Selective-Area-Grown PbTe-Pb Planar Josephson Junctions for Quantum Devices

Planar Josephson junctions are predicted to host Majorana zero modes. The material platforms in previous studies are two-dimensional electron gases (InAs, InSb, InAsSb, and HgTe) coupled to a superconductor such as Al or Nb. Here, we introduce a new material platform for planar JJs, the PbTe-Pb hybrid. The semiconductor, PbTe, was grown as a thin film via selective area epitaxy. The Josephson junction was defined by a shadow wall during the deposition of superconductor Pb. Scanning transmission electron microscopy reveals a sharp semiconductor-superconductor interface. Gate-tunable supercurrents and multiple Andreev reflections are observed. A perpendicular magnetic field causes interference patterns of the switching current, exhibiting Fraunhofer-like and SQUID-like behaviors. We further demonstrate a prototype device for Majorana detection wherein phase bias and tunneling spectroscopy are applicable.

Topological Quantum Well States in Pb/Sb Thin-Film Heterostructures

Composite topological heterostructures, wherein topologically protected states are electronically tuned due to their proximity to other matter, are key avenues for exploring emergent physical phenomena. Particularly, pairing a topological material with a superconductor such as Pb is a promising means for generating a topological superconducting phase with exotic Majorana quasiparticles, but oft-neglected is the emergence of bulklike spin-polarized states that are quite relevant to applications. Using high-resolution photoemission spectroscopy and first-principles calculations, we report the emergence of bulk-like spin-polarized topological quantum well states with long coherence lengths in Pb films grown on the topological semimetal Sb. The results establish Pb/Sb heterostructures as topological superconductor candidates and advance the current understanding of topological coupling effects required for realizing emergent physics and for designing advanced spintronic device architectures.

Current-Phase Relation of a WTe2 Josephson Junction

When a topological insulator is incorporated into a Josephson junction, the system is predicted to reveal the fractional Josephson effect with a 4π-periodic current-phase relation. Here, we report the measurement of a 4π-periodic switching current through an asymmetric SQUID, formed by the higher-order topological insulator WTe₂. Contrary to the established opinion, we show that a high asymmetry in critical current and negligible loop inductance are not sufficient by themselves to reliably measure the current-phase relation. Instead, we find that our measurement is heavily influenced by additional inductances originating from the self-formed PdTe_x inside the junction. We therefore develop a method to numerically recover the current-phase relation of the system and find the 1.5 μm long junction to be best described in the short ballistic limit. Our results highlight the complexity of subtle inductance effects that can give rise to misleading topological signatures in transport measurements.

Realizing a Superconducting Square-Lattice Bismuth Monolayer

Interplay of crystal symmetry, strong spin-orbit coupling (SOC), and many-body interactions in low-dimensional materials provides a fertile ground for the discovery of unconventional electronic and magnetic properties and versatile functionalities. Two-dimensional (2D) allotropes of group 15 elements are appealing due to their structures and controllability over symmetries and topology under strong SOC. Here, we report the heteroepitaxial growth of a proximity-induced superconducting 2D square-lattice bismuth monolayer on superconducting Pb films. The square lattice of monolayer bismuth films in a C₄ symmetry together with a stripey moiré structure is clearly resolved by our scanning tunneling microscopy, and its atomic structure is revealed by density functional theory (DFT) calculations. A Rashba-type spin-split Dirac band is predicted by DFT calculations to exist at the Fermi level and becomes superconducting through the proximity effect from the Pb substrate. We suggest the possibility of a topological superconducting state in this system with magnetic dopants/field. This work introduces an intriguing material platform with 2D Dirac bands, strong SOC, topological superconductivity, and the moiré superstructure.

