Metallated carbon nanowires for potential quantum computing applications via substrate proximity

The realization of next-generation quantum computing devices is hindered by the formidable challenge of detecting and manipulating Majorana zero mode (MZM). In this study, we study if MZM exist in metallated carbyne nanowires. Through optimizations of distinct types of metallated carbyne, we have achieved an average magnetic moment surpassing 1μB for the cases of Mo, Tc, and Ru metallated carbyne. where their local moments exceed 2μB. The magnetism of the Ru atom displays periodic variations with increasing carbyne length. associated with a strong average spin-orbital coupling of ∼140meV. When the ferromagnetic Ru metallated carbyne, coupled with a superconducting Ru substrate, could trigger band inversions at the gamma (G) point and M point, where spin-orbital coupling triggers the transition between the band inversion and the Dirac gap. Our findings present an exciting opportunity to realize carbon-based materials capable of hosting MZM.

Realization of 2D metals at the ångström thickness limit

Two-dimensional (2D) metals are appealing for many emergent phenomena and have recently attracted research interests1-9. Unlike the widely studied 2D van der Waals (vdW) layered materials, 2D metals are extremely challenging to achieve, because they are thermodynamically unstable1,10. Here we develop a vdW squeezing method to realize diverse 2D metals (including Bi, Ga, In, Sn and Pb) at the ångström thickness limit. The achieved 2D metals are stabilized from a complete encapsulation between two MoS2 monolayers and present non-bonded interfaces, enabling access to their intrinsic properties. Transport and Raman measurements on monolayer Bi show excellent physical properties, for example, new phonon mode, enhanced electrical conductivity, notable field effect and large nonlinear Hall conductivity. Our work establishes an effective route for implementing 2D metals, alloys and other 2D non-vdW materials, potentially outlining a bright vision for a broad portfolio of emerging quantum, electronic and photonic devices.

Observation of Yu-Shiba-Rusinov-like states at the edge of CrBr3/NbSe2 heterostructure

The hybrid ferromagnet-superconductor heterostructures have attracted extensive attention as they potentially host topological superconductivity. Relevant experimental signatures have recently been reported in CrBr3/NbSe2 ferromagnet-superconductor heterostructure, but controversies remain. Here, we reinvestigate CrBr3/NbSe2 by an ultralow temperature scanning tunneling microscope with higher spatial and energy resolutions. We find that the single-layer CrBr3 film is insulating and acts likely as a vacuum barrier, the measured superconducting gap and vortex state on it are nearly the same as those of NbSe2 substrate. Meanwhile, in-gap features are observed at the edges of CrBr3 island, which display either a zero-energy conductance peak or a pair of particle-hole symmetric bound states. They are discretely distributed at the edges of CrBr3 film, and their appearance is found closely related to the atomic lattice reconstruction near the edges. By increasing tunneling transmissivity, the zero-energy conductance peak quickly splits, while the pair of nonzero in-gap bound states first approach each other, merge, and then split again. These behaviors are unexpected for Majorana edge modes, but in consistent with the conventional Yu-Shiba-Rusinov states. Our results provide critical information for further understanding the interfacial coupling in CrBr3/NbSe2 heterostructure.

Optical conductivity of the Majorana mode at the s- and d-wave topological superconductor edge

The Majorana fermion offers fascinating possibilities such as non-Abelian statistics and nonlocal robust qubits, and hunting it is one of the most important topics in current condensed matter physics. Most of the efforts have been focused on the Majorana bound state at zero energy in terms of scanning tunneling spectroscopy searching for the quantized conductance. On the other hand, a chiral Majorana edge channel appears at the surface of a three-dimensional topological insulator when engineering an interface between proximity-induced superconductivity and ferromagnetism. Recent advances in microwave spectroscopy of topological edge states open a new avenue for observing signatures of such Majorana edge states through the local optical conductivity. As a guide to future experiments, we show how the local optical conductivity and density of states present distinct qualitative features depending on the symmetry of the superconductivity, that can be tuned via the magnetization and temperature. In particular, the presence of the Majorana edge state leads to a characteristic nonmonotonic temperature dependence achieved by tuning the magnetization.

High Transition Temperature Driven by Type-II Dirac Fermions in Topological Superconductor B7Be2B7 Nanosheet

Topological superconductors (TSCs) offer a promising avenue for delving into exotic states of matter and fundamental physics. We propose a strategy for realizing high transition temperatures (high-Tc) in TSCs by leveraging nontrivial topology alongside a high carrier density near the Fermi level in metal-doped borophenes. We identified 39 candidates with exceptional thermodynamic stability from thousands of Be-intercalated borophenes (Be1-xBx) via extensive structural searches. Seven candidates exhibit high carrier densities, with B7Be2B7 emerging as a particularly promising candidate. This nanosheet displays both type-I and type-II Dirac fermions, indicative of Z 2 topological metals, thereby positioning it as an ideal platform for high-Tc TSCs. The high-density π electrons of B7Be2B7 originating from type-II Dirac fermions, coupled with the out-of-plane vibrations of B and Be atoms, significantly enhance the electron-phonon coupling (λ = 1.42), resulting in a substantially high-Tc of 31.5 K. These findings underscore the potential of metal-doped borophenes as a cutting-edge material platform for achieving high-Tc TSCs.

