Observation of topological superconductivity on the surface of an iron-based superconductor

Uniform Diffusion of Cooper Pairing Mediated by Hole Carriers in Topological Sb2Te3/Nb

Spin-helical Dirac Fermions at a doped topological insulator's boundaries can support Majorana quasiparticles when coupled with s-wave superconductors, but in n-doped systems, the requisite induced Cooper pairing in topological states is often buried at heterointerfaces or complicated by degenerate coupling with bulk conduction carriers. Rarely probed are p-doped topological structures with nondegenerate Dirac and bulk valence bands at the Fermi level, which may foster long-range superconductivity without sacrificing Majorana physics. Using ultrahigh-resolution photoemission, we report proximity pairing with a large decay length in p-doped topological Sb2Te3 on superconducting Nb. Despite no momentum-space degeneracy, the topological and bulk states of Sb2Te3/Nb exhibit the same isotropic superconducting gaps at low temperatures. Our results unify principles for realizing accessible pairing in Dirac Fermions relevant to topological superconductivity.

Visualization of Unconventional Rashba Bands and Vortex Zero Mode in the Topological Superconductor Candidate AuSn4

The noble metal alloy AuSn4 has recently been identified as an intrinsic surface topological superconductor, promisingly hosting the Majorana zero mode (MZM) for topological quantum computing. However, the atomic visualization of its nontrivial surface states and MZM remains elusive. Here, we report the direct observation of unconventional surface states and vortex zero mode in AuSn4 by scanning tunneling microscopy/spectroscopy. Unlike the trivial metallic bulk states of Sn-terminated surfaces, the Au-terminated surfaces exhibit pronounced surface states near the Fermi level, arising from unconventional Rashba bands characterized by shared helical spin textures. In the superconducting state, the Sn-terminated surfaces exhibit conventional Caroli-de Gennes-Matricon bound states, while the Au-terminated surfaces display sharp zero-energy core states resembling MZMs in a nonquantum-limit condition. This distinction may result from the dominant contribution of unconventional Rashba bands on the Au-terminated surface. Our results provide a new platform for studying termination-dependent topological surface states and MZM in noble-metal-based superconductors.

Field-Free Superconducting Diode Effect and Magnetochiral Anisotropy in FeTe0.7Se0.3 Junctions with the Inherent Asymmetric Barrier

Nonreciprocal electrical transport, characterized by an asymmetric relationship between the current and voltage, plays a crucial role in modern electronic industries. Recent studies have extended this phenomenon to superconductors, introducing the concept of the superconducting diode effect (SDE). The SDE is characterized by unequal critical supercurrents along opposite directions. Due to the requirement on broken inversion symmetry, the SDE is commonly accompanied by electrical magnetochiral anisotropy (eMCA) in the resistive state. Achieving a magnetic-field-free SDE with field tunability is pivotal for advancements in superconductor devices. Conventionally, field-free SDE has been achieved in Josephson junctions by intentionally intercalating an asymmetric barrier layer. Alternatively, internal magnetism was employed. Both approaches pose challenges in the selection of superconductors and fabrication processes, thereby impeding the development of SDE. Here, we present a field-free SDE in FeTe0.7Se0.3 (FTS) junction with eMCA, a phenomenon absent in FTS single nanosheets. The field-free property is associated with the presence of a gradient oxide layer on the upper surface of each FTS nanosheet, while eMCA is linked to spin splitting arising from the absence of inversion symmetry. Both SDE and eMCA respond to magnetic fields with distinct temperature dependencies. This work presents a versatile and straightforward strategy for advancing superconducting electronics.

Real-Space Topology-Engineering of Skyrmionic Spin Textures in a van der Waals Ferromagnet Fe3GaTe2

Realizing magnetic skyrmions in two-dimensional (2D) van der Waals (vdW) ferromagnets offers unparalleled prospects for future spintronic applications. The room-temperature ferromagnet Fe3GaTe2 provides an ideal platform for tailoring these magnetic solitons. Here, skyrmions of distinct topological charges are artificially introduced and engineered by using magnetic force microscopy (MFM). The skyrmion lattice is realized by a specific field-cooling process and can be further erased and painted via delicate manipulation of the tip stray field. The skyrmion lattice with opposite topological charges (S = ±1) can be tailored at the target regions to form topological skyrmion junctions (TSJs) with specific configurations. The delicate interplay of TSJs and spin-polarized device current were finally investigated via the in situ transport measurements, alongside the topological stability of TSJs. Our results demonstrate that Fe3GaTe2 not only serves as a potential building block for skyrmion-based spintronic devices, but also presents prospects for Fe3GaTe2-based heterostructures with the engineered topological spin textures.

Growth of Single Crystalline 2D Materials beyond Graphene on Non-metallic Substrates

The advent of 2D materials has ushered in the exploration of their synthesis, characterization and application. While plenty of 2D materials have been synthesized on various metallic substrates, interfacial interaction significantly affects their intrinsic electronic properties. Additionally, the complex transfer process presents further challenges. In this context, experimental efforts are devoted to the direct growth on technologically important semiconductor/insulator substrates. This review aims to uncover the effects of substrate on the growth of 2D materials. The focus is on non-metallic substrate used for epitaxial growth and how this highlights the necessity for phase engineering and advanced characterization at atomic scale. Special attention is paid to monoelemental 2D structures with topological properties. The conclusion is drawn through a discussion of the requirements for integrating 2D materials with current semiconductor-based technology and the unique properties of heterostructures based on 2D materials. Overall, this review describes how 2D materials can be fabricated directly on non-metallic substrates and the exploration of growth mechanism at atomic scale.

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.

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.

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.