Evolution of 4π-Periodic Supercurrent in the Presence of an In-Plane Magnetic Field

In the presence of a 4π-periodic contribution to the current phase relation, for example in topological Josephson junctions, odd Shapiro steps are expected to be missing. While missing odd Shapiro steps have been observed in several material systems and interpreted in the context of topological superconductivity, they have also been observed in topologically trivial junctions. Here, we study the evolution of such trivial missing odd Shapiro steps in Al-InAs junctions in the presence of an in-plane magnetic field B^θ. We find that the odd steps reappear at a crossover B^θ value, exhibiting an in-plane field angle anisotropy that depends on spin-orbit coupling effects. We interpret this behavior by theoretically analyzing the Andreev bound state spectrum and the transitions induced by the nonadiabatic dynamics of the junction and attribute the observed anisotropy to mode-to-mode coupling. Our results highlight the complex phenomenology of missing Shapiro steps and the underlying current phase relations in planar Josephson junctions designed to realize Majorana states.

Phase diagram of superconductivity in the integer quantum Hall regime

An interplay between pairing and topological orders has been predicted to give rise to superconducting states supporting exotic emergent particles, such as Majorana particles obeying non-Abelian braid statistics. We consider a system of spin polarized electrons on a Hofstadter lattice with nearest-neighbor attractive interaction and solve the mean-field Bogoliubov-de Gennes equations in a self-consistent fashion, leading to gauge-invariant observables and a rich phase diagram as a function of the chemical potential, the magnetic field, and the interaction. As the strength of the attractive interaction is increased, the system first makes a transition from a quantum Hall phase to a skyrmion lattice phase that is fully gapped in the bulk but has topological chiral edge current, characterizing a topologically nontrivial state. This is followed by a vortex phase in which the vortices carrying Majorana modes form a lattice; the spectrum contains a low-energy Majorana band arising from the coupling between neighboring vortex-core Majorana modes but does not have chiral edge currents. For some parameters, a dimer vortex lattice occurs with no Majorana band. The experimental feasibility and the observable consequences of skyrmions as well as Majorana modes are indicated.

Manifestation of Majorana modes overlap in the Aharonov-Bohm effect

One of the key features of the Majorana bound states emerging in topological superconducting (SC) wires is increasing oscillations of their energy under the growth of magnetic field or chemical potential due to concomitant enhancement of hybridization of the Majorana mode wave functions initially localized at the opposite edges of the structure. In this study we found that the other consequence of it is a shift of Aharonov-Bohm (AB) oscillations of linear-response conductance in an interference device where two ends of the SC wire connected with a normal contact via non-SC wires (arms). In addition, it is accompanied by an oscillation period doubling. The numerical calculations for the spinful system are supported by the analytical results for different spinless models allowing to track the conductance evolution as the hybridization of the Majorana modes increases. It is shown that since the coupling between the different arms and normal contact is implemented only via the different-type Majoranas the AB oscillations acquire a fundamentalπ/2 shift in comparison with the effect for an analogous system of zero-energy quantum dots.

Gate-Tunable Transport in Quasi-One-Dimensional α-Bi4I4 Field Effect Transistors

Bi₄I₄ belongs to a novel family of quasi-one-dimensional (1D) topological insulators (TIs). While its β phase was demonstrated to be a prototypical weak TI, the α phase, long thought to be a trivial insulator, was recently predicted to be a rare higher order TI. Here, we report the first gate tunable transport together with evidence for unconventional band topology in exfoliated α-Bi₄I₄ field effect transistors. We observe a Dirac-like longitudinal resistance peak and a sign change in the Hall resistance; their temperature dependences suggest competing transport mechanisms: a hole-doped insulating bulk and one or more gate-tunable ambipolar boundary channels. Our combined transport, photoemission, and theoretical results indicate that the gate-tunable channels likely arise from novel gapped side surface states, two-dimensional (2D) TI in the bottommost layer, and/or helical hinge states of the upper layers. Markedly, a gate-tunable supercurrent is observed in an α-Bi₄I₄ Josephson junction, underscoring the potential of these boundary channels to mediate topological superconductivity.

