Inducing superconductivity in Weyl semimetal microstructures by selective ion sputtering

Magnetoresistive-coupled transistor using the Weyl semimetal NbP

Semiconductor transistors operate by modulating the charge carrier concentration of a channel material through an electric field coupled by a capacitor. This mechanism is constrained by the fundamental transport physics and material properties of such devices-attenuation of the electric field, and limited mobility and charge carrier density in semiconductor channels. In this work, we demonstrate a new type of transistor that operates through a different mechanism. The channel material is a Weyl semimetal, NbP, whose resistivity is modulated via a magnetic field generated by an integrated superconductor. Due to the exceptionally large electron mobility of this material, which reaches over 1,000,000 cm2/Vs, and the strong magnetoresistive coupling, the transistor can generate significant transconductance amplification at nanowatt levels of power. This type of device can enable new low-power amplifiers, suitable for qubit readout operation in quantum computers.

Modulations in Superconductors: Probes of Underlying Physics

The importance of modulations is elevated to an unprecedented level, due to the delicate conditions required to bring out exotic phenomena in quantum materials, such as topological materials, magnetic materials, and superconductors. Recently, state-of-the-art modulation techniques in material science, such as electric-double-layer transistor, piezoelectric-based strain apparatus, angle twisting, and nanofabrication, have been utilized in superconductors. They not only efficiently increase the tuning capability to the broader ranges but also extend the tuning dimensionality to unprecedented degrees of freedom, including quantum fluctuations of competing phases, electronic correlation, and phase coherence essential to global superconductivity. Here, for a comprehensive review, these techniques together with the established modulation methods, such as elemental substitution, annealing, and polarization-induced gating, are contextualized. Depending on the mechanism of each method, the modulations are categorized into stoichiometric manipulation, electrostatic gating, mechanical modulation, and geometrical design. Their recent advances are highlighted by applications in newly discovered superconductors, e.g., nickelates, Kagome metals, and magic-angle graphene. Overall, the review is to provide systematic modulations in emergent superconductors and serve as the coordinate for future investigations, which can stimulate researchers in superconductivity and other fields to perform various modulations toward a thorough understanding of quantum materials.

Superconductor Vortex Spectrum Including Fermi Arc States in Time-Reversal Symmetric Weyl Semimetals

Using semiclassics to surmount the hurdle of bulk-surface inseparability, we derive the superconductor vortex spectrum in nonmagnetic Weyl semimetals and show that it stems from the Berry phase of orbits made of Fermi arcs on opposite surfaces and bulk chiral modes. Tilting the vortex transmutes it between bosonic, fermionic, and supersymmetric, produces periodic peaks in the density of states that signify novel nonlocal Majorana modes, and yields a thickness-independent spectrum at magic "magic angles." We propose (Nb,Ta)P as candidate materials and tunneling spectroscopy as the ideal experiment.

Ionic Liquid Gating of SrTiO3 Lamellas Fabricated with a Focused Ion Beam

In this work, we combine two previously incompatible techniques for defining electronic devices: shaping three-dimensional crystals by focused ion beam (FIB), and two-dimensional electrostatic accumulation of charge carriers. The principal challenge for this integration is nanometer-scale surface damage inherent to any FIB-based fabrication. We address this by using a sacrificial protective layer to preserve a selected pristine surface. The test case presented here is accumulation of 2D carriers by ionic liquid gating at the surface of a micron-scale SrTiO₃ lamella. Preservation of surface quality is reflected in superconductivity of the accumulated carriers. This technique opens new avenues for realizing electrostatic charge tuning in materials that are not available as large or exfoliatable single crystals, and for patterning the geometry of the accumulated carriers.