Evidence of superconducting Fermi arcs

An essential ingredient for the production of Majorana fermions for use in quantum computing is topological superconductivity1,2. As bulk topological superconductors remain elusive, the most promising approaches exploit proximity-induced superconductivity3, making systems fragile and difficult to realize4-7. Due to their intrinsic topology8, Weyl semimetals are also potential candidates1,2, but have always been connected with bulk superconductivity, leaving the possibility of intrinsic superconductivity of their topological surface states, the Fermi arcs, practically without attention, even from the theory side. Here, by means of angle-resolved photoemission spectroscopy and ab initio calculations, we identify topological Fermi arcs on two opposing surfaces of the non-centrosymmetric Weyl material trigonal PtBi2 (ref. 9). We show these states become superconducting at temperatures around 10 K. Remarkably, the corresponding coherence peaks appear as the strongest and sharpest excitations ever detected by photoemission from solids. Our findings indicate that superconductivity in PtBi2 can occur exclusively at the surface, rendering it a possible platform to host Majorana modes in intrinsically topological superconductor-normal metal-superconductor Josephson junctions.

Coexistence of topological node surface and Dirac fermions in phonon-mediated superconductor YB2C2

The interaction between nontrivial topology and superconductivity in condensed matter physics has attracted tremendous research interest as it could give rise to exotic phenomena. Herein, based on first-principles calculations, we investigate the electronic structures, mechanical properties, topological properties, dynamic stability, electron-phonon coupling (EPC), and superconducting properties of the synthesized real material YB2C2. It is a tetragonal structure with P4/mbm symmetry and exhibits excellent stability. The calculated electronic band structures reveal that a zero-dimension (0D) Dirac point and two-dimensional (2D) nodal surface coexist near the Fermi level. A spin-orbit coupling (SOC) Dirac point with the topological Fermi arc is observed on the (001) surface. These nodal surfaces are protected by a two-fold screw axis and time-reversal symmetry. Based on the Bardeen-Cooper-Schrieffer theory, the superconducting transition temperature (Tc) in the range 1.25-4.45 K with different Coulomb repulsion constant μ* for YB2C2 is estimated to be consistent with previous experimental results. In addition, the EPC is mainly from the coupling between the dx2-y2 and dz2 orbitals of the Y atom and low-energy phonon modes. The presence of superconductivity and nontrivial topological surface state in YB2C2 suggests that it may be a candidate material for topological superconductors.

Toward large-scale, ordered and tunable Majorana-zero-modes lattice on iron-based superconductors

Majorana excitations are the quasiparticle analog of Majorana fermions in solid materials. Typical examples are the Majorana zero modes (MZMs) and the dispersing Majorana modes. When probed by scanning tunneling spectroscopy, the former manifest as a pronounced conductance peak locating precisely at zero-energy, while the latter behaves as constant or slowly varying density of states. The MZMs obey non-abelian statistics and are believed to be building blocks for topological quantum computing, which is highly immune to the environmental noise. Existing MZM platforms include hybrid structures such as topological insulator, semiconducting nanowire or 1D atomic chains on top of a conventional superconductor, and single materials such as the iron-based superconductors (IBSs) and 4Hb-TaS2. Very recently, ordered and tunable MZM lattice has also been realized in IBS LiFeAs, providing a scalable and applicable platform for future topological quantum computation. In this review, we present an overview of the recent local probe studies on MZMs. Classified by the material platforms, we start with the MZMs in the iron-chalcogenide superconductors where FeTe0.55Se0.45and (Li0.84Fe0.16)OHFeSe will be discussed. We then review the Majorana research in the iron-pnictide superconductors as well as other platforms beyond the IBSs. We further review recent works on ordered and tunable MZM lattice, showing that strain is a feasible tool to tune the topological superconductivity. Finally, we give our summary and perspective on future Majorana research.

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.

Emergent ferromagnetism with superconductivity in Fe(Te,Se) van der Waals Josephson junctions

Ferromagnetism and superconductivity are two key ingredients for topological superconductors, which can serve as building blocks of fault-tolerant quantum computers. Adversely, ferromagnetism and superconductivity are typically also two hostile orderings competing to align spins in different configurations, and thus making the material design and experimental implementation extremely challenging. A single material platform with concurrent ferromagnetism and superconductivity is actively pursued. In this paper, we fabricate van der Waals Josephson junctions made with iron-based superconductor Fe(Te,Se), and report the global device-level transport signatures of interfacial ferromagnetism emerging with superconducting states for the first time. Magnetic hysteresis in the junction resistance is observed only below the superconducting critical temperature, suggesting an inherent correlation between ferromagnetic and superconducting order parameters. The 0-π phase mixing in the Fraunhofer patterns pinpoints the ferromagnetism on the junction interface. More importantly, a stochastic field-free superconducting diode effect was observed in Josephson junction devices, with a significant diode efficiency up to 10%, which unambiguously confirms the spontaneous time-reversal symmetry breaking. Our work demonstrates a new way to search for topological superconductivity in iron-based superconductors for future high Tc fault-tolerant qubit implementations from a device perspective.

Atomic-Scale Andreev Probe of Unconventional Superconductivity

Recent emergence of low-dimensional unconventional superconductors and their exotic interface properties calls for new approaches to probe the pairing symmetry, a fundamental and frequently elusive property of the superconducting condensate. Here, we introduce the unique capability of tunneling Andreev reflection (TAR) to probe unconventional pairing symmetry, utilizing the sensitivity of this technique to specific Andreev reflections. Specifically, suppression of the lowest-order Andreev reflection due to quantum interference but emergence of the higher-order Andreev processes provides direct evidence of the sign-changing order parameter in the paradigmatic FeSe superconductor. TAR spectroscopy also reveals two superconducting gaps, points to a possibility of a nodal gap structure, and directly confirms that superconductivity is locally suppressed along the nematic twin boundary, with preferential and near-complete suppression of the larger energy gap. Our findings therefore enable new, atomic-scale insight into microscopic, inhomogeneous, and interfacial properties of emerging quantum materials.