Majorana/Andreev crossover and the fate of the topological phase transition in inhomogeneous nanowires

Majorana bound states (MBS) and Andreev bound states (ABS) in realistic Majorana nanowires setups have similar experimental signatures which make them hard to distinguishing one from the other. Here, we characterize the continuous Majorana/Andreev crossover interpolating between fully-separated, partially-separated, and fully-overlapping Majorana modes, in terms of global and local topological invariants, fermion parity, quasiparticle densities, Majorana pseudospin and spin polarizations, density overlaps and transition probabilities between opposite Majorana components. We found that in inhomogeneous wires, the transition between fully-overlapping trivial ABS and nontrivial MBS does not necessarily mandate the closing of the bulk gap of quasiparticle excitations, but a simple parity crossing of partially-separated Majorana modes (ps-MM) from trivial to nontrivial regimes. We demonstrate that fully-separated and fully-overlapping Majorana modes correspond to the two limiting cases at the opposite sides of a continuous crossover: the only distinction between the two can be obtained by estimating the degree of separations of the Majorana components. This result does not contradict the bulk-edge correspondence: indeed, the field inhomogeneities driving the Majorana/Andreev crossover have a length scale comparable with the nanowire length, and therefore correspond to a nonlocal perturbation which breaks the topological protection of the MBS.

InSbAs Two-Dimensional Electron Gases as a Platform for Topological Superconductivity

Topological superconductivity can be engineered in semiconductors with strong spin-orbit interaction coupled to a superconductor. Experimental advances in this field have often been triggered by the development of new hybrid material systems. Among these, two-dimensional electron gases (2DEGs) are of particular interest due to their inherent design flexibility and scalability. Here, we discuss results on a 2D platform based on a ternary 2DEG (InSbAs) coupled to in situ grown aluminum. The spin-orbit coupling in these 2DEGs can be tuned with the As concentration, reaching values up to 400 meV Å, thus exceeding typical values measured in its binary constituents. In addition to a large Landé g-factor of ∼55 (comparable to that of InSb), we show that the clean superconductor-semiconductor interface leads to a hard induced superconducting gap. Using this new platform, we demonstrate the basic operation of phase-controllable Josephson junctions, superconducting islands, and quasi-1D systems, prototypical device geometries used to study Majorana zero modes.

Effect of Sr Doping on Structural and Transport Properties of Bi2Te3

Search for doped superconducting topological insulators is of prime importance for new quantum technologies. We report on fabrication of Sr-doped Bi2Te3 single crystals. We found that Bridgman grown samples have p-type conductivity in the low 1019 cm−3, high mobility of 4000 cm2V−1s−1, crystal structure independent on nominal dopant content, and no signs of superconductivity. We also studied molecular beam epitaxy grown SrxBi2−xTe3 films on lattice matched (1 1 1) BaF2 polar surface. Contrary to the bulk crystals thin films have n-type conductivity. Carrier concentration, mobility and c-lattice constant demonstrate pronounced dependence on Sr concentration x. Variation of the parameters did not lead to superconductivity. We revealed, that transport and structural parameters are governed by Sr dopants incorporation in randomly inserted Bi bilayers into the parent matrix. Thus, our data shed light on the structural position of dopant in Bi2Te3 and should be helpful for further design of topological insulator-based superconductors.

Ising pairing in atomically thin superconductors

Ising-type pairing in atomically thin superconducting materials has emerged as a novel means of generating devices with resilience to a magnetic field applied parallel to the two-dimensional (2D) plane. In this mini-review, we canvas the state of the field by giving a historical account of 2D superconductors with strongly enhanced in-plane upper critical fields, together with the type-I and type-II Ising pairing mechanisms. We highlight the vital role of spin-orbit coupling in these superconductors and discuss other effects such as symmetry breaking, atomic thicknesses, etc. Finally, we summarize the recent theoretical proposals and highlight the open questions, such as exploring topological superconductivity in these systems and looking for more materials with Ising pairing.