Realization of Honeycomb Tellurene with Topological Edge States

The two-dimensional (2D) honeycomb lattice has attracted intensive research interest due to the appearance of Dirac-type band structures as the consequence of two sublattices in the honeycomb structure. Introducing strong spin-orbit coupling (SOC) leads to a gap opening at the Dirac point, transforming the honeycomb lattice into a 2D topological insulator as a platform for the quantum spin Hall effect (QSHE). In this work, we realize a 2D honeycomb-structured film with tellurium, the heaviest nonradioactive element in Group VI, namely, tellurene, via molecular beam epitaxy. We revealed the gap opening of 160 meV at the Dirac point due to the strong SOC in the honeycomb-structured tellurene by angle-resolved photoemission spectroscopy. The topological edge states of tellurene are detected via scanning tunneling microscopy/spectroscopy. These results demonstrate that tellurene is a novel 2D honeycomb lattice with strong SOC, and they unambiguously prove that tellurene is a promising candidate for a room-temperature QSHE system.

Topological Complex Charge Conservation in Nontrivial Z2 × Z2 Domain Walls

Localized topological modes such as solitons, Majorana Fermions, and skyrmions are attracting great interest as robust information carriers for future devices. Here, a novel conserved quantity for topological domain wall networks of a Z2 × Z2 order generated with spin-polarized current in Sr2VO3FeAs is discovered. Domain walls are mobilized by the scanning tunneling current, which also observes in atomic scale active dynamics of domain wall vertices including merge, bifurcation, pair creation, and annihilation. Within this dynamics, the product of the topological complex charges defined for domain wall vertices is conserved with a novel boundary-charge correspondence rule. These results may open an avenue toward topological electronics based on domain wall vertices in generic Z2 × Z2 systems.

Topological band inversion and chiral Majorana mode in hcp thallium

The chiral Majorana fermion is an exotic particle that is its own antiparticle. It can arise in a one-dimensional edge of topological materials, and especially that in a topological superconductor can be exploited in non-Abelian quantum computation. While the chiral Majorana mode (CMM) remains elusive, a promising situation is realized when superconductivity coexists with a topologically non-trivial surface state. Here, we perform fully non-empirical calculation for the CMM considering superconductivity and surface relaxation, and show that hexagonal close-packed thallium (Tl) has an ideal electronic state that harbors the CMM. Thekz=0plane of Tl is a mirror plane, realizing a full-gap band inversion corresponding to a topological crystalline insulating phase. Its surface and hinge are stable and easy to make various structures. Another notable feature is that the surface Dirac point is very close to the Fermi level, so that a small Zeeman field can induce a topological transition. Our calculation indicates that Tl will provide a new platform of the Majorana fermion.

Magnetic field filtering of the boundary supercurrent in unconventional metal NiTe2-based Josephson junctions

Topological materials with boundary (surface/edge/hinge) states have attracted tremendous research interest. Additionally, unconventional (obstructed atomic) materials have recently drawn lots of attention owing to their obstructed boundary states. Experimentally, Josephson junctions (JJs) constructed on materials with boundary states produce the peculiar boundary supercurrent, which was utilized as a powerful diagnostic approach. Here, we report the observations of boundary supercurrent in NiTe2-based JJs. Particularly, applying an in-plane magnetic field along the Josephson current can rapidly suppress the bulk supercurrent and retain the nearly pure boundary supercurrent, namely the magnetic field filtering of supercurrent. Further systematic comparative analysis and theoretical calculations demonstrate the existence of unconventional nature and obstructed hinge states in NiTe2, which could produce hinge supercurrent that accounts for the observation. Our results reveal the probable hinge states in unconventional metal NiTe2, and demonstrate in-plane magnetic field as an efficient method to filter out the bulk contributions and thereby to highlight the hinge states hidden in topological/unconventional materials.

Dislocation Majorana bound states in iron-based superconductors

We show that lattice dislocations of topological iron-based superconductors such as FeTe1-xSex will intrinsically trap non-Abelian Majorana quasiparticles, in the absence of any external magnetic field. Our theory is motivated by the recent experimental observations of normal-state weak topology and surface magnetism that coexist with superconductivity in FeTe1-xSex, the combination of which naturally achieves an emergent second-order topological superconductivity in a two-dimensional subsystem spanned by screw or edge dislocations. This exemplifies a new embedded higher-order topological phase in class D, where Majorana zero modes appear around the "corners" of a low-dimensional embedded subsystem, instead of those of the full crystal. A nested domain wall theory is developed to understand the origin of these defect Majorana zero modes. When the surface magnetism is absent, we further find that s± pairing symmetry itself is capable of inducing a different type of class-DIII embedded higher-order topology with defect-bound Majorana Kramers pairs. We also provide detailed discussions on the real-world material candidates for our proposals, including FeTe1-xSex, LiFeAs, β-PdBi2, and heterostructures of bismuth, etc. Our work establishes lattice defects as a new venue to achieve high-temperature topological quantum information processing.

