Topological Superconductors Research Articles

Magnetic flux induced topological superconductivity in magnetic atomic rings

Magnetic flux induced topological superconductivity in magnetic atomic rings

Long-range Pairing in Monolayer NbSe2 Facilitates the Emergence of Topological Superconducting States

Abstract NbSe2, which simultaneously exhibits superconductivity and spin-orbit coupling, is anticipated to pave the way for topological superconductivity and unconventional electron pairing. In this paper, we systematically study topological superconducting (TSC) phases in monolayer NbSe2 through mixing on-site s-wave pairing (ps) with long-range pairing (psA1) based on a tight-binding model. We observe rich phases with both fixed and sensitive Chern numbers (CNs) depending on the chemical potential (μ) and out-of-plane magnetic field (Vz). As psA1 increases, the TSC phase manifests matching and mismatching features according to whether there is a bulk-boundary correspondence (BBC). Strikingly, the introduction of long-range pairing significantly reduces the critical Vz to form TSC phases compared with the pure s-wave paring. Moreover, the TSC phase can be modulated even at Vz=0 under appropriate μ and psA1, which is identified by the robust topological edge states (TESs) of ribbons. Additionally, the long-range pairing influences the hybridization of bulk and edge states, resulting in a matching/mismatching BBC with localized/oscillating TESs on the ribbon. Our finding is helpful for realization of TSC states in experiment, as well as designing and regulating TSC materials.

Giant Tunability of Rashba Splitting at Cation-Exchanged Polar Oxide Interfaces by Selective Orbital Hybridization.

The 2D electron gas (2DEG) at oxide interfaces exhibits extraordinary properties, such as 2D superconductivity and ferromagnetism, coupled to strongly correlated electrons in narrow d-bands. In particular, 2DEGs in KTaO3 (KTO) with 5d t2g orbitals exhibit larger atomic spin-orbit coupling and crystal-facet-dependent superconductivity absent for 3d 2DEGs in SrTiO3 (STO). Herein, by tracing the interfacial chemistry, weak anti-localization magneto-transport behavior, and electronic structures of (001), (110), and (111) KTO 2DEGs, unambiguously cation exchange across KTO interfaces is discovered. Therefore, the origin of the 2DEGs at KTO-based interfaces is dramatically different from the electronicreconstruction observed at STO interfaces. More importantly, as the interface polarization grows with the higher order planes in the KTO case, the Rashba spin splitting becomes maximal for the superconducting (111) interfaces approximately twice that of the (001) interface. The larger Rashba spin splitting couples strongly to the asymmetric chiral texture of the orbital angular moment, and results mainly from the enhanced inter-orbital hopping of the t2g bands and more localized wave functions. This finding has profound implications for the search for topological superconductors, as well as the realization of efficient spin-charge interconversion for low-power spin-orbitronics based on (110) and (111) KTO interfaces.

Coexistence of superconductivity and topological phase in kagome metals ANb3Bi5 (A = K, Rb, Cs)

The AV3Sb5 prototype kagome materials have been demonstrated as a versatile platform for exploring exotic properties in condensed matter physics, including charge density waves, superconductivity, non-trivial electron topology, as well as topological superconductivity. Here we identify that ANb3Bi5 (A = K, Rb, Cs) exhibit non-trivial coexisting superconductivity and topological properties via first-principles calculations. The negative formation energy and the absence of imaginary phonon dispersion demonstrate both thermodynamics and dynamics stabilities of ANb3Bi5 (A = K, Rb, Cs) under ambient conditions. By analytically solving the Allen-Dynes-modified McMillan formula, the superconducting transition temperatures are predicted to be 2.11, 2.15 and 2.21 K for KNb3Bi5, RbNb3Bi5, and CsNb3Bi5, respectively. More importantly, the kagome materials proposed here can be classified into Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb{Z}}}_{2}$$\\end{document} topological metals due to the non-trivial topological index and the obvious surface states around the Fermi level. Such coexistence of superconductivity and non-trivial band characters in ANb3Bi5 (A = K, Rb, Cs) offer us more insights to study the relationship between superconductivity and topological properties, and to design innate topological superconductors.