Sub-gap Fano resonances in a topological superconducting wire with on-site Coulomb interactions

We consider theoretically a 1D-semiconducting wire with strong Rashba interaction in proximity withs-wave superconductor, driven into topological phase by external magnetic field. Additionally, we take into account on-site Coulomb interactions inside the wire. The system is modelled by a tight binding Hamiltonian with Rashba hopping term and induceds-wave superconductivity. Calculations are performed utilizing recursive Green's function method, and Coulomb interactions are treated selfconsistently within Hubbard I approximation. For the Hubbard levels residing withinp-wave superconducting gap, particle-hole symmetric four-resonance structure develops in the density of states, apart from Majorana resonance. One pair of particle-hole symmetric resonances is created by the discrete II-Hubbard levels of the particular site, and the second pair of Hubbard sub-bands originates from recursive summation over the sites of the wire. Quantum interference between both types of pairs of states creates in-gap charge-conjugated Fano resonances with opposite asymmetry factors. We demonstrate that when quantum interference is dominated by two-particle tunneling, the Majorana resonance is strongly diminished, while it is not altered when single-particle tunneling dominates in interference process. We also discuss some consequences for experimental distinction of true Majorana states, and show that on-site Coulomb interactions support the appearance of topological phase.

Phase interference for probing topological fractional charge in a BiSbTeSe2-based Josephson junction array

Fractional charges can be induced by magnetic fluxes at the interface between a topological insulator (TI) and a type-II superconductor due to axion electrodynamics. In a Josephson junction array with a hole in the middle, these electronic states can have phase interference in an applied magnetic field with4×2πperiod, in addition to the 2πinterference of the Cooper pairs. Here, we test an experimental configuration for probing the fractional charge and report the observation of phase interference effect in superconducting arrays with a hole in the middle in both Au- and TI-based devices. Our numerical simulations based on resistive shunted capacitive junction model are in good agreement with the experimental results. However, no clear sign of an axion charge-related interference effect was observed. We will discuss possible reasons and perspectives for future experiments.

Phase-induced topological superconductivity in a planar heterostructure

Topological superconductivity in quasi-one-dimensional systems is a novel phase of matter with possible implications for quantum computation. Despite years of effort, a definitive signature of this phase in experiments is still debated. A major cause of this ambiguity is the side effects of applying a magnetic field: induced in-gap states, vortices, and alignment issues. Here we propose a planar semiconductor-superconductor heterostructure as a platform for realizing topological superconductivity without applying a magnetic field to the two-dimensional electron gas hosting the topological state. Time-reversal symmetry is broken only by phase biasing the proximitizing superconductors, which can be achieved using extremely small fluxes or bias currents far from the quasi-one-dimensional channel. Our platform is based on interference between this phase biasing and the phase arising from strong spin-orbit coupling in closed electron trajectories. The principle is demonstrated analytically using a simple model, and then shown numerically for realistic devices. We show a robust topological phase diagram, as well as explicit wavefunctions of Majorana zero modes. We discuss experimental issues regarding the practical implementation of our proposal, establishing it as an accessible scheme with contemporary experimental techniques.

Atomically Thin Quantum Spin Hall Insulators

Atomically thin topological materials are attracting growing attention for their potential to radically transform classical and quantum electronic device concepts. Among them is the quantum spin Hall (QSH) insulator-a 2D state of matter that arises from interplay of topological band inversion and strong spin-orbit coupling, with large tunable bulk bandgaps up to 800 meV and gapless, 1D edge states. Reviewing recent advances in materials science and engineering alongside theoretical description, the QSH materials library is surveyed with focus on the prospects for QSH-based device applications. In particular, theoretical predictions of nontrivial superconducting pairing in the QSH state toward Majorana-based topological quantum computing are discussed, which are the next frontier in QSH materials research.