Observation of Emergent Superconductivity in the Topological Insulator Ta2Pd3Te5 via Pressure Manipulation

Topological insulators offer significant potential to revolutionize diverse fields driven by nontrivial manifestations of their topological electronic band structures. However, the realization of superior integration between exotic topological states and superconductivity for practical applications remains a challenge, necessitating a profound understanding of intricate mechanisms. Here, we report experimental observations for a novel superconducting phase in the pressurized second-order topological insulator candidate Ta2Pd3Te5, and the high-pressure phase maintains its original ambient pressure lattice symmetry up to 45 GPa. Our in situ high-pressure synchrotron X-ray diffraction, electrical transport, infrared reflectance, and Raman spectroscopy measurements, in combination with rigorous theoretical calculations, provide compelling evidence for the association between the superconducting behavior and the densified phase. The electronic state change around 20 GPa was found to modify the topology of the Fermi surface directly, which synergistically fosters the emergence of robust superconductivity. In-depth comprehension of the fascinating properties exhibited by the compressed Ta2Pd3Te5 phase is achieved, highlighting the extraordinary potential of topological insulators for exploring and investigating high-performance electronic advanced devices under extreme conditions.

Magnetotransport Signatures of Superconducting Cooper Pairs Carried by Topological Surface States in Bismuth Selenide

As topological insulators (TIs) are becoming increasingly intriguing, the community is exploring transformative applications that require interfacing TIs with other materials such as ferromagnets or superconductors. Herein, we report on the manifestations of superconducting electrons carried by topological surface states (TSS) in Bi2Se3 films. As key signatures of TSS-carried Cooper pairs, we uncover the hysteresis of magnetoresistance (MR) and the switching behavior of anisotropic magnetoresistance (AMR). For in-plane fields perpendicular to the injected current, AMR shows negative switching (resistance drop) when the contacts become superconducting, which is consistent with a cooperative Zeeman effect enabled by the spin-momentum locking of TSS. The MR and AMR behaviors are robust, occurring reliably in multiple samples, from different sources, and with different defect concentrations. Our findings can guide novel developments in superconductor/TI quantum devices relying on supercurrent detection as well as lead to more refined transport signatures of Majorana zero-modes in the future.

Intrinsic surface p-wave superconductivity in layered AuSn4

The search for topological superconductivity (TSC) is currently an exciting pursuit, since non-trivial topological superconducting phases could host exotic Majorana modes. However, the difficulty in fabricating proximity-induced TSC heterostructures, the sensitivity to disorder and stringent topological restrictions of intrinsic TSC place serious limitations and formidable challenges on the materials and related applications. Here, we report a new type of intrinsic TSC, namely intrinsic surface topological superconductivity (IS-TSC) and demonstrate it in layered AuSn4 with Tc of 2.4 K. Different in-plane and out-of-plane upper critical fields reflect a two-dimensional (2D) character of superconductivity. The two-fold symmetric angular dependences of both magneto-transport and the zero-bias conductance peak (ZBCP) in point-contact spectroscopy (PCS) in the superconducting regime indicate an unconventional pairing symmetry of AuSn4. The superconducting gap and surface multi-bands with Rashba splitting at the Fermi level (EF), in conjunction with first-principle calculations, strongly suggest that 2D unconventional SC in AuSn4 originates from the mixture of p-wave surface and s-wave bulk contributions, which leads to a two-fold symmetric superconductivity. Our results provide an exciting paradigm to realize TSC via Rashba effect on surface superconducting bands in layered materials.

Proximity superconductivity in atom-by-atom crafted quantum dots

Gapless materials in electronic contact with superconductors acquire proximity-induced superconductivity in a region near the interface1,2. Numerous proposals build on this addition of electron pairing to originally non-superconducting systems and predict intriguing phases of matter, including topological3-7, odd-frequency8, nodal-point9 or Fulde-Ferrell-Larkin-Ovchinnikov10 superconductivity. Here we investigate the most miniature example of the proximity effect on only a single spin-degenerate quantum level of a surface state confined in a quantum corral11 on a superconducting substrate, built atom by atom by a scanning tunnelling microscope. Whenever an eigenmode of the corral is pitched close to the Fermi energy by adjusting the size of the corral, a pair of particle-hole symmetric states enters the gap of the superconductor. We identify these as spin-degenerate Andreev bound states theoretically predicted 50 years ago by Machida and Shibata12, which had-so far-eluded detection by tunnel spectroscopy but were recently shown to be relevant for transmon qubit devices13,14. We further find that the observed anticrossings of the in-gap states are a measure of proximity-induced pairing in the eigenmodes of the quantum corral. Our results have direct consequences on the interpretation of impurity-induced in-gap states in superconductors, corroborate concepts to induce superconductivity into surface states and further pave the way towards superconducting artificial lattices.