Recent Advances in Moiré Superlattice Systems by Angle-Resolved Photoemission Spectroscopy

The last decade has witnessed a flourish in 2D materials including graphene and transition metal dichalcogenides (TMDs) as atomic-scale Legos. Artificial moiré superlattices via stacking 2D materials with a twist angle and/or a lattice mismatch have recently become a fertile playground exhibiting a plethora of emergent properties beyond their building blocks. These rich quantum phenomena stem from their nontrivial electronic structures that are effectively tuned by the moiré periodicity. Modern angle-resolved photoemission spectroscopy (ARPES) can directly visualize electronic structures with decent momentum, energy, and spatial resolution, thus can provide enlightening insights into fundamental physics in moiré superlattice systems and guides for designing novel devices. In this review, first, a brief introduction is given on advanced ARPES techniques and basic ideas of band structures in a moiré superlattice system. Then ARPES research results of various moiré superlattice systems are highlighted, including graphene on substrates with small lattice mismatches, twisted graphene/TMD moiré systems, and high-order moiré superlattice systems. Finally, it discusses important questions that remain open, challenges in current experimental investigations, and presents an outlook on this field of research.

Exchange interaction for the triplet superconductor UTe2

UTe2 is one triplet superconductor that defies conventional relation between ferromagnetism and superconductivity. Our search for a theoretical explanation starts with one spin-triplet state of two electrons and construct a two-particle exchange interaction that favors the formation of Cooper pairs under the configuration. A modified application of the Bardeen-Cooper-Schrieffer (BCS) theory using parameters derived from ab-initio density functional calculations for electrons and phonons enables us to derive the critical temperature of 1.64 K and an average superconducting gap of 0.25 meV at 0 K. We extend the investigation further into the superconductivity under pressure, showing how Tc and the gap of UTe2 change under compression in ways that are consistent with the results of experiment.

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.

Topological Superconductivity in Doped Magnetic Moiré Semiconductors

We show that topological superconductivity may emerge upon doping of transition metal dichalcogenide heterobilayers above an integer-filling magnetic state of the topmost valence moiré band. The effective attraction between charge carriers is generated by an electric p-wave Feshbach resonance arising from interlayer excitonic physics and has a tunable strength, which may be large. Together with the low moiré carrier densities reachable by gating, this robust attraction enables access to the long-sought p-wave BEC-BCS transition. The topological protection arises from an emergent time reversal symmetry occurring when the magnetic order and long wavelength magnetic fluctuations do not couple different valleys. The resulting topological superconductor features helical Majorana edge modes, leading to half-integer quantized spin-thermal Hall conductivity and to charge currents induced by circularly polarized light or other time-reversal symmetry-breaking fields.

Tuning electronic and phononic states with hidden order in disordered crystals

Disorder in crystals is rarely random, and instead involves local correlations whose presence and nature are hidden from conventional crystallographic probes. This hidden order can sometimes be controlled, but its importance for physical properties of materials is not well understood. Using simple models for electronic and interatomic interactions, we show how crystals with identical average structures but different types of hidden order can have very different electronic and phononic band structures. Increasing the strength of local correlations within hidden-order states can open band gaps and tune mode (de)localisation-both mechanisms allowing for fundamental changes in physical properties without long-range symmetry breaking. Taken together, our results demonstrate how control over hidden order offers a new mechanism for tuning material properties, orthogonal to the conventional principles of (ordered) structure/property relationships.

Review of Single Crystal Synthesis of 11 Iron-Based Superconductors

The 11 system in the iron-based superconducting family has become one of the most extensively studied materials in the research of high-temperature superconductivity, due to their simple structure and rich physical properties. Many exotic properties, such as multiband electronic structure, electronic nematicity, topology and antiferromagnetic order, provide strong support for the theory of high-temperature superconductivity, and have been at the forefront of condensed matter physics in the past decade. One noteworthy aspect is that a high upper critical magnetic field, large critical current density and lower toxicity give the 11 system good application prospects. However, the research on 11 iron-based superconductors faces numerous obstacles, mainly stemming from the challenges associated with producing high-quality single crystals. Since the discovery of FeSe superconductivity in 2008, researchers have made significant progress in crystal growth, overcoming the hurdles that initially impeded their studies. Consequently, they have successfully established the complete phase diagrams of 11 iron-based superconductors, including FeSe_1-xTe_x, FeSe_1-xS_x and FeTe_1-xS_x. In this paper, we aim to provide a comprehensive summary of the preparation methods employed for 11 iron-based single crystals over the past decade. Specifically, we will focus on hydrothermal, chemical vapor transport (CVT), self-flux and annealing methods. Additionally, we will discuss the quality, size, and superconductivity properties exhibited by single crystals obtained through different preparation methods. By exploring these aspects, we can gain a better understanding of the advantages and limitations associated with each technique. High-quality single crystals serve as invaluable tools for advancing both the theoretical understanding and practical utilization of high-temperature superconductivity.