Ultrafast Sub-100 fs All-Optical Modulation and Efficient Third-Harmonic Generation in Weyl Semimetal Niobium Phosphide Thin Films

Since their experimental discovery in 2015, Weyl semimetals have generated a large amount of attention due their intriguing physical properties that arise from their linear electron dispersion relation and topological surface states. In particular, in the field of nonlinear (NL) optics and light harvesting, Weyl semimetals have shown outstanding performances and achieved record NL conversion coefficients. In this context, the first steps toward Weyl semimetal nanophotonics are performed here by thoroughly characterizing the linear and NL optical behavior of epitaxially grown niobium phosphide (NbP) thin films, covering the visible to the near-infrared regime of the electromagnetic spectrum. Despite the measured high linear absorption, third-harmonic generation studies demonstrate high conversion efficiencies up to 10^-4 % that can be attributed to the topological electron states at the surface of the material. Furthermore, nondegenerate pump-probe measurements with sub-10 fs pulses reveal a maximum modulation depth of ≈1%, completely decaying within 100 fs and therefore suggesting the possibility of developing all-optical switching devices based on NbP. Altogether, this work reveals the promising NL optical properties of Weyl semimetal thin films, which outperform bulk crystals of the same material, laying the grounds for nanoscale applications, enabled by top-down nanostructuring, such as light-harvesting, on-chip frequency conversion, and all-optical processing.

Superconductivity in Mo-P compounds under pressure and in double-Weyl semimetal Hex-MoP2

Based on first-principles calculations, we predict five global stable molybdenum phosphorus compounds in the pressure range of 0-300 GPa. All of them display superconductivity with different transition temperatures. Meanwhile, we find that a metastable crystal hex-MoP₂, crystallized in a noncentrosymmetric structure, is a double-Weyl semimetal and the Weyl point is in the H-K path. The long Fermi arcs and the topological surface states, which can be observed by angle-resolved photoemission spectroscopy, emerge at the (100) surface below the Fermi level. Furthermore, we find that the superconductivity in hex-MoP₂ can be enhanced by carrier doping. Due to the breaking of inversion symmetry, the unconventional spin-triplet pairing coexists with spin-singlet pairing in channel . Based on our theoretical model, there are the superconducting band gaps in both pairings. Our work provides a new platform of hex-MoP₂ for studying both topological double-Weyl semimetal and superconductivity.

Sondheimer oscillations as a probe of non-ohmic flow in WP2 crystals

As conductors in electronic applications shrink, microscopic conduction processes lead to strong deviations from Ohm's law. Depending on the length scales of momentum conserving (lMC) and relaxing (lMR) electron scattering, and the device size (d), current flows may shift from ohmic to ballistic to hydrodynamic regimes. So far, an in situ methodology to obtain these parameters within a micro/nanodevice is critically lacking. In this context, we exploit Sondheimer oscillations, semi-classical magnetoresistance oscillations due to helical electronic motion, as a method to obtain lMR even when lMR ≫ d. We extract lMR from the Sondheimer amplitude in WP2, at temperatures up to T ~ 40 K, a range most relevant for hydrodynamic transport phenomena. Our data on μm-sized devices are in excellent agreement with experimental reports of the bulk lMR and confirm that WP2 can be microfabricated without degradation. These results conclusively establish Sondheimer oscillations as a quantitative probe of lMR in micro-devices.

Tip-induced superconductivity

It is widely believed that topological superconductivity, a hitherto elusive phase of quantum matter, can be achieved by inducing superconductivity in topological materials. In search of such topological superconductors, certain topological insulators (like, Bi₂Se₃) were successfully turned into superconductors by metal-ion (Cu, Pd, Sr, Nb etc) intercalation. Superconductivity could be induced in topological materials through applying pressure as well. For example, a pressure-induced superconducting phase was found in the topological insulator Bi₂Se₃. However, in all such cases, no conclusive signature of topological superconductivity was found. In this review, we will discuss about another novel way of inducing superconductivity in a non-superconducting topological material-by creating a mesoscopic interface on the material with a non-superconducting, normal metallic tip where the mesoscopic interface becomes superconducting. Such a phase is now known as a tip-induced superconducting (TISC) phase. This was first realized on Cd₃As₂in India. Following that, a large number of other topological materials were shown to display TISC. Since the TISC phase emerges only at a confined region under a mesoscopic point contact, traditional bulk tools for characterizing superconductivity cannot be employed to detect/confirm such a phase. On the other hand, such a point contact geometry is ideal for probing the possible existence of a temperature and magnetic field dependent superconducting energy gap and a temperature and magnetic field dependent critical current. We will review the details of the experimental signatures that can be used to prove the existence of superconductivity even when the 'text-book' tests for detecting superconductivity cannot be performed. Then, we will review various systems where a TISC phase could be realized.