Topological Superconductors from a Materials Perspective

Topological superconductors (TSCs) have garnered significant research and industry attention in the past two decades. By hosting Majorana bound states which can be used as qubits that are robust against local perturbations, TSCs offer a promising platform toward (nonuniversal) topological quantum computation. However, there has been a scarcity of TSC candidates, and the experimental signatures that identify a TSC are often elusive. In this Perspective, after a short review of the TSC basics and theories, we provide an overview of the TSC materials candidates, including natural compounds and synthetic material systems. We further introduce various experimental techniques to probe TSCs, focusing on how a system is identified as a TSC candidate and why a conclusive answer is often challenging to draw. We conclude by calling for new experimental signatures and stronger computational support to accelerate the search for new TSC candidates.

Hunting for Majoranas

Over the past decade, there have been considerable efforts to observe non-abelian quasiparticles in novel quantum materials and devices. These efforts are motivated by the goals of demonstrating quantum statistics of quasiparticles beyond those of fermions and bosons and of establishing the underlying science for the creation of topologically protected quantum bits. In this Review, we focus on efforts to create topological superconducting phases that host Majorana zero modes. We consider the lessons learned from existing experimental efforts, which are motivating both improvements to present platforms and the exploration of new approaches. Although the experimental detection of non-abelian quasiparticles remains challenging, the knowledge gained thus far and the opportunities ahead offer high potential for discovery and advances in this exciting area of quantum physics.

Evidence for unconventional superconductivity and nontrivial topology in PdTe

PdTe is a superconductor with T_c ~ 4.25 K. Recently, evidence for bulk-nodal and surface-nodeless gap features has been reported in PdTe. Here, we investigate the physical properties of PdTe in both the normal and superconducting states via specific heat and magnetic torque measurements and first-principles calculations. Below T_c, the electronic specific heat initially decreases in T³ behavior (1.5 K < T < T_c) then exponentially decays. Using the two-band model, the superconducting specific heat can be well described with two energy gaps: one is 0.372 meV and another 1.93 meV. The calculated bulk band structure consists of two electron bands (α and β) and two hole bands (γ and η) at the Fermi level. Experimental detection of the de Haas-van Alphen (dHvA) oscillations allows us to identify four frequencies (F_α = 65 T, F_β = 658 T, F_γ = 1154 T, and F_η = 1867 T for H // a), consistent with theoretical predictions. Nontrivial α and β bands are further identified via both calculations and the angle dependence of the dHvA oscillations. Our results suggest that PdTe is a candidate for unconventional superconductivity.

Light-Induced Giant Rashba Spin-Orbit Coupling at Superconducting KTaO3 (110) Heterointerfaces

The 2D electron system (2DES) at the KTaO₃ surface or heterointerface with 5d orbitals hosts extraordinary physical properties, including a stronger Rashba spin-orbit coupling (RSOC), higher superconducting transition temperature, and potential of topological superconductivity. Herein, a huge enhancement of RSOC under light illumination achieved at a superconducting amorphous-Hf_0.5 Zr_0.5 O₂ /KTaO₃ (110) heterointerfaces is reported. The superconducting transition is observed with T_c = 0.62 K and the temperature-dependent upper critical field reveals the interaction between spin-orbit scattering and superconductivity. A strong RSOC with B_so = 1.9 T is revealed by weak antilocalization in the normal state, which undergoes sevenfold enhancement under light illumination. Furthermore, RSOC strength develops a dome-shaped dependence of carrier density with the maximum of B_so = 12.6 T achieved near the Lifshitz transition point n_c ≈ 4.1 × 10¹³ cm^-2 . The highly tunable giant RSOC at KTaO₃ (110)-based superconducting interfaces show great potential for spintronics.

Optical bulk-boundary dichotomy in a quantum spin Hall insulator

The bulk-boundary correspondence is a critical concept in topological quantum materials. For instance, a quantum spin Hall insulator features a bulk insulating gap with gapless helical boundary states protected by the underlying Z₂ topology. However, the bulk-boundary dichotomy and distinction are rarely explored in optical experiments, which can provide unique information about topological charge carriers beyond transport and electronic spectroscopy techniques. Here, we utilize mid-infrared absorption micro-spectroscopy and pump-probe micro-spectroscopy to elucidate the bulk-boundary optical responses of Bi₄Br₄, a recently discovered room-temperature quantum spin Hall insulator. Benefiting from the low energy of infrared photons and the high spatial resolution, we unambiguously resolve a strong absorption from the boundary states while the bulk absorption is suppressed by its insulating gap. Moreover, the boundary absorption exhibits strong polarization anisotropy, consistent with the one-dimensional nature of the topological boundary states. Our infrared pump-probe microscopy further measures a substantially increased carrier lifetime for the boundary states, which reaches one nanosecond scale. The nanosecond lifetime is about one to two orders longer than that of most topological materials and can be attributed to the linear dispersion nature of the helical boundary states. Our findings demonstrate the optical bulk-boundary dichotomy in a topological material and provide a proof-of-principal methodology for studying topological optoelectronics.

