between the surface states. A charging model allows us to use the penetrating electric field as a measurement of the intersurface capacitance C_{TI} and the surface state energy-density relationship µ(n), which is found to be consistent with independent angle-resolved photoemission spectroscopy measurements. At high magnetic fields, increased field penetration through the surface states is observed, strongly suggestive of the opening of a surface state band gap due to broken time-reversal symmetry.

Inhomogeneous high temperature melting and decoupling of charge density waves in spin-triplet superconductor UTe2.

Charge, spin and Cooper-pair density waves have now been widely detected in exotic superconductors. Understanding how these density waves emerge - and become suppressed by external parameters - is a key research direction in condensed matter physics. Here we study the temperature and magnetic-field evolution of charge density waves in the rare spin-triplet superconductor candidate UTe2 using scanning tunneling microscopy/spectroscopy. We reveal that charge modulations composed of three different wave vectors gradually weaken in a spatially inhomogeneous manner, while persisting to surprisingly high temperatures of 10-12 K. We also reveal an unexpected decoupling of the three-component charge density wave state. Our observations match closely to the temperature scale potentially related to short-range magnetic correlations, providing a possible connection between density waves observed by surface probes and intrinsic bulk features. Importantly, charge density wave modulations become suppressed with magnetic field both below and above superconducting Tc in a comparable manner. Our work points towards an intimate connection between hidden magnetic correlations and the origin of the unusual charge density waves in UTe2.

Orphan high field superconductivity in non-superconducting uranium ditelluride.

Reentrant superconductivity is an uncommon phenomenon in which the destructive effects of magnetic field on superconductivity are mitigated, allowing a zero-resistance state to survive under conditions that would otherwise destroy it. Typically, the reentrant superconducting region derives from a zero-field parent superconducting phase. Here, we show that in UTe2 crystals extreme applied magnetic fields give rise to an unprecedented high-field superconductor that lacks a zero-field antecedent. This high-field orphan superconductivity exists at angles offset between 29o and 42o from the crystallographic b to c axes with applied fields between 37 T and 52 T. The stability of field-induced orphan superconductivity presented in this work defies both empirical precedent and theoretical explanation and demonstrates that high-field superconductivity can exist in an otherwise non-superconducting material.

Skyrmion lattice formation and destruction mechanisms probed with TR-SANS.

Magnetic skyrmions are topologically protected, nanoscale whirls of the spin configuration that tend to form hexagonally ordered arrays. As a topologically non-trivial structure, the nucleation and annihilation of the skyrmion, as well as the interaction between skyrmions, varies from conventional magnetic systems. Recent works have suggested that the ordering kinetics in these materials occur over millisecond or longer timescales, which is unusually slow for magnetic dynamics. The current work investigates the skyrmion ordering kinetics, particularly during lattice formation and destruction, using time-resolved small angle neutron scattering (TR-SANS). Evaluating the time-resolved structure and intensity of the neutron diffraction pattern reveals the evolving real-space structure of the skyrmion lattice and the timeframe of the formation. Measurements were performed on three prototypical skyrmion materials: MnSi, (Fe,Co)Si, and Cu2OSeO3. To probe lattice formation and destruction kinetics, the systems were prepared in the stable skyrmion state, and then a square-wave magnetic field modulation was applied. The measurements show that the skyrmions quickly form ordered domains, with a significant distribution in lattice parameters, which then converge to the final structure; the results confirm the slow kinetics, with formation times between 10 ms and 99 ms. Comparisons are made between the measured formation times and the fundamental material properties, suggesting the ordering temperature, saturation magnetization and magnetocrystalline anisotropy may be driving the timeframes. Micromagnetic simulations were also performed and support a scaling of the kinetics with sample volume, a behavior which is caused by the reconciling of misaligned domains.

Topological insulator quantum dot with tunable barriers.

Thin (6-7 quintuple layer) topological insulator Bi(2)Se(3) quantum dot devices are demonstrated using ultrathin (2-4 quintuple layer) Bi(2)Se(3) regions to realize semiconducting barriers which may be tuned from ohmic to tunneling conduction via gate voltage. Transport spectroscopy shows Coulomb blockade with large charging energy >5 meV and additional features implying excited states.

Intrinsic electron-phonon resistivity of Bi2Se3 in the topological regime.

We measure the temperature-dependent carrier density and resistivity of the topological surface state of thin exfoliated Bi(2)Se(3) in the absence of bulk conduction. When the gate-tuned chemical potential is near or below the Dirac point, the carrier density is strongly temperature-dependent, reflecting thermal activation from the nearby bulk valence band, while, above the Dirac point, unipolar n-type surface conduction is observed with negligible thermal activation of bulk carriers. In this regime, linear resistivity vs temperature reflects intrinsic electron-acoustic phonon scattering. A quantitative comparison with a theoretical transport calculation including both phonon and disorder effects gives the ratio of deformation potential to Fermi velocity D/hν(F)=4.7 Å(-1). This strong phonon scattering in the Bi(2)Se(3) surface state gives intrinsic limits for the conductivity and charge carrier mobility at room temperature of ~550 µS per surface and ~10,000 cm(2)/V s.

Insulating behavior in ultrathin bismuth selenide field effect transistors.

Ultrathin (approximately three quintuple layer) field-effect transistors (FETs) of topological insulator Bi(2)Se(3) are prepared by mechanical exfoliation on 300 nm SiO(2)/Si susbtrates. Temperature- and gate-voltage-dependent conductance measurements show that ultrathin Bi(2)Se(3) FETs are n-type and have a clear OFF state at negative gate voltage, with activated temperature-dependent conductance and energy barriers up to 250 meV.

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.