Theory of universal differential conductance of magnetic Weyl type-II junctions

We study the transport properties of junctions of normal and superconducting Weyl semimetal with tilted dispersion, in the presence of magnetization induced by magnetic strips. The sub gap tunnelling conductance shows robust signatures in the presence of different orientation and strength of magnetization of the magnetic strips. We obtain the analytical results for the normal-magnetic-superconducting junction in the thin barrier limit and demonstrate that these results have no analogues to their conventional counterparts and junctions with Dirac electrons in two-dimensions. We discuss possible experimental setups to test our theoretical predictions.

Micro-Scale Device-An Alternative Route for Studying the Intrinsic Properties of Solid-State Materials: The Case of Semiconducting TaGeIr

An efficient application of a material is only possible if we know its physical and chemical properties, which is frequently obstructed by the presence of micro- or macroscopic inclusions of secondary phases. While sometimes a sophisticated synthesis route can address this issue, often obtaining pure material is not possible. One example is TaGeIr, which has highly sample-dependent properties resulting from the presence of several impurity phases, which influence electronic transport in the material. The effect of these minority phases was avoided by manufacturing, with the help of focused-ion-beam, a μm-scale device containing only one phase-TaGeIr. This work provides evidence for intrinsic semiconducting behavior of TaGeIr and serves as an example of selective single-domain device manufacturing. This approach gives a unique access to the properties of compounds that cannot be synthesized in single-phase form, sparing costly and time-consuming synthesis efforts.

Vortex End Majorana Zero Modes in Superconducting Dirac and Weyl Semimetals

Time-reversal invariant Dirac and Weyl semimetals in three dimensions (3D) can host open Fermi arcs and spin-momentum locking Fermi loops on the surfaces. We find that when they become superconducting with s-wave pairing and the doping is lower than a critical level, straight π-flux vortex lines terminating at surfaces with Fermi arcs or spin-momentum locking Fermi loops can realize 1D topological superconductivity and harbor Majorana zero modes at their ends. Remarkably, we find that the vortex-generation-associated Zeeman field can open (when the surfaces have only Fermi arcs) or enhance the topological gap protecting Majorana zero modes, which is contrary to the situation in superconducting topological insulators. By studying the tilting effect of bulk Dirac and Weyl cones, we further find that type-I Dirac and Weyl semimetals in general have a much broader topological regime than type-II ones. Our findings build up a connection between time-reversal invariant Dirac and Weyl semimetals and Majorana zero modes in vortices.

h/e oscillations in interlayer transport of delafossites

Microstructures can be carefully designed to reveal the quantum phase of the wave-like nature of electrons in a metal. Here, we report phase-coherent oscillations of out-of-plane magnetoresistance in the layered delafossites PdCoO₂ and PtCoO₂ The oscillation period is equivalent to that determined by the magnetic flux quantum, h/e, threading an area defined by the atomic interlayer separation and the sample width, where h is Planck's constant and e is the charge of an electron. The phase of the electron wave function appears robust over length scales exceeding 10 micrometers and persisting up to temperatures of T > 50 kelvin. We show that the experimental signal stems from a periodic field modulation of the out-of-plane hopping. These results demonstrate extraordinary single-particle quantum coherence lengths in delafossites.