Competing Vortex Topologies in Iron-Based Superconductors

In this Letter, we establish a new theoretical paradigm for vortex Majorana physics in the recently discovered topological iron-based superconductors (TFeSCs). While TFeSCs are widely accepted as an exemplar of topological insulators (TIs) with intrinsic s-wave superconductivity, our theory implies that such a common belief could be oversimplified. Our main finding is that the normal-state bulk Dirac nodes, usually ignored in TI-based vortex Majorana theories for TFeSCs, will play a key role of determining the vortex state topology. In particular, the interplay between TI and Dirac nodal bands will lead to multiple competing topological phases for a superconducting vortex line in TFeSCs, including an unprecedented hybrid topological vortex state that carries both Majorana bound states and a gapless dispersion. Remarkably, this exotic hybrid vortex phase generally exists in the vortex phase diagram for our minimal model for TFeSCs and is directly relevant to TFeSC candidates such as LiFeAs. When the fourfold rotation symmetry is broken by vortex-line tilting or curving, the hybrid vortex gets topologically trivialized and becomes Majorana free, which could explain the puzzle of ubiquitous trivial vortices observed in LiFeAs. The origin of the Majorana signal in other TFeSC candidates such as FeTe_{x}Se_{1-x} and CaKFe_{4}As_{4} is also interpreted within our theory framework. Our theory sheds new light on theoretically understanding and experimentally engineering Majorana physics in high-temperature iron-based systems.

Artificial Graphene Nanoribbons: A Test Bed for Topology and Low-Dimensional Dirac Physics

We synthesize artificial graphene nanoribbons by positioning carbon monoxide molecules on a copper surface to confine its surface state electrons into artificial atoms positioned to emulate the low-energy electronic structure of graphene derivatives. We demonstrate that the dimensionality of artificial graphene can be reduced to one dimension with proper "edge" passivation, with the emergence of an effectively gapped one-dimensional nanoribbon structure. These one-dimensional structures show evidence of topological effects analogous to graphene nanoribbons. Guided by first-principles calculations, we spatially explore robust, zero-dimensional topological states by altering the topological invariants of quasi-one-dimensional artificial graphene nanostructures. The robustness and flexibility of our platform allow us to toggle the topological invariants between trivial and nontrivial on the same nanostructure. Ultimately, we spatially manipulate the states to understand fundamental coupling between adjacent topological states that are finely engineered and simulate complex Hamiltonians.

Spanning Fermi arcs in a two-dimensional magnet

The discovery of topological states of matter has led to a revolution in materials research. When external or intrinsic parameters break symmetries, global properties of topological materials change drastically. A paramount example is the emergence of Weyl nodes under broken inversion symmetry. While a rich variety of non-trivial quantum phases could in principle also originate from broken time-reversal symmetry, realizing systems that combine magnetism with complex topological properties is remarkably elusive. Here, we demonstrate that giant open Fermi arcs are created at the surface of ultrathin hybrid magnets where the Fermi-surface topology is substantially modified by hybridization with a heavy-metal substrate. The interplay between magnetism and topology allows us to control the shape and the location of the Fermi arcs by tuning the magnetization direction. The hybridization points in the Fermi surface can be attributed to a non-trivial mixed topology and induce hot-spots in the Berry curvature, dominating spin and charge transport as well as magneto-electric coupling effects.

It has been predicted that elemental Iron, with low dimensionality, will be a topological metal hosting Weyl nodes. Here, Chen et al. grow iron on tungsten, a heavy metal with a strong spin-orbit interaction, and using momentum microscopy, show the emergence of giant open Fermi arcs which can be shaped by varying the magnetization of the iron.

Emergent Multifunctional Magnetic Proximity in van der Waals Layered Heterostructures

Proximity effect, which is the coupling between distinct order parameters across interfaces of heterostructures, has attracted immense interest owing to the customizable multifunctionalities of diverse 3D materials. This facilitates various physical phenomena, such as spin order, charge transfer, spin torque, spin density wave, spin current, skyrmions, and Majorana fermions. These exotic physics play important roles for future spintronic applications. Nevertheless, several fundamental challenges remain for effective applications: unavoidable disorder and lattice mismatch limits in the growth process, short characteristic length of proximity, magnetic fluctuation in ultrathin films, and relatively weak spin-orbit coupling (SOC). Meanwhile, the extensive library of atomically thin, 2D van der Waals (vdW) layered materials, with unique characteristics such as strong SOC, magnetic anisotropy, and ultraclean surfaces, offers many opportunities to tailor versatile and more effective functionalities through proximity effects. Here, this paper focuses on magnetic proximity, i.e., proximitized magnetism and reviews the engineering of magnetism-related functionalities in 2D vdW layered heterostructures for next-generation electronic and spintronic devices. The essential factors of magnetism and interfacial engineering induced by magnetic layers are studied. The current limitations and future challenges associated with magnetic proximity-related physics phenomena in 2D heterostructures are further discussed.

