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Braiding Majorana zero modes is essential for fault-tolerant topological quantum computing. Iron-based superconductors with nontrivial band topology have recently emerged as a surprisingly promising platform for creating distinct Majorana zero modes in magnetic vortices in a single material and at relatively high temperatures. The magnetic field-induced Abrikosov vortex lattice makes it difficult to braid a set of Majorana zero modes or to study the coupling of a Majorana doublet due to overlapping wave functions. Here we report the observation of the proposed quantum anomalous vortex with integer quantized vortex core states and the Majorana zero mode induced by magnetic Fe adatoms deposited on the surface. We observe its hybridization with a nearby field-induced Majorana vortex in iron-based superconductor FeTe0.55Se0.45. We also observe vortex-free Yu-Shiba-Rusinov bound states at the Fe adatoms with a weaker coupling to the substrate, and discover a reversible transition between Yu-Shiba-Rusinov states and Majorana zero mode by manipulating the exchange coupling strength. The dual origin of the Majorana zero modes, from magnetic adatoms and external magnetic field, provides a new single-material platform for studying their interactions and braiding in superconductors bearing topological band structures., Comment: 41 pages, 14 figures This is a replacement of the origin article. We have reorder the figures, added more data and modified the words a lot while the results are not affected

In materials chiral fermions such as Weyl fermions are characterized by nonzero chiral charges, which are singular points of Berry curvature in momentum space. Recently, new types of chiral fermions beyond Weyl fermions have been discovered in structurally chiral crystals CoSi, RhSi and PtAl. Here, we have synthesized RhSn single crystals, which have opposite structural chirality to the CoSi crystals we previously studied. Using angle-resolved photoemission spectroscopy, we show that the bulk electronic structures of RhSn are consistent with the band calculations and observe evident surface Fermi arcs and helical surface bands, confirming the existence of chiral fermions in RhSn. It is noteworthy that the helical surface bands of the RhSn and CoSi crystals have opposite handedness, meaning that the chiral fermions are reversed in the crystals of opposite structural chirality. Our discovery establishes a direct connection between chiral fermions in momentum space and chiral lattices in real space., Comment: 18 pages, 4 figures

Magnetic topological insulators (TIs) with nontrivial topological electronic structure and broken time-reversal symmetry exhibit various exotic topological quantum phenomena. The realization of such exotic phenomena at high temperature is one of central topics in this area. We reveal that MnBi6Te10 is a magnetic TI with an antiferromagnetic ground state below 10.8 K whose nontrivial topology is manifested by Dirac-like surface states. The ferromagnetic axion insulator state with Z4 = 2 emerges once spins polarized at field as low as 0.1 T, accompanied with saturated anomalous Hall resistivity up to 10 K. Such a ferromagnetic state is preserved even external field down to zero at 2 K. Theoretical calculations indicate that the few-layer ferromagnetic MnBi6Te10 is also topologically nontrivial with a non-zero Chern number. Angle-resolved photoemission spectroscopy experiments further reveal three types of Dirac surface states arising from different terminations on the cleavage surfaces, one of which has insulating behavior with an energy gap of ~ 28 meV at the Dirac point. These outstanding features suggest that MnBi6Te10 is a promising system to realize various topological quantum effects at zero field and high temperature., Comment: 18 pages, 4 figures and 1 table

In magnetic topological insulators (TIs), the interplay between magnetic order and nontrivial topology can induce fascinating topological quantum phenomena, such as the quantum anomalous Hall effect, chiral Majorana fermions and axion electrodynamics. Recently, a great deal of attention has been focused on the intrinsic magnetic TIs, where disorder effects can be eliminated to a large extent, which is expected to facilitate the emergence of topological quantum phenomena. In despite of intensive efforts, experimental evidence of the topological surface states (SSs) remains elusive. Here, by combining first-principles calculations and angle-resolved photoemission spectroscopy (ARPES) experiments, we have revealed that EuSn2As2 is an antiferromagnetic TI with observation of Dirac SSs consistent with our prediction. We also observe nearly gapless Dirac SSs in antiferromagnetic TIs MnBi2nTe3n+1 (n = 1 and 2), which were absent in previous ARPES results. These results provide clear evidence for nontrivial topology of these intrinsic magnetic TIs. Furthermore, we find that the topological SSs show no observable changes across the magnetic transition within the experimental resolution, indicating that the magnetic order has quite small effect on the topological SSs, which can be attributed to weak hybridization between the localized magnetic moments, from either 4f or 3d orbitals, and the topological electronic states. This provides insights for further research that the correlations between magnetism and topological states need to be strengthened to induce larger gaps in the topological SSs, which will facilitate the realization of topological quantum phenomena at higher temperatures., Comment: 22 pages, 5 figures, to be published in PRX