Monolayer Superconductivity and Tunable Topological Electronic Structure at the Fe(Te,Se)/Bi2 Te3 Interface

The interface between 2D topological Dirac states and an s-wave superconductor is expected to support Majorana-bound states (MBS) that can be used for quantum computing applications. Realizing these novel states of matter and their applications requires control over superconductivity and spin-orbit coupling to achieve spin-momentum-locked topological interface states (TIS) which are simultaneously superconducting. While signatures of MBS have been observed in the magnetic vortex cores of bulk FeTe_0.55 Se_0.45 , inhomogeneity and disorder from doping make these signatures unclear and inconsistent between vortices. Here superconductivity is reported in monolayer (ML) FeTe_1-y Se_y (Fe(Te,Se)) grown on Bi₂ Te₃ by molecular beam epitaxy (MBE). Spin and angle-resolved photoemission spectroscopy (SARPES) directly resolve the interfacial spin and electronic structure of Fe(Te,Se)/Bi₂ Te₃ heterostructures. For y = 0.25, the Fe(Te,Se) electronic structure is found to overlap with the Bi₂ Te₃ TIS and the desired spin-momentum locking is not observed. In contrast, for y = 0.1, reduced inhomogeneity measured by scanning tunneling microscopy (STM) and a smaller Fe(Te,Se) Fermi surface with clear spin-momentum locking in the topological states are found. Hence, it is demonstrated that the Fe(Te,Se)/Bi₂ Te₃ system is a highly tunable platform for realizing MBS where reduced doping can improve characteristics important for Majorana interrogation and potential applications.

Controlling Dzyaloshinskii-Moriya interaction in a centrosymmetric nonsymmorphic crystal

Presence of the Dzyaloshinskii-Moriya (DM) interaction in limited noncentrosymmetric materials leads to novel spin textures and exotic chiral physics. The emergence of DM interaction in centrosymmetric crystals could greatly enrich material realization. Here we show that an itinerant centrosymmetric crystal respecting a nonsymmorphic space group is a new platform for the DM interaction. Taking P4/nmm space group as an example, we demonstrate that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction induces the DM interactions, in addition to the Heisenberg exchange and the Kaplan-Shekhtman-Entin-wohlman-Aharony (KSEA) interaction. The direction of DM vector depends on the positions of magnetic atoms in the real space, and the amplitude depends on the location of the Fermi surface in the reciprocal space. The diversity stems from the position-dependent site groups and the momentum-dependent electronic structures guaranteed by the nonsymmorphic symmetries. Our study unveils the role of the nonsymmorphic symmetries in affecting magnetism, and suggests that the nonsymmorphic crystals can be promising platforms to design magnetic interactions.

Magnetotransport property of oxygen-annealed Fe1+yTe thin films

Fe-based superconductors are one of the current research focuses. FeTe is unique in the series of FeSe_1-xTe_x, since it is nonsuperconducting near the FeTe side in the phase diagram in contrast to the presence of superconductivity in other region. However, FeTe thin films become superconducting after oxygen annealing and the mechanism remains elusive. Here, we report the temperature dependences of resistivity, Hall effect and magnetoresistance (MR) of a series of FeTe thin films with different amounts of excess Fe and oxygen. These properties show dramatic changes with excess Fe and oxygen incorporation. We found the Hall coefficients are positive for the oxygen-annealed samples, in contrast to the transition from positive to negative below 50 K for the vacuum-annealed samples. For all samples, both the resistivity and Hall coefficient show a dramatic drop, respectively, at around 50 K-75 K, implying coexistence of superconductivity and antiferromagnetic order for the oxygen-annealed samples. The vacuum-annealed samples show both positive and negative values of MR depending on temperature, while negative MR dominates for the oxygen-annealed samples. We also found that oxygen annealing reduces the excess Fe in FeTe, which has been neglected before. The results are discussed in terms of several contributions, and a comparison is made between the oxygen-annealed FeTe thin films and FeSe_1-xTe_x. This work is helpful for shedding light on the understanding of oxygen-annealed FeTe thin films.

Tuning Multiple Landau Quantization in Transition-Metal Dichalcogenide with Strain

Landau quantization associated with the quantized cyclotron motion of electrons under magnetic field provides the effective way to investigate topologically protected quantum states with entangled degrees of freedom and multiple quantum numbers. Here we report the cascade of Landau quantization in a strained type-II Dirac semimetal NiTe₂ with spectroscopic-imaging scanning tunneling microscopy. The uniform-height surfaces exhibit single-sequence Landau levels (LLs) at a magnetic field originating from the quantization of topological surface state (TSS) across the Fermi level. Strikingly, we reveal the multiple sequence of LLs in the strained surface regions where the rotation symmetry is broken. First-principles calculations demonstrate that the multiple LLs attest to the remarkable lifting of the valley degeneracy of TSS by the in-plane uniaxial or shear strains. Our findings pave a pathway to tune multiple degrees of freedom and quantum numbers of TMDs via strain engineering for practical applications such as high-frequency rectifiers, Josephson diode and valleytronics.

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

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

Build-up and dephasing of Floquet-Bloch bands on subcycle timescales

Strong light fields have created opportunities to tailor novel functionalities of solids1-5. Floquet-Bloch states can form under periodic driving of electrons and enable exotic quantum phases6-15. On subcycle timescales, lightwaves can simultaneously drive intraband currents16-29 and interband transitions18,19,30,31, which enable high-harmonic generation16,18,19,21,22,25,28-30 and pave the way towards ultrafast electronics. Yet, the interplay of intraband and interband excitations and their relation to Floquet physics have been key open questions as dynamical aspects of Floquet states have remained elusive. Here we provide this link by visualizing the ultrafast build-up of Floquet-Bloch bands with time-resolved and angle-resolved photoemission spectroscopy. We drive surface states on a topological insulator32,33 with mid-infrared fields-strong enough for high-harmonic generation-and directly monitor the transient band structure with subcycle time resolution. Starting with strong intraband currents, we observe how Floquet sidebands emerge within a single optical cycle; intraband acceleration simultaneously proceeds in multiple sidebands until high-energy electrons scatter into bulk states and dissipation destroys the Floquet bands. Quantum non-equilibrium calculations explain the simultaneous occurrence of Floquet states with intraband and interband dynamics. Our joint experiment and theory study provides a direct time-domain view of Floquet physics and explores the fundamental frontiers of ultrafast band-structure engineering.