Topological superconductivity induced by a Kitaev spin liquid

Topological superconductivity induced by a Kitaev spin liquid

Topologically trivial gap-filling in superconducting Fe(Se,Te) by one-dimensional defects

Structural distortions and imperfections are a crucial aspect of materials science, on the macroscopic scale providing strength, but also enhancing corrosion and reducing electrical and thermal conductivity. At the nanometre scale, multi-atom imperfections, such as atomic chains and crystalline domain walls have conversely been proposed as a route to topological superconductivity, whose most prominent characteristic is the emergence of Majorana Fermions that can be used for error-free quantum computing. Here, we shed more light on the nature of purported domain walls in Fe(Se,Te) that may host 1D dispersing Majorana modes. We show that the displacement shift of the atomic lattice at these line-defects results from sub-surface impurities that warp the topmost layer(s). Using the electric field between the tip and sample, we manage to reposition the sub-surface impurities, directly visualizing the displacement shift and the underlying defect-free lattice. These results, combined with observations of a completely different type of 1D defect where superconductivity remains fully gapped, highlight the topologically trivial nature of 1D defects in Fe(Se,Te).

Magnetotransport properties of BiSe whiskers

Doped Bi2Se3 superconductors, such as CuxBi2Se3, SrxBi2Se3, NbxBi2Se3 are shown to be nematic superconductors in addition to the observed topological superconductivity. Recently it was found superconductivity in PdxBi2Se3 whiskers. The superconductivity has a residual character and probably exists on the whisker surface. The present paper deals with checking a possible nematicity existing in PdxBi2Se3 whiskers. The suppression of superconductivity was measured in the magnetic fields with induction up to 1.5 T. It was found the dependency of upper critical fields on the angle of magnetic field application. The dependency is explained in the framework of Ginzburg–Landau model and described by rather small anisotropy parameter 1.2. Besides blurring of temperature Curie near 5.3 K was observed of about 0.5 K that additionally confirmed the nematicity in PdxBi2Se3 whiskers. The rather high Curie temperature as well as nematicity existing is probably connected with strong spin–orbit interaction (SOI) of the charge carriers in the whiskers which stabilizing the superconductive state. When the temperature exceeds T c weak antilocalization of charge carriers is observed in the whisker magnetoresistance.

Topological superconductors with spin-triplet pairings and Majorana Fermi arcs

Abstract We construct a three-dimensional topological superconductor Bogoliubov-de Gennes(BdG) Hamiltonian with the normal state being a three dimensional topological insulator. By introducing inter-orbital spin-triplet pairings term △3, there are topological Majorana nodes in the bulk, and they are connected by Majorana Fermi arcs on the surface, similar to the case of Weyl semimetal. Furthermore, by adding an inversion breaking term to the normal state, momentum independent pairing terms with different parities can coexist in the BdG Hamiltonian, which creates more Majorana modes similar to Andreev bound states and a richer phase diagram.

Topological phase transition in compressed van der Waals superlattice heterostructure BiTeCl/HfTe2

Abstract Based on first-principles calculations, we investigate the electronic band structures and topological properties of heterostructure BiTeCl/HfTe2 under c-direction strain. In the primitive structure, this material undergoes a phase transition from an insulator with a narrow indirect gap to a metal by strong spin–orbital coupling. When strain effect is considered, band inversion at time-reversal invariant point Z is responsible for the topological phase transition. These nontrivial topologies are caused by two different types of band crossings. The observable topological surface states in (110) surface also support that this material experiences topological phase transition twice. The layered heterostructure with van der Waals force provides us with a new desirable platform upon which to control topological phase transition and construct topological superconductors.

Theory of Majorana Zero Modes in Unconventional Superconductors

Abstract Majorana fermions are spin-1/2 neutral particles that are their own antiparticles; they were initially predicted by Ettore Majorana in particle physics but their observation still remains elusive. The concept of Majorana fermions has been borrowed by condensed matter physics, where, unlike particle physics, Majorana fermions emerge as zero-energy quasiparticles that can be engineered by combining electrons and holes and have therefore been called Majorana zero modes. In this review, we provide a pedagogical explanation of the basic properties of Majorana zero modes in unconventional superconductors and their consequences in experimental observables, putting a special emphasis on the initial theoretical discoveries. In particular, we first show that Majorana zero modes are self-conjugated and emerge as a special type of zero-energy surface Andreev bound states at the boundary of unconventional superconductors. We then explore Majorana zero modes in 1D spin-polarized p-wave superconductors, where we address the formation of topological superconductivity and the physical realization in superconductor–semiconductor hybrids. In this part we highlight that Majorana quasiparticles appear as zero-energy edge states, exhibiting charge neutrality, spin-polarization, and spatial nonlocality as unique properties that can already be seen from their energies and wavefunctions. Next, we discuss the analytically obtained Green’s functions of p-wave superconductors and demonstrate that the emergence of Majorana zero modes is always accompanied by the formation of odd-frequency spin-triplet pairing as a unique result of the self-conjugate nature of Majorana zero modes. We finally address the signatures of Majorana zero modes in tunneling spectroscopy, including the anomalous proximity effect, and the phase-biased Josephson effect.