Surface superconductivity in the type II Weyl semimetal TaIrTe4

The search for unconventional superconductivity in Weyl semimetal materials is currently an exciting pursuit, since such superconducting phases could potentially be topologically non-trivial and host exotic Majorana modes. The layered material TaIrTe4 is a newly predicted time-reversal invariant type II Weyl semimetal with the minimum number of Weyl points. Here, we report the discovery of surface superconductivity in Weyl semimetal TaIrTe4. Our scanning tunneling microscopy/spectroscopy (STM/STS) visualizes Fermi arc surface states of TaIrTe4 that are consistent with the previous angle-resolved photoemission spectroscopy results. By a systematic study based on STS at ultralow temperature, we observe uniform superconducting gaps on the sample surface. The superconductivity is further confirmed by electrical transport measurements at ultralow temperature, with an onset transition temperature (T c) up to 1.54 K being observed. The normalized upper critical field h*(T/T c) behavior and the stability of the superconductivity against the ferromagnet indicate that the discovered superconductivity is unconventional with the p-wave pairing. The systematic STS, and thickness- and angular-dependent transport measurements reveal that the detected superconductivity is quasi-1D and occurs in the surface states. The discovery of the surface superconductivity in TaIrTe4 provides a new novel platform to explore topological superconductivity and Majorana modes.

Hard Superconducting Gap and Diffusion-Induced Superconductors in Ge-Si Nanowires

We show a hard superconducting gap in a Ge-Si nanowire Josephson transistor up to in-plane magnetic fields of 250 mT, an important step toward creating and detecting Majorana zero modes in this system. A hard gap requires a highly homogeneous tunneling heterointerface between the superconducting contacts and the semiconducting nanowire. This is realized by annealing devices at 180 °C during which aluminum interdiffuses and replaces the germanium in a section of the nanowire. Next to Al, we find a superconductor with lower critical temperature (T_C = 0.9 K) and a higher critical field (B_C = 0.9-1.2 T). We can therefore selectively switch either superconductor to the normal state by tuning the temperature and the magnetic field and observe that the additional superconductor induces a proximity supercurrent in the semiconducting part of the nanowire even when the Al is in the normal state. In another device where the diffusion of Al rendered the nanowire completely metallic, a superconductor with a much higher critical temperature (T_C = 2.9 K) and critical field (B_C = 3.4 T) is found. The small size of these diffusion-induced superconductors inside nanowires may be of special interest for applications requiring high magnetic fields in arbitrary direction.

Spectroscopic fingerprint of chiral Majorana modes at the edge of a quantum anomalous Hall insulator/superconductor heterostructure

With the recent discovery of the quantum anomalous Hall insulator (QAHI), which exhibits the conductive quantum Hall edge states without external magnetic field, it becomes possible to create a topological superconductor (SC) by introducing superconductivity into these edge states. In this case, 2 distinct topological superconducting phases with 1 or 2 chiral Majorana edge modes were theoretically predicted, characterized by Chern numbers (N) of 1 and 2, respectively. We present spectroscopic evidence from Andreev reflection experiments for the presence of chiral Majorana modes in an Nb/(Cr_0.12Bi_0.26Sb_0.62)₂Te₃ heterostructure with distinct signatures attributed to 2 different topological superconducting phases. The results are in qualitatively good agreement with the theoretical predictions.

Signatures of Topological Superconductivity in Bulk-Insulating Topological Insulator BiSbTe1.25Se1.75 in Proximity with Superconducting NbSe2

The combination of superconductivity and spin-momentum locking at the interface between an s-wave superconductor and a three-dimensional topological insulator (3D-TI) is predicted to generate exotic p-wave topological superconducting phases that can host Majorana Fermions. However, large bulk conductivities of previously investigated 3D-TI samples and Fermi level mismatches between 3D bulk superconductors and 2D topological surface states have thwarted significant progress. Here, we employ bulk-insulating topological insulators in proximity with two-dimensional superconductor NbSe₂ assembled via van der Waals epitaxy. Experimentally measured differential conductance yields unusual features including a double-gap spectrum, an intrinsic asymmetry that vanishes with small in-plane magnetic fields, and differential conductance ripples at biases significantly larger than the superconducting gap. We explain our results on the basis of proximity-induced superconductivity of topological surface states, while also considering possibilities of topologically trivial superconductivity arising from Rashba-type surface states. Our work demonstrates the possibility of obtaining p-wave superconductors by proximity effects on bulk-insulating TIs.