Topological Insulator Metamaterials

Confinement of electromagnetic fields at the subwavelength scale via metamaterial paradigms is an established method to engineer light-matter interaction in most common material systems, from insulators to semiconductors and from metals to superconductors. In recent years, this approach has been extended to the realm of topological materials, providing a new avenue to access nontrivial features of their electronic band structure. In this review, we survey various topological material classes from a photonics standpoint, including crystal growth and lithographic structuring methods. We discuss how exotic electronic features such as spin-selective Dirac plasmon polaritons in topological insulators or hyperbolic plasmon polaritons in Weyl semimetals may give rise to unconventional magneto-optic, nonlinear, and circular photogalvanic effects in metamaterials across the visible to infrared spectrum. Finally, we dwell on how these effects may be dynamically controlled by applying external perturbations in the form of electric and magnetic fields or ultrafast optical pulses. Through these examples and future perspectives, we argue that topological insulator, semimetal and superconductor metamaterials are unique systems to bridge the missing links between nanophotonic, electronic, and spintronic technologies.

Topological Nodal Surface and Quadratic Dirac Semimetal States and van Hove Singularities in ScH3 and LuH3 Superconductors

The coexistence of non-trivial topology and superconductivity in a material may induce a novel physical phenomenon known as topological superconductivity. Topological superconductors have been the subject of intense research, yet there are severe limitations in their application due to a lack of suitable materials. Topological nodal surface semimetals with nearly flat nodal surfaces near the Fermi level can be promising materials to achieve topological superconductivity. Here, we use first-principles calculations to examine the topological electronic characteristics of two new superconductors, ScH₃ and LuH₃, at both ambient and high pressures. Our studies show that both ScH₃ and LuH₃ have van Hove singularities, which confirms their superconductivity. Interestingly, both materials host topological nodal surface states under the protection of time reversal and spatial inversion symmetries in the absence of spin-orbit coupling (SOC). These nodal surfaces are distinguished by a pair of unique drum-head-like surface states not previously observed in nodal surface semimetals. Moreover, the nodal surfaces transform into essential spin-orbit quadratic Dirac points when SOC is included. Our findings demonstrate that ScH₃ and LuH₃ are good candidates to investigate the exotic properties of both nodal surface semimetals (NSSMs) and quadratic Dirac semimetal states and also provide a platform to explore the coexistence of topology and superconductivity in NSSMs with promising applications in high-speed electronics and topological quantum computing.

Statistical Majorana Bound State Spectroscopy

Tunnel spectroscopy data for the detection of Majorana bound states (MBS) is often criticized for its proneness to misinterpretation of genuine MBS with low-lying Andreev bound states. Here, we suggest a protocol removing this ambiguity by extending single shot measurements to sequences performed at varying system parameters. We demonstrate how such sampling, which we argue requires only moderate effort for current experimental platforms, resolves the statistics of Andreev side lobes, thus providing compelling evidence for the presence or absence of a Majorana center peak.

Emergent Majorana zero-modes in an intrinsic anti-ferromagnetic topological superconductor Mn2B2 monolayer

Topological superconductors (TSCs) are an exotic field due to the existence of Majorana zero-modes (MZM) in the edge states that obey non-Abelian statistics and can be used to implement topological quantum computations, especially for two-dimensional (2D) materials. Here we predict manganese diboride (Mn₂B₂) as an intrinsic 2D anti-ferromagnetic (AFM) TSC based on the magnetic and electronic structures of Mn and B atoms. Once Mn₂B₂ ML enters a superconducting state, MZM will be induced by the spin-polarized helical gapless edge states. The Z₂ topological non-trivial properties are confirmed by Wannier charge centers (WCC) and the platform of the spin Hall conductivity near the Fermi level. Phonon-electron coupling (EPC) implies s-wave superconductivity and the critical temperature (T_c) is 6.79 K.

Kagome superconductors AV3Sb5 (A = K, Rb, Cs)

The quasi-two-dimensional kagome materials AV3Sb5 (A = K, Rb, Cs) were found to be a prime example of kagome superconductors, a new quantum platform to investigate the interplay between electron correlation effects, topology and geometric frustration. In this review, we report recent progress on the experimental and theoretical studies of AV3Sb5 and provide a broad picture of this fast-developing field in order to stimulate an expanded search for unconventional kagome superconductors. We review the electronic properties of AV3Sb5, the experimental measurements of the charge density wave state, evidence of time-reversal symmetry breaking and other potential hidden symmetry breaking in these materials. A variety of theoretical proposals and models that address the nature of the time-reversal symmetry breaking are discussed. Finally, we review the superconducting properties of AV3Sb5, especially the potential pairing symmetries and the interplay between superconductivity and the charge density wave state.

