Induced superconductivity in the three-dimensional topological insulator HgTe

Topological superconducting vortex from trivial electronic bands

Superconducting vortices are promising traps to confine non-Abelian Majorana quasi-particles. It has been widely believed that bulk-state topology, of either normal-state or superconducting ground-state wavefunctions, is crucial for enabling Majorana zero modes in solid-state systems. This common belief has shaped two major search directions for Majorana modes, in either intrinsic topological superconductors or trivially superconducting topological materials. Here we show that Majorana-carrying superconducting vortex is not exclusive to bulk-state topology, but can arise from topologically trivial quantum materials as well. We predict that the trivial bands in superconducting HgTe-class materials are responsible for inducing anomalous vortex topological physics that goes beyond any existing theoretical paradigms. A feasible scheme of strain-controlled Majorana engineering and experimental signatures for vortex Majorana modes are also discussed. Our work provides new guidelines for vortex-based Majorana search in general superconductors.

Evolution of Topological Surface States Following Sb Layer Adsorption on Bi2Se3

Thin antimony layers adsorbed on bismuth selenide (Bi2Se3) present an exciting topological insulator system. Much recent effort has been made to understand the synthesis and electronic properties of the heterostructure, particularly the migration of the topological surface states under adsorption. However, the intertwinement of the topological surface states of the pristine Bi2Se3 substrate with the Sb adlayer remains unclear. In this theoretical work, we apply density functional theory (DFT) to model heterostructures of single and double atomic layers of Sb on a bismuth selenide substrate. We thereby discuss established and alternative structural models, as well as the hybridization of topological surface states with the Sb states. Concerning the geometry, we reveal the possibility of structures with inverted Sb layers which are energetically close to the established ones. The formation energy differences are below 10 meV/atom. Concerning the hybridization, we trace the band structure evolution as a function of the adlayer-substrate distance. By following changes in the connection between the Kramers pairs, we extract a series of topological phase transitions. This allows us to explain the origin of the complex band structure, and ultimately complete our knowledge about this peculiar system.

Topologization of β-antimonene on Bi2Se3 via proximity effects

Topological surface states usually emerge at the boundary between a topological and a conventional insulator. Their precise physical character and spatial localization depend on the complex interplay between the chemical, structural and electronic properties of the two insulators in contact. Using a lattice-matched heterointerface of single and double bilayers of β-antimonene and bismuth selenide, we perform a comprehensive experimental and theoretical study of the chiral surface states by means of microscopy and spectroscopic measurements complemented by first-principles calculations. We demonstrate that, although β-antimonene is a trivial insulator in its free-standing form, it inherits the unique symmetry-protected spin texture from the substrate via a proximity effect that induces outward migration of the topological state. This "topologization" of β-antimonene is found to be driven by the hybridization of the bands from either side of the interface.

Perfect Crossed Andreev Reflection in Dirac Hybrid Junctions in the Quantum Hall Regime

Perfect crossed Andreev reflection (CAR) is striking for high-efficiency Cooper pair splitting, which bears promising applications in quantum communication. Recent experimental advances have disclosed the way to explore CAR in Dirac fermion systems under ultrastrong magnetic fields. We develop a scattering approach to study quantum-Hall-superconductor-quantum-Hall junctions formed by a two-dimensional time-reversal symmetric Dirac semimetal. We propose two different setups of the hybrid junction in the quantum limit, where only zeroth Landau levels are involved in transport to exploit perfect CAR. In both setups, the CAR probability can reach unity without applying bias voltage and is controllable by the magnetic field strength, the junction width, the length, and the doping of the superconductor. CAR dominates the nonlocal transport and is directly measurable by the differential conductances. We also identify a quantized spin injection per CAR event in one of the two setups. Our proposal is experimentally feasible and will be helpful for exploring high-efficiency Cooper pair splitting and spin injection in Dirac materials.

Soliton defects and topological [Formula: see text]-periodic superconductivity from an orbital magnetic field effect in edge Josephson junctions

Recently, much research has been dedicated to understanding topological superconductivity and Majorana zero modes induced by a magnetic field in hybrid proximity structures. This paper proposes a realization of topological superconductivity in a short Josephson junction at an edge of a 2D topological insulator subject to a perpendicular magnetic field. The magnetic field effect is entirely orbital, coming from a gradient of the order parameter phase at the edge, which results in a soliton defect at the junction with a pair of gapless Andreev bound states. The latter are reducible to Majorana zero modes by a unitary rotation and protected by a chiral symmetry. Furthermore, both ground state and excitations are quasiperiodic in the magnetic flux enclosed in the junction, with the period equal to the double flux quantum [Formula: see text]. This behaviour follows from the gauge invariance of the [Formula: see text]-phase periodicity of the Majorana states and manifests itself as [Formula: see text]-spaced magnetic oscillations of the critical current. Another proposed observable is a persistent current occurring in the absence of an external phase bias. Beside the oscillations, it shows a sign reversal prompted by the neutral Majorana zero modes. These findings offer the possibility to access topological superconductivity through low-field dc magnetotransport measurements.