Nontrivial superconductivity in topological MoTe2-x S x crystals

Topological Weyl semimetals (TWSs) with pairs of Weyl points and topologically protected Fermi arc states have broadened the classification of topological phases and provide superior platform for study of topological superconductivity. Here we report the nontrivial superconductivity and topological features of sulfur-doped Td -phase MoTe2 with enhanced Tc compared with type-II TWS MoTe2 It is found that Td -phase S-doped MoTe2 (MoTe2-x S x , x ∼ 0.2) is a two-band s-wave bulk superconductor (∼0.13 meV and 0.26 meV), where the superconducting behavior can be explained by the s+- pairing model. Further, measurements of the quasi-particle interference (QPI) patterns and a comparison with band-structure calculations reveal the existence of Fermi arcs in MoTe2-x S x More interestingly, a relatively large superconducting gap (∼1.7 meV) is detected by scanning tunneling spectroscopy on the sample surface, showing a hint of topological nontrivial superconductivity based on the pairing of Fermi arc surface states. Our work demonstrates that the Td -phase MoTe2-x S x is not only a promising topological superconductor candidate but also a unique material for study of s+- superconductivity.

High Mobility HgTe Microstructures for Quantum Spin Hall Studies

The topic of two-dimensional topological insulators has blossomed after the first observation of the quantum spin Hall (QSH) effect in HgTe quantum wells. However, studies have been hindered by the relative fragility of the edge states. Their stability has been a subject of both theoretical and experimental investigation in the past decade. Here, we present a new generation of high quality (Cd,Hg)Te/HgTe-structures based on a new chemical etching method. From magnetotransport measurements on macro- and microscopic Hall bars, we extract electron mobilities μ up to about 400 × 10³ cm²/(V s), and the mean free path λ_mfp becomes comparable to the sample dimensions. The Hall bars show quantized spin Hall conductance, which is remarkably stable up to 15 K. The clean and robust edge states allow us to fabricate high quality side-contacted Josephson junctions, which are significant in the context of topological superconductivity. Our results open up new avenues for fundamental research on QSH effect as well as potential applications in spintronics and topological quantum computation.

Josephson effect in junctions of conventional and topological superconductors

We present a theoretical analysis of the equilibrium Josephson current-phase relation in hybrid devices made of conventional s-wave spin-singlet superconductors (S) and topological superconductor (TS) wires featuring Majorana end states. Using Green's function techniques, the topological superconductor is alternatively described by the low-energy continuum limit of a Kitaev chain or by a more microscopic spinful nanowire model. We show that for the simplest S-TS tunnel junction, only the s-wave pairing correlations in a spinful TS nanowire model can generate a Josephson effect. The critical current is much smaller in the topological regime and exhibits a kink-like dependence on the Zeeman field along the wire. When a correlated quantum dot (QD) in the magnetic regime is present in the junction region, however, the Josephson current becomes finite also in the deep topological phase as shown for the cotunneling regime and by a mean-field analysis. Remarkably, we find that the S-QD-TS setup can support φ0-junction behavior, where a finite supercurrent flows at vanishing phase difference. Finally, we also address a multi-terminal S-TS-S geometry, where the TS wire acts as tunable parity switch on the Andreev bound states in a superconducting atomic contact.

Proximity effect in a two-dimensional electron gas coupled to a thin superconducting layer

There have recently been several experiments studying induced superconductivity in semiconducting two-dimensional electron gases that are strongly coupled to thin superconducting layers, as well as probing possible topological phases supporting Majorana bound states in such setups. We show that a large band shift is induced in the semiconductor by the superconductor in this geometry, thus making it challenging to realize a topological phase. Additionally, we show that while increasing the thickness of the superconducting layer reduces the magnitude of the band shift, it also leads to a more significant renormalization of the semiconducting material parameters and does not reduce the challenge of tuning into a topological phase.