Multiple topological phase transitions unveiling gapless topological superconductivity in magnet/unconventional superconductor hybrid platform

We propose a theoretical framework for generating gapless topological superconductivity (GTSC) hosting Majorana flat edge modes (MFEMs) in the presence of a two-dimensional (2D) array of magnetic adatoms with noncollinear spin texture deposited on top of an unconventional superconductor. Our observations reveal two distinct topological phase transitions within the emergent Shiba band depending on the exchange coupling strength (J) between magnetic adatom spins and superconducting electrons: the first one designates transition from gapless non-topological to gapless topological phase at lower J, while the second one denotes transition from gapless topological to a trivial gapped superconducting phase at higher J. The gapless topological superconducting phase survives at intermediate values of J, hosting MFEMs. Furthermore, we investigate the nature of the bulk effective pairings, which indicate that GTSC appears due to the interplay between pseudo “s-wave” and pseudo “px+py” types of pairing. Consequently, our study opens a promising avenue for the experimental realization of GTSC in 2D Shiba lattice based on d-wave superconductors as a high-temperature platform.

Moiré-enabled topological superconductivity in twisted bilayer graphene

Twisted van der Waals materials have risen as highly tunable platforms for realizing unconventional superconductivity. Here we demonstrate how a topological superconducting state can be driven in a twisted graphene multilayer at a twist angle of approximately 1.6 degrees proximitized to other 2D materials. We show that an encapsulated twisted bilayer subject to induced Rashba spin–orbit coupling, s-wave superconductivity, and exchange field generates a topological superconducting state enabled by the moiré pattern. We demonstrate the emergence of a variety of topological states with different Chern numbers, that are highly tunable through doping, strain, and bias voltage. Our proposal does not depend on fine-tuning the twist angle, but solely on the emergence of moiré minibands and is applicable for twist angles between 1.3 and 3 degrees. Our results establish the potential of twisted graphene bilayers to create topological superconductivity without requiring ultraflat dispersions.

Topological superconductivity induced by spin-orbit coupling, perpendicular magnetic field, and superlattice potential

Topological superconductivity induced by spin-orbit coupling, perpendicular magnetic field, and superlattice potential

Larger in-plane upper critical field and superconducting diode effect observed in topological superconductor candidate InNbS2 nanoribbons

Larger in-plane upper critical field and superconducting diode effect observed in topological superconductor candidate InNbS2 nanoribbons

Explicit-time Floquet topological superconductivity in a microwave/infrared frequency AC voltage-driven Josephson junction

Anomalous Floquet topological superconductivity with chirality can be achieved by applying a dc-bias voltage across the Josephson junction with a sandwiched magnetic topological insulator (TI), in which the intrinsic Josephson phase provides a time-dependent periodic driving [R.-X. Zhang and S. Das Sarma, ]. In this work, we remove the bias voltage and connect the magnetic TI to an external AC voltage source to modulate the chemical potential, thus bringing about an explicit-time Floquet periodic driving. In the context of the driving, the system is similarly found to convert into a two-dimensional anomalous Floquet topological superconductor with chirality. By tuning the AC voltage source's frequency, we obtain a rich variety of novel Floquet topological superconducting phases with chirality. Particularly, by manipulating such static parameters as Zeeman field and superconducting pairing potential, a series of topological superconducting phase transitions are also exhibited, accompanied by exotic Floquet topological superconducting phases with chirality. Published by the American Physical Society 2024

High Quality Fe1+yTe Synthesized by Chemical Vapor Deposition with Conspicuous Vortex Flow