Coexistence of Robust Edge States and Superconductivity in Few-Layer Stanene

High-quality stanene films have been actively pursued for realizing not only quantum spin Hall edge states without backscattering, but also intrinsic superconductivity, two central ingredients that may further endow the systems to host topological superconductivity. Yet to date, convincing evidence of topological edge states in stanene remains to be seen, let alone the coexistence of these two ingredients, owing to the bottleneck of growing high-quality stanene films. Here we fabricate one- to five-layer stanene films on the Bi(111) substrate and observe the robust edge states using scanning tunneling microscopy/spectroscopy. We also measure distinct superconducting gaps on different-layered stanene films. Our first-principles calculations further show that hydrogen passivation plays a decisive role as a surfactant in improving the quality of the stanene films, while the Bi substrate endows the films with nontrivial topology. The coexistence of nontrivial topology and intrinsic superconductivity renders the system a promising candidate to become the simplest topological superconductor based on a single-element system.

Role of Majorana fermions in high-harmonic generation from Kitaev chain

The observation of Majorana fermions as collective excitations in condensed-matter systems is an ongoing quest, and several state-of-the-art experiments have been performed in the last decade. As a potential avenue in this direction, we simulate the high-harmonic spectrum of Kitaev's superconducting chain model that hosts Majorana edge modes in its topological phase. It is well-known that this system exhibits a topological-trivial superconducting phase transition. We demonstrate that high-harmonic spectroscopy is sensitive to the phase transition in presence of open boundary conditions due to the presence or absence of these edge modes. The population dynamics of the Majorana edge modes are different from the bulk modes, which is the underlying reason for the distinct harmonic profile of both the phases. On the contrary, in presence of periodic boundary conditions with only bulk modes, high-harmonic spectroscopy becomes insensitive to the phase transition with similar harmonic profiles in both phases.

Topographic signatures and manipulations of Fe atoms, CO molecules and NaCl islands on superconducting Pb(111)

Topological superconductivity emerging in one- or two-dimensional hybrid materials is predicted as a key ingredient for quantum computing. However, not only the design of complex heterostructures is primordial for future applications but also the characterization of their electronic and structural properties at the atomic scale using the most advanced scanning probe microscopy techniques with functionalized tips. We report on the topographic signatures observed by scanning tunneling microscopy (STM) of carbon monoxide (CO) molecules, iron (Fe) atoms and sodium chloride (NaCl) islands deposited on superconducting Pb(111). For the CO adsorption a comparison with the Pb(110) substrate is demonstrated. We show a general propensity of these adsorbates to diffuse at low temperature under gentle scanning conditions. Our findings provide new insights into high-resolution probe microscopy imaging with terminated tips, decoupling atoms and molecules by NaCl islands or tip-induced lateral manipulation of iron atoms on top of the prototypical Pb(111) superconducting surface.

Discovery of segmented Fermi surface induced by Cooper pair momentum

[Figure: see text].

Majorana Zero Modes in Ferromagnetic Wires without Spin-Orbit Coupling

We present a novel controllable platform for engineering Majorana zero modes. The platform consists of a ferromagnetic metallic wire placed among conventional superconductors, which are in proximity to ferromagnetic insulators. We demonstrate that Majorana zero modes emerge localised at the edges of the ferromagnetic wire, due to the interplay of the applied supercurrents and the induced by proximity exchange fields with conventional superconductivity. Our mechanism does not rely on the pairing of helical fermions by combining conventional superconductivity with spin-orbit coupling, but rather exploits the misalignment between the magnetization of the ferromagnetic insulators and that of the ferromagnetic wire.

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.

Interaction-induced topological phase transition and Majorana edge states in low-dimensional orbital-selective Mott insulators

Topological phases of matter are among the most intriguing research directions in Condensed Matter Physics. It is known that superconductivity induced on a topological insulator's surface can lead to exotic Majorana modes, the main ingredient of many proposed quantum computation schemes. In this context, the iron-based high critical temperature superconductors are a promising platform to host such an exotic phenomenon in real condensed-matter compounds. The Coulomb interaction is commonly believed to be vital for the magnetic and superconducting properties of these systems. This work bridges these two perspectives and shows that the Coulomb interaction can also drive a canonical superconductor with orbital degrees of freedom into the topological state. Namely, we show that above a critical value of the Hubbard interaction the system simultaneously develops spiral spin order, a highly unusual triplet amplitude in superconductivity, and, remarkably, Majorana fermions at the edges of the system.

Evidence for a higher-order topological insulator in a three-dimensional material built from van der Waals stacking of bismuth-halide chains

Low-dimensional van der Waals materials have been extensively studied as a platform with which to generate quantum effects. Advancing this research, topological quantum materials with van der Waals structures are currently receiving a great deal of attention. Here, we use the concept of designing topological materials by the van der Waals stacking of quantum spin Hall insulators. Most interestingly, we find that a slight shift of inversion centre in the unit cell caused by a modification of stacking induces a transition from a trivial insulator to a higher-order topological insulator. Based on this, we present angle-resolved photoemission spectroscopy results showing that the real three-dimensional material Bi₄Br₄ is a higher-order topological insulator. Our demonstration that various topological states can be selected by stacking chains differently, combined with the advantages of van der Waals materials, offers a playground for engineering topologically non-trivial edge states towards future spintronics applications.

