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.

Perfect Andreev reflection due to the Klein paradox in a topological superconducting state.

In 1928, Dirac proposed a wave equation to describe relativistic electrons1. Shortly afterwards, Klein solved a simple potential step problem for the Dirac equation and encountered an apparent paradox: the potential barrier becomes transparent when its height is larger than the electron energy. For massless particles, backscattering is completely forbidden in Klein tunnelling, leading to perfect transmission through any potential barrier2,3. The recent advent of condensed-matter systems with Dirac-like excitations, such as graphene and topological insulators, has opened up the possibility of observing Klein tunnelling experimentally4-6. In the surface states of topological insulators, fermions are bound by spin-momentum locking and are thus immune from backscattering, which is prohibited by time-reversal symmetry. Here we report the observation of perfect Andreev reflection in point-contact spectroscopy-a clear signature of Klein tunnelling and a manifestation of the underlying 'relativistic' physics of a proximity-induced superconducting state in a topological Kondo insulator. Our findings shed light on a previously overlooked aspect of topological superconductivity and can serve as the basis for a unique family of spintronic and superconducting devices, the interface transport phenomena of which are completely governed by their helical topological states.

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.

Observation of the Superconducting Proximity Effect from Surface States in SmB_{6}/YB_{6} Thin Film Heterostructures via Terahertz Spectroscopy.

The ac conduction of epitaxially grown SmB_{6} thin films and superconducting heterostructures of SmB_{6}/YB_{6} are investigated via time-domain terahertz spectroscopy. A two-channel model of thickness-dependent bulk states and thickness-independent surface states accurately describes the measured conductance of bare SmB_{6} thin films, demonstrating the presence of surface states in SmB_{6}. While the observed reductions in the simultaneously measured superconducting gap, transition temperature, and superfluid density of SmB_{6}/YB_{6} heterostructures relative to bare YB_{6} indicate the penetration of proximity-induced superconductivity into the SmB_{6} overlayer; the corresponding SmB_{6}-thickness independence between different heterostructures indicates that the induced superconductivity is predominantly confined to the interface surface state of the SmB_{6}. This study demonstrates the ability of terahertz spectroscopy to probe proximity-induced superconductivity at an interface buried within a heterostructure, and our results show that SmB_{6} behaves as a predominantly insulating bulk surrounded by conducting surface states in both the normal and induced-superconducting states in both terahertz and dc responses, which is consistent with the topological Kondo insulator picture.

Optical signatures of multifold fermions in the chiral topological semimetal CoSi.

We report the optical conductivity in high-quality crystals of the chiral topological semimetal CoSi, which hosts exotic quasiparticles known as multifold fermions. We find that the optical response is separated into several distinct regions as a function of frequency, each dominated by different types of quasiparticles. The low-frequency intraband response is captured by a narrow Drude peak from a high-mobility electron pocket of double Weyl quasiparticles, and the temperature dependence of the spectral weight is consistent with its Fermi velocity. By subtracting the low-frequency sharp Drude and phonon peaks at low temperatures, we reveal two intermediate quasilinear interband contributions separated by a kink at 0.2 eV. Using Wannier tight-binding models based on first-principle calculations, we link the optical conductivity above and below 0.2 eV to interband transitions near the double Weyl fermion and a threefold fermion, respectively. We analyze and determine the chemical potential relative to the energy of the threefold fermion, revealing the importance of transitions between a linearly dispersing band and a flat band. More strikingly, below 0.1 eV our data are best explained if spin-orbit coupling is included, suggesting that at these energies, the optical response is governed by transitions between a previously unobserved fourfold spin-3/2 node and a Weyl node. Our comprehensive combined experimental and theoretical study provides a way to resolve different types of multifold fermions in CoSi at different energy. More broadly, our results provide the necessary basis to interpret the burgeoning set of optical and transport experiments in chiral topological semimetals.

Multiple Charge Density Waves and Superconductivity Nucleation at Antiphase Domain Walls in the Nematic Pnictide Ba_{1-x}Sr_{x}Ni_{2}As_{2}.

How superconductivity interacts with charge or nematic order is one of the great unresolved issues at the center of research in quantum materials. Ba_{1-x}Sr_{x}Ni_{2}As_{2} (BSNA) is a charge ordered pnictide superconductor recently shown to exhibit a sixfold enhancement of superconductivity due to nematic fluctuations near a quantum phase transition (at x_{c}=0.7) [1]. The superconductivity is, however, anomalous, with the resistive transition for 0.4

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.

Unconventional Charge Density Wave Order in the Pnictide Superconductor Ba(Ni_{1-x}Co_{x})_{2}As_{2}.

Ba(Ni_{1-x}Co_{x})_{2}As_{2} is a structural homologue of the pnictide high temperature superconductor, Ba(Fe_{1-x}Co_{x})_{2}As_{2}, in which the Fe atoms are replaced by Ni. Superconductivity is highly suppressed in this system, reaching a maximum T_{c}=2.3 K, compared to 24 K in its iron-based cousin, and the origin of this T_{c} suppression is not known. Using x-ray scattering, we show that Ba(Ni_{1-x}Co_{x})_{2}As_{2} exhibits a unidirectional charge density wave (CDW) at its triclinic phase transition. The CDW is incommensurate, exhibits a sizable lattice distortion, and is accompanied by the appearance of α Fermi surface pockets in photoemission [B. Zhou et al., Phys. Rev. B 83, 035110 (2011)PRBMDO1098-012110.1103/PhysRevB.83.035110], suggesting it forms by an unconventional mechanism. Co doping suppresses the CDW, paralleling the behavior of antiferromagnetism in iron-based superconductors. Our study demonstrates that pnictide superconductors can exhibit competing CDW order, which may be the origin of T_{c} suppression in this system.