Probing the magnetoelectric effect in noncentrosymmetric superconductors by equal-spin Andreev tunneling

In noncentrosymmetric superconductors (NCSs), the conversion of a charge current into spin magnetization-the so called magnetoelectric effect-is the direct indicator of the unconventional, mixed-parity order parameter. This paper proposes a scheme to detect the magnetoelectric effect by anomalous, equal-spin Andreev tunneling in NCS/ferromagnet contacts. The proposal relies on the ability to generate spin-polarized triplet pairing by passing an electric current through an NCS. Such an induced triplet pairing bears a similarity to the paradigmatic nonunitary pairing in triplet superfluids with a complex vector order parameter [Formula: see text]. The qualitative difference is that the induced nonunitary state can be realised in NCSs with a purely real [Formula: see text] by breaking the time-reversal symmetry in current-biased setups. This offers a possibility to access the unconventional superconductivity in NCSs through electrical transport measurements.

Fermiology and Superconductivity of Topological Surface States in PdTe_{2}

We study the low-energy surface electronic structure of the transition-metal dichalcogenide superconductor PdTe_{2} by spin- and angle-resolved photoemission, scanning tunneling microscopy, and density-functional theory-based supercell calculations. Comparing PdTe_{2} with its sister compound PtSe_{2}, we demonstrate how enhanced interlayer hopping in the Te-based material drives a band inversion within the antibonding p-orbital manifold well above the Fermi level. We show how this mediates spin-polarized topological surface states which form rich multivalley Fermi surfaces with complex spin textures. Scanning tunneling spectroscopy reveals type-II superconductivity at the surface, and moreover shows no evidence for an unconventional component of its superconducting order parameter, despite the presence of topological surface states.

Emerging tellurium nanostructures: controllable synthesis and their applications

Tellurium (Te) is a rare element in trace amounts of about one part per billion, comparable to that of platinum and ranked 75th in the abundance of the elements in the earth crust. Te nanostructures, as narrow bandgap semiconductors, have numerous potential applications in the fabrication of many modern devices. The past decades have witnessed an explosion in new strategies for synthesizing diverse emerging Te nanostructures with controlled compositions, sizes, shapes, and structures. Their structure-determined nature makes functional Te nanomaterials an attractive candidate for modern applications. This review focuses on the synthesis and morphology control of emerging Te nanostructures and summarizes the latest developments in the applications of Te nanostructures, such as their use as chemical transformation templates to access a huge family of nanowires/nanotubes, batteries, photodetectors, ion detection and removal, element doping, piezoelectric energy harvesting, gas sensing, thermoelectric devices and many other device applications. Various Te nanostructures with different shapes and structures will exploit the beneficial properties associated with their assembly process and nanofabrication. Finally, the prospects for future applications of Te nanomaterials are summarized and highlighted.

Creation of Spin-Triplet Cooper Pairs in the Absence of Magnetic Ordering

In superconducting spintronics, it is essential to generate spin-triplet Cooper pairs on demand. Up to now, proposals to do so concentrate on hybrid structures in which a superconductor (SC) is combined with a magnetically ordered material (or an external magnetic field). We, instead, identify a novel way to create and isolate spin-triplet Cooper pairs in the absence of any magnetic ordering. This achievement is only possible because we drive a system with strong spin-orbit interaction-the Dirac surface states of a strong topological insulator (TI)-out of equilibrium. In particular, we consider a bipolar TI-SC-TI junction, where the electrochemical potentials in the outer leads differ in their overall sign. As a result, we find that nonlocal singlet pairing across the junction is completely suppressed for any excitation energy. Hence, this junction acts as a perfect spin-triplet filter across the SC, generating equal-spin Cooper pairs via crossed Andreev reflection.

Thermal transport in topological-insulator-based superconducting hybrid structures with mixed singlet and triplet pairing states

In the framework of the Bogoliubov-de Gennes equation, we investigate the thermal transport properties in topological-insulator-based superconducting hybrid structures with mixed spin-singlet and spin-triplet pairing states, and emphasize the different manifestations of the spin-singlet and spin-triplet pairing states in the thermal transport signatures. It is revealed that the temperature-dependent differential thermal conductance strongly depends on the components of the pairing state, and the negative differential thermal conductance only occurs in the spin-singlet pairing state dominated regime. It is also found that the thermal conductance is profoundly sensitive to the components of the pairing state. In the spin-singlet pairing state controlled regime, the thermal conductance obviously oscillates with the phase difference and junction length. With increasing the proportion of the spin-triplet pairing state, the oscillating characteristic of the thermal conductance fades out distinctly. These results suggest an alternative route for distinguishing the components of pairing states in topological-insulator-based superconducting hybrid structures.