Superhigh Uniform Magnetic Cr Substitution in a 2D Mo2 C Superconductor for a Macroscopic-Scale Kondo Effect

Substitutional doping provides an effective strategy to tailor the properties of 2D materials, but it remains an open challenge to achieve tunable uniform doping, especially at high doping level. Here, uniform lattice substitution of a 2D Mo₂ C superconductor by magnetic Cr atoms with controlled concentration up to ≈46.9 at% by chemical vapor deposition and a specifically designed Cu/Cr/Mo trilayer growth substrate is reported. The concentration of Cr atoms can be easily tuned by simply changing the thickness of the Cr layer, and the samples retain the original structure of 2D Mo₂ C even at a very high Cr concentration. The controlled uniform Cr doping enables the tuning of the competition of the 2D superconductor and the Kondo effect across the whole sample. Transport measurements show that with increasing Cr concentration, the superconductivity of the 2D Cr-doped Mo₂ C crystals disappears along with the emergence of the Kondo effect, and the Kondo temperature increases monotonously. Using scanning tunneling microscopy/spectroscopy, the mechanism of the doping level effect on the interplay and evolution between superconductivity and the Kondo effect is revealed. This work paves a new way for the synthesis of 2D materials with widely tunable doping levels, and provides new understandings on the interplay between superconductivity and magnetism in the 2D limit.

Observation of backscattering induced by magnetism in a topological edge state

The boundary modes of topological insulators are protected by the symmetries of the nontrivial bulk electronic states. Unless these symmetries are broken, they can give rise to novel phenomena, such as the quantum spin Hall effect in one-dimensional (1D) topological edge states, where quasiparticle backscattering is suppressed by time-reversal symmetry (TRS). Here, we investigate the properties of the 1D topological edge state of bismuth in the absence of TRS, where backscattering is predicted to occur. Using spectroscopic imaging and spin-polarized measurements with a scanning tunneling microscope, we compared quasiparticle interference (QPI) occurring in the edge state of a pristine bismuth bilayer with that occurring in the edge state of a bilayer, which is terminated by ferromagnetic iron clusters that break TRS. Our experiments on the decorated bilayer edge reveal an additional QPI branch, which can be associated with spin-flip scattering across the Brioullin zone center between time-reversal band partners. The observed QPI characteristics exactly match with theoretical expectations for a topological edge state, having one Kramer's pair of bands. Together, our results provide further evidence for the nontrivial nature of bismuth and in particular, demonstrate backscattering inside a helical topological edge state induced by broken TRS through local magnetism.

One-Dimensional Edge Transport in Few-Layer WTe2

WTe2 is a layered transitional-metal dichalcogenide (TMD) with a number of intriguing topological properties. Recently, WTe2 has been predicted to be a higher-order topological insulator (HOTI) with topologically protected hinge states along the edges. The gapless nature of WTe2 complicates the observation of one-dimensional (1D) topological states in transport due to their small contribution relative to the bulk. Here, we study the behavior of the Josephson effect in magnetic field to distinguish edge from bulk transport. The Josephson effect in few-layer WTe2 reveals 1D states residing on the edges and steps. Moreover, our data demonstrates a combination of Josephson transport properties observed solely in another HOTI-bismuth, including Josephson transport over micrometer distances, extreme robustness in a magnetic field, and nonsinusoidal current-phase relation (CPR). Our observations strongly suggest the topological origin of the 1D states and that few-layer WTe2 is a HOTI.

Scanning tunneling spectroscopy studies of topological materials

Topological materials have become promising materials for next-generation devices by utilizing their exotic electronic states. Their exotic states caused by spin-orbital coupling usually locate on the surfaces or at the edges. Scanning tunneling spectroscopy (STS) is a powerful tool to reveal the local electronic structures of condensed matters. Therefore, STS provides us with an almost perfect method to access the exotic states of topological materials. In this topical review, we report the current investigations by several methods based on the STS technique for layered topological material from transition metal dichalcogenide Weyl semimetals (WTe₂ and MoTe₂) to two dimensional topological insulators (layered bismuth and silicene). The electronic characteristics of these layered topological materials are experimentally identified.

The effect of moiré superstructures on topological edge states in twisted bismuthene homojunctions

Creating and controlling the topological properties of two-dimensional topological insulators is essential for spintronic device applications. Here, we report the successful growth of bismuth homostructure consisting of monolayer bismuthene and single-layer black phosphorus-like Bi (BP-Bi) on the HOPG surface. Combining scanning tunneling microscopy/spectroscopy with noncontact atomic force microscopy, moiré superstructures with twist angles in the bismuth homostructure and the modulation of topological edge states of bismuthene were observed and studied. First-principles calculations reproduced the moiré superlattice and indicated that the structure fluctuation is ascribed to the stacking modes between bismuthene and BP-Bi, which induce spatially distributed interface interactions in the bismuth homostructure. The modulation of topological edge states is directly related to the variation of interlayer interactions. Our results suggest a promising pathway to tailor the topological states through interfacial interactions.