Coexistence of Bulk-Nodal and Surface-Nodeless Cooper Pairings in a Superconducting Dirac Semimetal

The interplay of nontrivial topology and superconductivity in condensed matter physics gives rise to exotic phenomena. However, materials are extremely rare where it is possible to explore the full details of the superconducting pairing. Here, we investigate the momentum dependence of the superconducting gap distribution in a novel Dirac material PdTe. Using high resolution, low temperature photoemission spectroscopy, we establish it as a spin-orbit coupled Dirac semimetal with the topological Fermi arc crossing the Fermi level on the (010) surface. This spin-textured surface state exhibits a fully gapped superconducting Cooper pairing structure below T_{c}∼4.5  K. Moreover, we find a node in the bulk near the Brillouin zone boundary, away from the topological Fermi arc. These observations not only demonstrate the band resolved electronic correlation between topological Fermi arc states and the way it induces Cooper pairing in PdTe, but also provide a rare case where surface and bulk states host a coexistence of nodeless and nodal gap structures enforced by spin-orbit coupling.

Revealing the Origin of Time-Reversal Symmetry Breaking in Fe-Chalcogenide Superconductor FeTe_{1-x}Se_{x}

Recently, evidence has emerged in the topological superconductor Fe-chalcogenide FeTe_{1-x}Se_{x} for time-reversal symmetry breaking (TRSB), the nature of which has strong implications on the Majorana zero modes (MZM) discovered in this system. It remains unclear, however, whether the TRSB resides in the topological surface state (TSS) or in the bulk, and whether it is due to an unconventional TRSB superconducting order parameter or an intertwined order. Here, by performing in superconducting FeTe_{1-x}Se_{x} crystals both surface-magneto-optic-Kerr effect measurements using a Sagnac interferometer and bulk magnetic susceptibility measurements, we pinpoint the TRSB to the TSS, where we also detect a Dirac gap. Further, we observe surface TRSB in nonsuperconducting FeTe_{1-x}Se_{x} of nominally identical composition, indicating that TRSB arises from an intertwined surface ferromagnetic (FM) order. The observed surface FM bears striking similarities to the two-dimensional (2D) FM found in 2D van der Waals crystals, and is highly sensitive to the exact chemical composition, thereby providing a means for optimizing the conditions for Majorana particles that are useful for robust quantum computing.

Topological superconductivity and large spin Hall effect in the kagome family Ti6X4 (X = Bi, Sb, Pb, Tl, and In)

Topological superconductors (TSC) become a focus of research due to the accompanying Majorana fermions. However, the reported TSC are extremely rare. Recent experiments reported kagome TSC AV3Sb5 (A = K, Rb, and Cs) exhibit unique superconductivity, topological surface states (TSS), and Majorana bound states. More recently, the first titanium-based kagome superconductor CsTi3Bi5 with nontrivial topology was successfully synthesized as a perspective TSC. Given that Cs contributes little to electronic structures of CsTi3Bi5 and binary compounds may be easier to be synthesized, here, by first-principle calculations, we predict five stable nonmagnetic kagome compounds Ti6X4 (X = Bi, Sb, Pb, Tl, and In) which exhibit superconductivity with critical temperature Tc = 3.8 K - 5.1 K, nontrivialZ 2 band topology, and TSS close to the Fermi level. Additionally, large intrinsic spin Hall effect is obtained in Ti6X4, which is caused by gapped Dirac nodal lines due to a strong spin-orbit coupling. This work offers new platforms for TSC and spintronic devices.

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.

Pressure Evolution of Ultrafast Photocarrier Dynamics and Electron-Phonon Coupling in FeTe0.5Se0.5

Understanding the coupling between electrons and phonons in iron chalcogenides FeTexSe1-x has remained a critical but arduous project in recent decades. The direct observation of the electron-phonon coupling effect through electron dynamics and vibrational properties has been lacking. Here, we report the first pressure-dependent ultrafast photocarrier dynamics and Raman scattering studies on an iron chalcogenide FeTe0.5Se0.5 to explore the interaction between electrons and phonons in this unconventional superconductor. The lifetime of the excited electrons evidently decreases as the pressure increases from 0 to 2.2 GPa, and then increases with further compression. The vibrational properties of the A1g phonon mode exhibit similar behavior, with a pronounced frequency reduction appearing at approximately 2.3 GPa. The dual evidence reveals the enhanced electron-phonon coupling strength with pressure in FeTe0.5Se0.5. Our results give an insight into the role of the electron-phonon coupling effect in iron-based superconductors.

Superconducting Fourfold Fe(Te,Se) Film on Sixfold Magnetic MnTe via Hybrid Symmetry Epitaxy

Epitaxial Fe(Te,Se) thin films have been grown on various substrates but never been grown on magnetic layers. Here we report the epitaxial growth of fourfold Fe(Te,Se) film on a sixfold antiferromagnetic insulator, MnTe. The Fe(Te,Se)/MnTe heterostructure shows a clear superconducting transition at around 11 K, and the critical magnetic field measurement suggests the origin of the superconductivity to be bulk-like. Structural characterizations suggest that the uniaxial lattice match between Fe(Te,Se) and MnTe allows a hybrid symmetry epitaxy mode, which was recently discovered between Fe(Te,Se) and Bi₂Te₃. Furthermore, the Te/Fe flux ratio during deposition of the Fe(Te,Se) layer is found to be critical for its superconductivity. Now that superconducting Fe(Te,Se) can be grown on two related hexagonal platforms, Bi₂Te₃ and MnTe, this result opens a new possibility of combining topological superconductivity of Fe(Te,Se) with the rich physics in the intrinsic magnetic topological materials (MnTe)_n(Bi₂Te₃)_m family.