RETRACTED: Chiral Majorana fermion modes in a quantum anomalous Hall insulator-superconductor structure

Majorana fermion is a hypothetical particle that is its own antiparticle. We report transport measurements that suggest the existence of one-dimensional chiral Majorana fermion modes in the hybrid system of a quantum anomalous Hall insulator thin film coupled with a superconductor. As the external magnetic field is swept, half-integer quantized conductance plateaus are observed at the locations of magnetization reversals, giving a distinct signature of the Majorana fermion modes. This transport signature is reproducible over many magnetic field sweeps and appears at different temperatures. This finding may open up an avenue to control Majorana fermions for implementing robust topological quantum computing.

Magnetoelectric Andreev Effect due to Proximity-Induced Nonunitary Triplet Superconductivity in Helical Metals

Noncentrosymmetric superconductors exhibit the magnetoelectric effect, which manifests itself in the appearance of the magnetic spin polarization in response to a dissipationless electric current (supercurrent). While much attention has been dedicated to the thermodynamic version of this phenomenon (Edelstein effect), nonequilibrium transport magnetoelectric effects have not been explored yet. We propose the magnetoelectric Andreev effect (MAE), which consists in the generation of spin-polarized triplet Andreev conductance by an electric supercurrent. The MAE stems from the spin polarization of the Cooper-pair condensate due to a supercurrent-induced nonunitary triplet pairing. We propose the realization of such a nonunitary pairing and MAE in superconducting proximity structures based on two-dimensional helical metals-strongly spin-orbit-coupled electronic systems with the Dirac spectrum such as the topological surface states. Our results uncover an unexplored route towards electrically controlled superconducting spintronics and are a smoking gun for induced unconventional superconductivity in spin-orbit-coupled materials.

Symmetry-protected ideal Weyl semimetal in HgTe-class materials

Ideal Weyl semimetals with all Weyl nodes exactly at the Fermi level and no coexisting trivial Fermi surfaces in the bulk, similar to graphene, could feature deep physics such as exotic transport phenomena induced by the chiral anomaly. Here, we show that HgTe and half-Heusler compounds, under a broad range of in-plane compressive strain, could be materials in nature realizing ideal Weyl semimetals with four pairs of Weyl nodes and topological surface Fermi arcs. Generically, we find that the HgTe-class materials with nontrivial band inversion and noncentrosymmetry provide a promising arena to realize ideal Weyl semimetals. Such ideal Weyl semimetals could further provide a unique platform to study emergent phenomena such as the interplay between ideal Weyl fermions and superconductivity in the half-Heusler compound LaPtBi.

Ideal Weyl semimetals, similar to graphene, show peculiar features such as exotic electronic transport. Here, Ruan et al. predict that strain-tuned HgTe-class materials can become ideal Weyl semimetals, which could provide a promising platform to study emergent topological phenomena.

Accessing topological superconductivity via a combined STM and renormalization group analysis

The search for topological superconductors has recently become a key issue in condensed matter physics, because of their possible relevance to provide a platform for Majorana bound states, non-Abelian statistics, and quantum computing. Here we propose a new scheme which links as directly as possible the experimental search to a material-based microscopic theory for topological superconductivity. For this, the analysis of scanning tunnelling microscopy, which typically uses a phenomenological ansatz for the superconductor gap functions, is elevated to a theory, where a multi-orbital functional renormalization group analysis allows for an unbiased microscopic determination of the material-dependent pairing potentials. The combined approach is highlighted for paradigmatic hexagonal systems, such as doped graphene and water-intercalated sodium cobaltates, where lattice symmetry and electronic correlations yield a propensity for a chiral singlet topological superconductor. We demonstrate that our microscopic material-oriented procedure is necessary to uniquely resolve a topological superconductor state.

Nonsinusoidal current-phase relationship in Josephson junctions from the 3D topological insulator HgTe

We use superconducting quantum interference device microscopy to characterize the current-phase relation (CPR) of Josephson junctions from the three-dimensional topological insulator HgTe (3D HgTe). We find clear skewness in the CPRs of HgTe junctions ranging in length from 200 to 600 nm. The skewness indicates that the Josephson current is predominantly carried by Andreev bound states with high transmittance, and the fact that the skewness persists in junctions that are longer than the mean free path suggests that the effect may be related to the helical nature of the Andreev bound states in the surface of HgTe. These experimental results suggest that the topological properties of the normal state can be inherited by the induced superconducting state, and that 3D HgTe is a promising material for realizing the many exciting proposals that require a topological superconductor.

Direct measurement of current-phase relations in superconductor/topological insulator/superconductor junctions

Proximity to a superconductor is predicted to induce exotic quantum phases in topological insulators. Here, scanning superconducting quantum interference device (SQUID) microscopy reveals that aluminum superconducting rings with topologically insulating Bi2Se3 junctions exhibit a conventional, nearly sinusoidal 2π-periodic current-phase relations. Pearl vortices occur in longer junctions, indicating suppressed superconductivity in aluminum, probably due to a proximity effect. Our observations establish scanning SQUID as a general tool for characterizing proximity effects and for measuring current-phase relations in new materials systems.