Realization of Epitaxial NbP and TaP Weyl Semimetal Thin Films

Weyl semimetals (WSMs) exhibit an electronic structure governed by linear band dispersions and degenerate (Weyl) points that lead to exotic physical phenomena. While WSMs were established in bulk monopnictide compounds several years ago, the growth of thin films remains a challenge. Here, we report the bottom-up synthesis of single-crystalline NbP and TaP thin films, 9 to 70 nm thick, by means of molecular beam epitaxy. The as-grown epitaxial films feature a phosphorus-rich stoichiometry, a tensile-strained unit cell, and a homogeneous surface termination, unlike their bulk crystal counterparts. These properties result in an electronic structure governed by topological surface states as directly observed using in situ momentum photoemission microscopy, along with a Fermi-level shift of -0.2 eV with respect to the intrinsic chemical potential. Although the Fermi energy of the as-grown samples is still far from the Weyl points, carrier mobilities close to 103 cm2/(V s) have been measured at room temperature in patterned Hall-bar devices. The ability to grow thin films of Weyl semimetals that can be tailored by doping or strain, is an important step toward the fabrication of functional WSM-based devices and heterostructures.

Proximity-induced surface superconductivity in Dirac semimetal Cd3As2

Cd₃As₂ is a three-dimensional Dirac semimetal with separated Dirac points in momentum space. In spite of extensive transport and spectroscopic studies on its exotic properties, the evidence of superconductivity in its surface states remains elusive. Here, we report the observation of proximity-induced surface superconductivity in Nb/Cd₃As₂ hybrid structures. Our four-terminal transport measurement identifies a pronounced proximity-induced pairing gap (gap size comparable to Nb) on the surfaces, which exhibits a flat conductance plateau in differential conductance spectra, consistent with our theoretical simulations. The surface supercurrent from Nb/Cd₃As₂/Nb junctions is also achieved with a Fraunhofer/SQUID-like pattern under out-of-plane/in-plane magnetic fields, respectively. The resultant mapping shows a predominant distribution on the top and bottom surfaces as the bulk carriers are depleted, which can be regarded as a higher dimensional analog of edge supercurrent in two-dimensional quantum spin Hall insulators. Our study provides the evidence of surface superconductivity in Dirac semimetals.

Surface superconductivity in a Dirac semimetal remains rarely studied. Here, Huang and Zhou et al. report the evidence of proximity-induced surface superconductivity in a superconductor/Dirac semimetal hybrid system Nb/Cd₃As₂.

Ultrahigh conductivity in Weyl semimetal NbAs nanobelts

In two-dimensional (2D) systems, high mobility is typically achieved in low-carrier-density semiconductors and semimetals. Here, we discover that the nanobelts of Weyl semimetal NbAs maintain a high mobility even in the presence of a high sheet carrier density. We develop a growth scheme to synthesize single crystalline NbAs nanobelts with tunable Fermi levels. Owing to a large surface-to-bulk ratio, we argue that a 2D surface state gives rise to the high sheet carrier density, even though the bulk Fermi level is located near the Weyl nodes. A surface sheet conductance up to 5-100 S per □ is realized, exceeding that of conventional 2D electron gases, quasi-2D metal films, and topological insulator surface states. Corroborated by theory, we attribute the origin of the ultrahigh conductance to the disorder-tolerant Fermi arcs. The evidenced low-dissipation property of Fermi arcs has implications for both fundamental study and potential electronic applications.