On-Chip Andreev Devices: Hard Superconducting Gap and Quantum Transport in Ballistic Nb-In0.75 Ga0.25 As-Quantum-Well-Nb Josephson Junctions

A superconducting hard gap in hybrid superconductor-semiconductor devices has been found to be necessary to access topological superconductivity that hosts Majorana modes (non-Abelian excitation). This requires the formation of homogeneous and barrier-free interfaces between the superconductor and semiconductor. Here, a new platform is reported for topological superconductivity based on hybrid Nb-In_0.75 Ga_0.25 As-quantum-well-Nb that results in hard superconducting gap detection in symmetric, planar, and ballistic Josephson junctions. It is shown that with careful etching, sputtered Nb films can make high-quality and transparent contacts to the In_0.75 Ga_0.25 As quantum well, and the differential resistance and critical current measurements of these devices are discussed as a function of temperature and magnetic field. It is demonstrated that proximity-induced superconductivity in the In_0.75 Ga_0.25 As-quantum-well 2D electron gas results in the detection of a hard gap in four out of seven junctions on a chip with critical current values of up to 0.2 µA and transmission probabilities of >0.96. The results, together with the large g-factor and Rashba spin-orbit coupling in In_0.75 Ga_0.25 As quantum wells, which indeed can be tuned by the indium composition, suggest that the Nb-In_0.75 Ga_0.25 As-Nb system can be an excellent candidate to achieve topological phase and to realize hybrid topological superconducting devices.

Exploring a Proximity-Coupled Co Chain on Pb(110) as a Possible Majorana Platform

Linear chains of magnetic atoms proximity coupled to an s-wave superconductor are predicted to host Majorana zero modes at the chain ends in the presence of strong spin-orbit coupling. Specifically, iron (Fe) chains on Pb(110) have been explored as a possible system to exhibit topological superconductivity and host Majorana zero modes [ Nadj-Perge , S. et al., Science 2014 , 346 , 602 - 607 ]. Here, we study chains of the transition metal cobalt (Co) on Pb(110) and check for topological signatures. Using spin-polarized scanning tunneling spectroscopy, we resolve ferromagnetic order in the d bands of the chains. Interestingly, also the subgap Yu-Shiba-Rusinov (YSR) bands carry a spin polarization as was predicted decades ago. Superconducting tips allow us to resolve further details of the YSR bands and in particular resonances at zero energy. We map the spatial distribution of the zero-energy signal and find it delocalized along the chain. Hence, despite the ferromagnetic coupling within the chains and the strong spin-orbit coupling in the superconductor, we do not find clear evidence of Majorana modes. Simple tight-binding calculations suggest that the spin-orbit-split bands may cross the Fermi level four times which suppresses the zero-energy modes.

Hard Superconducting Gap in InSb Nanowires

Topological superconductivity is a state of matter that can host Majorana modes, the building blocks of a topological quantum computer. Many experimental platforms predicted to show such a topological state rely on proximity-induced superconductivity. However, accessing the topological properties requires an induced hard superconducting gap, which is challenging to achieve for most material systems. We have systematically studied how the interface between an InSb semiconductor nanowire and a NbTiN superconductor affects the induced superconducting properties. Step by step, we improve the homogeneity of the interface while ensuring a barrier-free electrical contact to the superconductor and obtain a hard gap in the InSb nanowire. The magnetic field stability of NbTiN allows the InSb nanowire to maintain a hard gap and a supercurrent in the presence of magnetic fields (∼0.5 T), a requirement for topological superconductivity in one-dimensional systems. Our study provides a guideline to induce superconductivity in various experimental platforms such as semiconductor nanowires, two-dimensional electron gases, and topological insulators and holds relevance for topological superconductivity and quantum computation.