Law and Disorder: Special Stacking Units-Building the Intergrowth Ce6Co5Ge16.

A new structure type of composition Ce6Co5Ge16 was grown out of a molten Sn flux. Ce6Co5Ge16 crystallizes in the orthorhombic space group Cmcm, with highly anisotropic lattice parameters of a = 4.3293(5) Å, b = 55.438(8) Å, and c = 4.3104(4) Å. The resulting single crystals were characterized by X-ray diffraction, and the magnetic and transport properties are presented. The Sn-stabilized structure of Ce6Co5Ge16 is based on the stacking of disordered Ce cuboctahedra and is an intergrowth of existing structure types including AlB2, BaNiSn3, and AuCu3. The stacking of structural subunits has previously been shown to be significant in the fields of superconductivity, quantum materials, and optical materials. Herein, we present the synthesis, characterization, and complex magnetic behavior of Ce6Co5Ge16 at low temperature, including three distinct magnetic transitions.

Metastable Layered Cobalt Chalcogenides from Topochemical Deintercalation.

We present a general strategy to synthesize metastable layered materials via topochemical deintercalation of thermodynamically stable phases. Through kinetic control of the deintercalation reaction, we have prepared two hypothesized metastable compounds, CoSe and CoS, with the anti-PbO type structure from the starting compounds KCo2Se2 and KCo2S2, respectively. Thermal stability, crystal structure from X-ray and neutron diffraction, magnetic susceptibility, magnetization, and electrical resistivity are studied for these new layered chalcogenides; both CoSe and CoS are found to be weak itinerant ferromagnets with Curie temperatures close to 10 K. Due to the weak van der Waals forces between the layers, CoSe is found to be a suitable host for further intercalation of guest species such as Li-ethylenediamine. From first-principles calculations, we explain why the Co chalcogenides are ferromagnets instead of superconductors as in their iron analogues. Bonding analysis of the calculated electronic density of states both explains their phase stability and predicts the limits of our deintercalation technique. Our results have broad implications for the rational design of new two-dimensional building blocks for functional materials.

Quantum Critical Quasiparticle Scattering within the Superconducting State of CeCoIn_{5}.

The thermal conductivity κ of the heavy-fermion metal CeCoIn_{5} 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 H_{c2}, κ/T is found to increase as T→0, 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 κ/T with field reveals that the electron-electron scattering (or transport mass m^{⋆}) of those unpaired electrons diverges as H→H_{c2} from below, in the same way that it does in the normal state as H→H_{c2} from above. This shows that the unpaired electrons sense the proximity of the field-tuned quantum critical point of CeCoIn_{5} at H^{⋆}=H_{c2} even from inside the superconducting state. The fact that the quantum critical scattering of the unpaired electrons is much weaker than the average scattering of all electrons in the normal state reveals a k-space correlation between the strength of pairing and the strength of scattering, pointing to a common mechanism, presumably antiferromagnetic fluctuations.

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.

Tuning bulk and surface conduction in the proposed topological Kondo insulator SmB(6).

Bulk and surface state contributions to the electrical resistance of single-crystal samples of the topological Kondo-insulator compound SmB_{6} are investigated as a function of crystal thickness and surface charge density, the latter tuned by ionic liquid gating with electrodes patterned in a Corbino disk geometry on a single (100) surface. By separately tuning bulk and surface conduction channels, we show conclusive evidence for a model with an insulating bulk and metallic surface states, with a crossover temperature that depends solely on the relative contributions of each conduction channel. The surface conductance, on the order of 100 e^{2}/h, exhibits a field-effect mobility of 133 cm^{2}/Vs and a large carrier density of ∼2×10^{14} cm^{-2}, in good agreement with recent photoemission results. With the ability to gate modulate surface conduction by more than 25%, this approach provides promise for both fundamental and applied studies of gate-tuned devices structured on bulk crystal samples.

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.

Biofunctionalized gadolinium-containing prussian blue nanoparticles as multimodal molecular imaging agents.

Molecular imaging agents enable the visualization of phenomena with cellular and subcellular level resolutions and therefore have enormous potential in improving disease diagnosis and therapy assessment. In this article, we describe the synthesis, characterization, and demonstration of core-shell, biofunctionalized, gadolinium-containing Prussian blue nanoparticles as multimodal molecular imaging agents. Our multimodal nanoparticles combine the advantages of MRI and fluorescence. The core of our nanoparticles consists of a Prussian blue lattice with gadolinium ions located within the lattice interstices that confer high relaxivity to the nanoparticles providing MRI contrast. The relaxivities of our nanoparticles are nearly nine times those observed for the clinically used Magnevist. The nanoparticle MRI core is biofunctionalized with a layer of fluorescently labeled avidin that enables fluorescence imaging. Biotinylated antibodies are attached to the surface avidin and confer molecular specificity to the nanoparticles by targeting cell-specific biomarkers. We demonstrate our nanoparticles as multimodal molecular imaging agents in an in vitro model consisting of a mixture of eosinophilic cells and squamous epithelial cells. Our nanoparticles specifically detect eosinophilic cells and not squamous epithelial cells, via both fluorescence imaging and MRI in vitro. These results suggest the potential of our biofunctionalized Prussian blue nanoparticles as multimodal molecular imaging agents in vivo.

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.

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.