Abstract2D materials provide an ideal platform to explore novel superconducting behavior including Ising superconductivity, topological superconductivity and Majorana bound states in different 2D stoichiometric Ta‐, Nb‐, and Fe‐based crystals. However, tuning the element content in 2D compounds for regulating their superconductivity has not been realized. In this work, the synthesis of high quality Fe1+yTe with tunable Fe content by chemical vapor deposition (CVD) is reported. The quality and composition of Fe1+yTe are characterized by Raman spectroscopy, X‐ray photoelectron spectroscopy (XPS) and scanning transmission electron microscopy (STEM). The superconducting behavior of Fe1+yTe crystals with varying Fe contents is observed. The superconducting transition of selected Fe1.13±0.06Te sample is sharp (ΔTc = 1 K), while Fe1.43±0.07Te with a high‐Fe content shows a relative broad superconducting transition (ΔTc = 2.6 K) at zero magnetic field. Significantly, the conspicuous vortex flow and a transition from a 3D vortex liquid state to a 2D vortex liquid state is observed in Fe1.43±0.07Te sample. This work highlights the tunability of the superconducting properties of Fe1+yTe and sheds light on the vortex dynamics in Fe‐based superconductors, which facilitates them to understand the intrinsic mechanisms of high‐temperature superconductivity.

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. The kz=0 plane 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.

Superconducting diode effect sign change in epitaxial Al-InAs Josephson junctions

There has recently been a surge of interest in studying the superconducting diode effect (SDE) partly due to the possibility of uncovering the intrinsic properties of a material system. A change of sign of the SDE at finite magnetic field has previously been attributed to different mechanisms. Here, we observe the SDE in epitaxial Al-InAs Josephson junctions with strong Rashba spin-orbit coupling (SOC). We show that this effect strongly depends on the orientation of the in-plane magnetic field. In the presence of a strong magnetic field, we observe a change of sign in the SDE. Simulation and measurement of supercurrent suggest that depending on the superconducting widths, WS, this sign change may not necessarily be related to 0–π or topological transitions. We find that the strongest sign change in junctions with narrow WS is consistent with SOC-induced asymmetry of the critical current under magnetic-field inversion, while in wider WS, the sign reversal could be related to 0–π transitions and topological superconductivity.

Vacancy Spectroscopy of Non-Abelian Kitaev Spin Liquids.

Spin vacancies in the non-Abelian Kitaev spin liquid are known to harbor Majorana zero modes, potentially enabling topological quantum computing at elevated temperatures. Here, we study the spectroscopic signatures of such Majorana zero modes in a scanning tunneling setup where a non-Abelian Kitaev spin liquid with a finite density of spin vacancies forms a tunneling barrier between a tip and a substrate. Our key result is a well-defined peak close to zero bias voltage in the derivative of the tunneling conductance whose voltage and intensity both increase with the density of vacancies. This "quasi-zero-voltage peak" is identified as the closest analog of the zero-voltage peak observed in topological superconductors that additionally reflects the fractionalized nature of spin-liquid-based Majorana zero modes. We further highlight a single-fermion Van Hove singularity at a higher voltage that reveals the energy scale of the emergent Majorana fermions in the Kitaev spin liquid. Our proposed signatures are within reach of current experiments on the candidate material α-RuCl_{3}.

Orbital-Selective Mott Transition Effects and Nontrivial Topology of Iron Chalcogenide.

The iron-based superconductor FeSe_{1-x}Te_{x} has recently gained significant attention as a host of two distinct physical phenomena: (i)Majorana zero modes that can serve as potential topologically protected qubits, and (ii)a realization of the orbital-selective Mott transition. In this Letter, we connect these two phenomena and provide new insights into the interplay between strong electronic correlations and nontrivial topology in FeSe_{1-x}Te_{x}. Using linearized quasiparticle self-consistent GW plus dynamical mean-field theory, we show that the topologically protected Dirac surface state has substantial Fe(d_{xy}) character. The proximity to the orbital-selective Mott transition plays a dual role: it facilitates the appearance of the topological surface state by bringing the Dirac cone close to the chemical potential but destroys the Z_{2} topological superconductivity when the system is too close to the orbital-selective Mott phase. We derive a reduced effective Hamiltonian that describes the topological band. Its parameters capture all the chemical trends found in the first principles calculation. Our findings provide a framework for further study of the interplay between strong electronic correlations and nontrivial topology in other iron-based superconductors.