4π-Periodic Supercurrent from Surface States in Cd_{3}As_{2} Nanowire-Based Josephson Junctions

The combination of superconductivity and surface states in Dirac semimetal can produce a 4π-periodic supercurrent in a Josephson junction configuration, which can be revealed by the missing of odd Shapiro steps (especially the n=1 step). However, the suppression of the n=1 step is also anticipated in the high-power oscillatory regime of the ordinary 2π-periodic Josephson effect, which is irrelevant to the 4π-periodic supercurrent. Here, in order to identify the origin of the suppressed n=1 step, we perform the measurements of radio frequency irradiation on Nb-Dirac semimetal Cd_{3}As_{2} nanowire-Nb junctions with continuous power dependence at various frequencies. Besides the n=1 step suppression, we uncover a residual supercurrent of first node at the n=0 step, which provides a direct and predominant signature of the 4π-periodic supercurrent. Furthermore, by tuning the gate voltage, we can modulate the surface and bulk state contribution and the visibility of the n=1 step. Our results provide deep insights to explore the topological superconductivity in Dirac semimetals.

Inducing Strong Superconductivity in WTe2 by a Proximity Effect

The search for proximity-induced superconductivity in topological materials has generated widespread interest in the condensed matter physics community. The superconducting states inheriting nontrivial topology at interfaces are expected to exhibit exotic phenomena such as topological superconductivity and Majorana zero modes, which hold promise for applications in quantum computation. However, a practical realization of such hybrid structures based on topological semimetals and superconductors has hitherto been limited. Here, we report the strong proximity-induced superconductivity in type-II Weyl semimetal WTe₂, in a van der Waals hybrid structure obtained by mechanically transferring NbSe₂ onto various thicknesses of WTe₂. When the WTe₂ thickness ( t_WTe2) reaches 21 nm, the superconducting transition occurs around the critical temperature ( T_c) of NbSe₂ with a gap amplitude (Δ_p) of 0.38 meV and an unexpected ultralong proximity length ( l_p) up to 7 μm. With the thicker 42 nm WTe₂ layer, however, the proximity effect yields T_c ≈ 1.2 K, Δ_p = 0.07 meV, and a short l_p of less than 1 μm. Our theoretical calculations, based on the Bogoliubov-de Gennes equations in the clean limit, predict that the induced superconducting gap is a sizable fraction of the NbSe₂ superconducting one when t_WTe2 is less than 30 nm and then decreases quickly as t_WTe2 increases. This agrees qualitatively well with the experiments. Such observations form a basis in the search for superconducting phases in topological semimetals.

Quantum limit transport and destruction of the Weyl nodes in TaAs

Weyl fermions are a recently discovered ingredient for correlated states of electronic matter. A key difficulty has been that real materials also contain non-Weyl quasiparticles, and disentangling the experimental signatures has proven challenging. Here we use magnetic fields up to 95 T to drive the Weyl semimetal TaAs far into its quantum limit, where only the purely chiral 0th Landau levels of the Weyl fermions are occupied. We find the electrical resistivity to be nearly independent of magnetic field up to 50 T: unusual for conventional metals but consistent with the chiral anomaly for Weyl fermions. Above 50 T we observe a two-order-of-magnitude increase in resistivity, indicating that a gap opens in the chiral Landau levels. Above 80 T we observe strong ultrasonic attenuation below 2 K, suggesting a mesoscopically textured state of matter. These results point the way to inducing new correlated states of matter in the quantum limit of Weyl semimetals.

π and 4π Josephson Effects Mediated by a Dirac Semimetal

Cd_{3}As_{2} is a three-dimensional topological Dirac semimetal with connected Fermi-arc surface states. It has been suggested that topological superconductivity can be achieved in the nontrivial surface states of topological materials by utilizing the superconductor proximity effect. Here we report observations of both π and 4π periodic supercurrents in aluminum-Cd_{3}As_{2}-aluminum Josephson junctions. The π period is manifested by both the magnetic-field dependence of the critical supercurrent and the appearance of half-integer Shapiro steps in the ac Josephson effect. Our macroscopic theory suggests that the π period arises from interference between the induced bulk superconductivity and the induced Fermi-arc surface superconductivity. The 4π period is manifested by the missing first Shapiro steps and is expected for topological superconductivity.