Signature of a pair of Majorana zero modes in superconducting gold surface states

Under certain conditions, a fermion in a superconductor can separate in space into two parts known as Majorana zero modes, which are immune to decoherence from local noise sources and are attractive building blocks for quantum computers. Promising experimental progress has been made to demonstrate Majorana zero modes in materials with strong spin-orbit coupling proximity coupled to superconductors. Here we report signatures of Majorana zero modes in a material platform utilizing the surface states of gold. Using scanning tunneling microscope to probe EuS islands grown on top of gold nanowires, we observe two well-separated zero-bias tunneling conductance peaks aligned along the direction of the applied magnetic field, as expected for a pair of Majorana zero modes. This platform has the advantage of having a robust energy scale and the possibility of realizing complex designs using lithographic methods.

Recent Advances in Tin: From Two-Dimensional Quantum Spin Hall Insulator to Bulk Dirac Semimetal

An atomic layer of tin in a buckled honeycomb lattice, termed stanene, is a promising large-gap two-dimensional topological insulator for realizing room-temperature quantum-spin-Hall effect and therefore has drawn tremendous interest in recent years. Because the electronic structures of Sn allotropes are sensitive to lattice strain, e.g. the semimetallic α-phase of Sn can transform into a three-dimensional topological Dirac semimetal under compressive strain, recent experimental advances have demonstrated that stanene layers on different substrates can also host various electronic properties relating to in-plane strain, interfacial charge transfer, layer thickness, and so on. Thus, comprehensive understanding of the growth mechanism at the atomic scale is highly desirable for precise control of such tunable properties. Herein, the fundamental properties of stanene and α-Sn films, recent achievements in epitaxial growth, challenges in high-quality synthesis, and possible applications of stanene are discussed.

Mechanical Analogue of a Majorana Bound State

The discovery of topologically nontrivial electronic systems has opened a new age in condensed matter research. From topological insulators to topological superconductors and Weyl semimetals, it is now understood that some of the most remarkable and robust phases in electronic systems (e.g., quantum Hall or anomalous quantum Hall) are the result of topological protection. These powerful ideas have recently begun to be explored also in bosonic systems. Topologically protected acoustic, mechanical, and optical edge states have been demonstrated in a number of systems that recreate the requisite topological conditions. Such states that propagate without backscattering could find important applications in communications and energy technologies. Here, a topologically bound mechanical state, a different class of nonpropagating protected state that cannot be destroyed by local perturbations, is demonstrated. It is in particular a mechanical analogue of the well-known Majorana bound states (MBSs) of electronic topological superconductor systems. The topological binding is implemented by creating a Kekulé distortion vortex on a 2D mechanical honeycomb superlattice that can be mapped to a magnetic flux vortex in a topological superconductor.

Nanosystems, Edge Computing, and the Next Generation Computing Systems

It is widely recognized that nanoscience and nanotechnology and their subfields, such as nanophotonics, nanoelectronics, and nanomechanics, have had a tremendous impact on recent advances in sensing, imaging, and communication, with notable developments, including novel transistors and processor architectures. For example, in addition to being supremely fast, optical and photonic components and devices are capable of operating across multiple orders of magnitude length, power, and spectral scales, encompassing the range from macroscopic device sizes and kW energies to atomic domains and single-photon energies. The extreme versatility of the associated electromagnetic phenomena and applications, both classical and quantum, are therefore highly appealing to the rapidly evolving computing and communication realms, where innovations in both hardware and software are necessary to meet the growing speed and memory requirements. Development of all-optical components, photonic chips, interconnects, and processors will bring the speed of light, photon coherence properties, field confinement and enhancement, information-carrying capacity, and the broad spectrum of light into the high-performance computing, the internet of things, and industries related to cloud, fog, and recently edge computing. Conversely, owing to their extraordinary properties, 0D, 1D, and 2D materials are being explored as a physical basis for the next generation of logic components and processors. Carbon nanotubes, for example, have been recently used to create a new processor beyond proof of principle. These developments, in conjunction with neuromorphic and quantum computing, are envisioned to maintain the growth of computing power beyond the projected plateau for silicon technology. We survey the qualitative figures of merit of technologies of current interest for the next generation computing with an emphasis on edge computing.

Observation of a Majorana zero mode in a topologically protected edge channel

Superconducting proximity pairing in helical edge modes, such as those of topological insulators, is predicted to provide a unique platform for realizing Majorana zero modes (MZMs). We used scanning tunneling microscopy measurements to probe the influence of proximity-induced superconductivity and magnetism on the helical hinge states of bismuth(111) films grown on a superconducting niobium substrate and decorated with magnetic iron clusters. Consistent with model calculations, our measurements revealed the emergence of a localized MZM at the interface between the superconducting helical edge channel and the iron clusters, with a strong magnetization component along the edge. Our experiments also resolve the MZM’s spin signature, which distinguishes it from trivial in-gap states that may accidentally occur at zero energy in a superconductor.