Converting a Monolayered NbSe2 into an Ising Superconductor with Nontrivial Band Topology via Physical or Chemical Pressuring

Two-dimensional transition metal dichalcogenides possessing superconductivity and strong spin-orbit coupling exhibit high in-plane upper critical fields due to Ising pairing. Yet to date, whether such systems can become topological Ising superconductors remains to be materialized. Here we show that monolayered NbSe₂ can be converted into Ising superconductors with nontrivial band topology via physical or chemical pressuring. Using first-principles calculations, we first demonstrate that a hydrostatic pressure higher than 2.5 GPa can induce a p-d band inversion, rendering nontrivial band topology to NbSe₂. We then illustrate that Te-doping can function as chemical pressuring in inducing nontrivial topology in NbSe_2-xTe_x with x ≥ 0.8, due to a larger atomic radius and stronger spin-orbit coupling of Te. We also evaluate the upper critical fields within both approaches, confirming the enhanced Ising superconductivity nature, as experimentally observed. Our findings may prove to be instrumental in material realization of topological Ising superconductivity in two-dimensional systems.

An Improved Smart Meta-Superconductor MgB2

Increasing and improving the critical transition temperature (TC), current density (JC) and the Meissner effect (HC) of conventional superconductors are the most important problems in superconductivity research, but progress has been slow for many years. In this study, by introducing the p-n junction nanostructured electroluminescent inhomogeneous phase with a red wavelength to realize energy injection, we found the improved property of smart meta-superconductors MgB2, the critical transition temperature TC increases by 0.8 K, the current density JC increases by 37%, and the diamagnetism of the Meissner effect HC also significantly improved, compared with pure MgB2. Compared with the previous yttrium oxide inhomogeneous phase, the p-n junction has a higher luminescence intensity, a longer stable life and simpler external field requirements. The coupling between superconducting electrons and surface plasmon polaritons may be explained by this phenomenon. The realization of smart meta-superconductor by the electroluminescent inhomogeneous phase provides a new way to improve the performance of superconductors.

Yu-Shiba-Rusinov States in a Superconductor with Topological Z_{2} Bands

A Yu-Shiba-Rusinov (YSR) state is a localized in-gap state induced by a magnetic impurity in a superconductor. Recent experiments used an STM tip to manipulate the exchange coupling between an Fe adatom and the FeTe_{0.55}Se_{0.45} superconductor possessing a Z_{2} nontrivial band structure with topological surface states. As the tip moves close to the single Fe adatom, the energy of the in-gap state modulates and exhibits a zero-energy crossing followed by an unusual return to zero energy, which cannot be understood by coupling the magnetic impurity to the superconducting topological surface Dirac cone. Here, we numerically and analytically study the YSR states in superconductors with nontrivial Z_{2} bands and show the emergence of the two zero-energy crossings as a function of the exchange coupling between the magnetic impurity and the bulk states. We analyze the role of the topological surface states and compare in-gap states to systems with trivial Z_{2} bands. The spin polarization of the YSR states is further studied for future experimental measurement.

Ordered and tunable Majorana-zero-mode lattice in naturally strained LiFeAs

Majorana zero modes (MZMs) obey non-Abelian statistics and are considered building blocks for constructing topological qubits^1,2. Iron-based superconductors with topological bandstructures have emerged as promising hosting materials, because isolated candidate MZMs in the quantum limit have been observed inside the topological vortex cores^3-9. However, these materials suffer from issues related to alloying induced disorder, uncontrolled vortex lattices^10-13 and a low yield of topological vortices^5-8. Here we report the formation of an ordered and tunable MZM lattice in naturally strained stoichiometric LiFeAs by scanning tunnelling microscopy/spectroscopy. We observe biaxial charge density wave (CDW) stripes along the Fe-Fe and As-As directions in the strained regions. The vortices are pinned on the CDW stripes in the As-As direction and form an ordered lattice. We detect that more than 90 per cent of the vortices are topological and possess the characteristics of isolated MZMs at the vortex centre, forming an ordered MZM lattice with the density and the geometry tunable by an external magnetic field. Notably, with decreasing the spacing of neighbouring vortices, the MZMs start to couple with each other. Our findings provide a pathway towards tunable and ordered MZM lattices as a platform for future topological quantum computation.

Magnetic Weyl Semimetal in K_{2}Mn_{3}(AsO_{4})_{3} with the Minimum Number of Weyl Points

The "hydrogen atom" of magnetic Weyl semimetals, with the minimum number of Weyl points, has received growing attention recently due to the possible presence of Weyl-related phenomena. Here, we report a nontrivial electronic structure of the ferromagnetic alluaudite-type compound K_{2}Mn_{3}(AsO_{4})_{3}. It exhibits only a pair of Weyl points constrained in the z direction by the twofold rotation symmetry, leading to extremely long Fermi arc surface states. In addition, the study of its low-energy effective model results in the discovery of various topological superconducting states, such as the hydrogen atom of a Weyl superconductor. Our Letter provides a feasible platform to explore the intrinsic properties related to Weyl points, and the related device applications.

Triplet Superconductivity from Nonlocal Coulomb Repulsion in an Atomic Sn Layer Deposited onto a Si(111) Substrate

Atomic layers deposited on semiconductor substrates introduce a platform for the realization of the extended electronic Hubbard model, where the consideration of electronic repulsion beyond the on-site term is paramount. Recently, the onset of superconductivity at 4.7 K has been reported in the hole-doped triangular lattice of tin atoms on a silicon substrate. Through renormalization group methods designed for weak and intermediate coupling, we investigate the nature of the superconducting instability in hole-doped Sn/Si(111). We find that the extended Hubbard nature of interactions is crucial to yield triplet pairing, which is f-wave (p-wave) for moderate (higher) hole doping. In light of persisting challenges to tailor triplet pairing in an electronic material, our finding promises to pave unprecedented ways for engineering unconventional triplet superconductivity.

High-Temperature Majorana Zero Modes

We employ analytical and numerical approaches to show that unpaired Majorana zero modes can occur in cores of Abrikosov vortices at the interface between a three-dimensional topological insulator, such as Bi_{2}Se_{3}, and a twisted bilayer of high-T_{c} cuprate superconductor, such as Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}. When the twist angle is close to 45° the latter has been predicted to form a fully gapped topological superconductor up to temperatures approaching its native T_{c}≃90  K. Majorana zero modes in these structures will persist up to unprecedented high temperatures and, depending on the quality of the interface, may be protected by gaps with larger magnitudes than other candidate systems.

Nonequilibrium topological spin textures in momentum space

Optically excited systems can host unprecedented phenomena and reveal key information. The spin-channel physics in the photoexcited dynamics of quantum matter remains largely unexplored. This study finds the topological surface state under contemporary time-resolved pump-probe spectroscopy an exceptionally capable platform in this regard. Spin signals exhibit interesting tornado-like spiral patterns, and the unusual topological optical activity can be indicative of spintronic applications. This exemplifies a purely nonequilibrium topological winding phenomenon, where all the hidden helicity factors in the light–matter-coupled system are robustly encoded. These results open a direction of nonequilibrium topological spin states in quantum materials.

Nonequilibrium quantum dynamics of many-body systems is the frontier of condensed matter physics; recent advances in various time-resolved spectroscopic techniques continue to reveal rich phenomena. Angle-resolved photoemission spectroscopy (ARPES) as one powerful technique can resolve electronic energy, momentum, and spin along the time axis after excitation. However, dynamics of spin textures in momentum space remains mostly unexplored. Here, we demonstrate theoretically that the photoexcited surface state of genuine or magnetically doped topological insulators shows intriguing topological spin textures (i.e., tornado-like patterns) in the spin-resolved ARPES. We systematically reveal its origin as a unique nonequilibrium photoinduced topological winding phenomenon. As all intrinsic and extrinsic topological helicity factors of both material and light are embedded in a robust and delicate manner, the tornado patterns not only allow a remarkable tomography of such important system information, but also enable various unique dichroic topological switchings of the momentum-space spin texture. These results open a direction of nonequilibrium topological spin states in quantum materials.

High-T c superconductor Fe(Se,Te) monolayer: an intrinsic, scalable and electrically tunable Majorana platform

Iron-based superconductors have been identified as a novel platform for realizing Majorana zero modes (MZMs) without heterostructures, due to their intrinsic topological properties and high-T c superconductivity. In the two-dimensional limit, the FeTe1-x Se x monolayer, a topological band inversion has recently been experimentally observed. Here, we propose to create MZMs by applying an in-plane magnetic field to the FeTe1-x Se x monolayer and tuning the local chemical potential via electric gating. Owing to the anisotropic magnetic couplings on edges, an in-plane magnetic field drives the system into an intrinsic high-order topological superconductor phase with Majorana corner modes. Furthermore, MZMs can occur at the domain wall of chemical potentials at either one edge or certain type of tri-junction in the two-dimensional bulk. Our study not only reveals the FeTe1-x Se x monolayer as a promising Majorana platform with scalability and electrical tunability and within reach of contemporary experimental capability, but also provides a general principle to search for realistic realization of high-order topological superconductivity.

Charge-Density-Wave-Induced Peak-Dip-Hump Structure and the Multiband Superconductivity in a Kagome Superconductor CsV_{3}Sb_{5}

The entanglement of charge density wave (CDW), superconductivity, and topologically nontrivial electronic structure has recently been discovered in the kagome metal AV_{3}Sb_{5} (A=K, Rb, Cs) family. With high-resolution angle-resolved photoemission spectroscopy, we study the electronic properties of CDW and superconductivity in CsV_{3}Sb_{5}. The spectra around K[over ¯] is found to exhibit a peak-dip-hump structure associated with two separate branches of dispersion, demonstrating the isotropic CDW gap opening below E_{F}. The peak-dip-hump line shape is contributed by linearly dispersive Dirac bands in the lower branch and a dispersionless flat band close to E_{F} in the upper branch. The electronic instability via Fermi surface nesting could play a role in determining these CDW-related features. The superconducting gap of ∼0.4  meV is observed on both the electron band around Γ[over ¯] and the flat band around K[over ¯], implying the multiband superconductivity. The finite density of states at E_{F} in the CDW phase is most likely in favor of the emergence of multiband superconductivity, particularly the enhanced density of states associated with the flat band. Our results not only shed light on the controversial origin of the CDW, but also offer insights into the relationship between CDW and superconductivity.

Phase-Manipulation-Induced Majorana Mode and Braiding Realization in Iron-Based Superconductor Fe(Te,Se)

A recent experiment reported the evidence of dispersing one-dimensional Majorana mode trapped by the crystalline domain walls in FeSe_{0.45}Te_{0.55}. Here, we perform the first-principles calculations to show that iron atoms in the domain wall spontaneously form the ferromagnetic order in line with orientation of the wall. The ferromagnetism can impose a π phase difference between the domain-wall-separated surface superconducting regimes under the appropriate width and magnetization of the wall. Accordingly, the topological surface superconducting state of FeSe_{0.45}Te_{0.55} can give rise to one-dimensional Majorana modes trapped by the wall. More interestingly, we further propose a surface junction in the form of FeSe_{0.45}Te_{0.55}-ferromagnet-FeSe_{0.45}Te_{0.55}, which can be adopted to create and fuse the Majorana zero modes through controlling the width or magnetization of the interior ferromagnetic barrier. The braiding and readout of Majorana zero modes can be realized by the designed device. Such surface junction has the potential application in the superconducting topological quantum computation.