Recently, iron-chalcogenide superconductors have emerged as a new and promising platform for studying and manipulating Majorana zero mode (MZM). By combining topological band structure and superconductivity in a multiband material, they provide significant advantages such as higher superconducting transition temperature (Tc) and isolated Majorana mode. However, iron-chalcogenide superconductors, especially Fe(Te,Se), suffer from strong inhomogeneity which may hamper their practical application. On the other hand, some iron-pnictide (Fe-As) superconductors, such as LiFeAs, have been demonstrated to have a similar topological band structure, yet no MZM has been observed in its vortex cores, raising a question of universality of MZM presence in iron-based superconductors. In this work, by using high-resolution angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy, we identify the first Fe-As superconductor CaKFe4As4 (Tc = 35 K) which has both the superconducting Dirac surface states and the MZMs inside its vortex cores. The topological band inversion is largely due to the down-shift of the pz band caused by the bilayer band folding in this material. More strikingly, the energies and spatial line profiles of MZM and multiple quantized Caroli-de Gennes-Matricon bound states observed inside the topological vortex can be accurately reproduced by a simple theoretical model derived from a surface Dirac cone, firmly establishing Majorana nature of the zero mode.

Based on the first-principles calculations and experimental measurements, we report that the hexagonal phase of ternary transition metal pnictides TT'X (T=Zr, Hf; T'=Ru; X=P, As), which are well-known noncentrosymmetric superconductors with relatively high transition temperatures, host nontrivial bulk topology. Before the superconducting phase transition, we find that HfRuP belongs to a Weyl semimetal phase with 12 pairs of type-II Weyl points, while ZrRuAs, ZrRuP and HfRuAs belong to a topological crystalline insulating phase with trivial Fu-Kane $\mathbb Z_2$ indices but $nontrivial$ mirror Chern numbers. High-quality single crystal samples of the noncentrosymmetric superconductors with these two different topological states have been obtained and the superconductivity is verified experimentally. The wide-range band structures of ZrRuAs have been identified by ARPES and reproduced by theoretical calculations. Combined with intrinsic superconductivity, the nontrivial topology of the normal state may generate unconventional superconductivity in both bulk and surfaces. Our findings could largely inspire the experimental searching for possible topological superconductivity in these compounds., Comment: Published version, 15 pages, 4 figures

We present a phenomenological Green's function to characterize the superconducting and pseudogap phases of the cuprates based on a microscopic theory of doped Mott insulators. In this framework, the "Fermi arc" and "kink" phenomena observed by angle-resolved photoemission spectroscopy (ARPES) experiments in the pseudogap phase can be systematically explained as a function of doping, which is further connected to the two-gap feature in the superconducting phase with dichotomy between the nodal and antinodal physics. We demonstrate that a phase-string-induced fractionalization plays the key role in giving rise to such a peculiar Green's function with a unique two-component structure., Comment: 19 pages, 12 figures; Complete version with modified figures

We study the systematic doping evolution of nodal dispersions by in-situ angle-resolved photoemission spectroscopy on the continuously doped surface of a high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$. We reveal that the nodal dispersion has three segments separated by two kinks, located at ~10 meV and roughly 70 meV, respectively. The three segments have different band velocities and different doping dependence. In particular, the velocity of the high-energy segment increases monotonically as the doping level decreases and can even surpass the bare band velocity. We propose that electron fractionalization is a possible cause for this anomalous nodal dispersion and may even play a key role in the understanding of exotic properties of cuprates.

Majorana zero-modes (MZMs) are spatially-localized zero-energy fractional quasiparticles with non-Abelian braiding statistics that hold a great promise for topological quantum computing. Due to its particle-antiparticle equivalence, an MZM exhibits robust resonant Andreev reflection and 2e2/h quantized conductance at low temperature. By utilizing variable-tunnel-coupled scanning tunneling spectroscopy, we study tunneling conductance of vortex bound states on FeTe0.55Se0.45 superconductors. We report observations of conductance plateaus as a function of tunnel coupling for zero-energy vortex bound states with values close to or even reaching the 2e2/h quantum conductance. In contrast, no such plateau behaviors were observed on either finite energy Caroli-de Genne-Matricon bound states or in the continuum of electronic states outside the superconducting gap. This unique behavior of the zero-mode conductance reaching a plateau strongly supports the existence of MZMs in this iron-based superconductor, which serves as a promising single-material platform for Majorana braiding at a relatively high temperature.

Vortices in topological superconductors host Majorana zero modes (MZMs), which are proposed to be building blocks of fault-tolerant topological quantum computers. Recently, a new single-material platform for realizing MZM has been discovered in iron-based superconductors, without involving hybrid semiconductor-superconductor structures. Here we report on a detailed scanning tunneling spectroscopy study of a FeTe0.55Se0.45 single crystal, revealing two distinct classes of vortices present in this system which differ by a half-integer level shift in the energy spectra of the vortex bound states. This level shift is directly tied with the presence or absence of zero-bias peak and also alters the ratios of higher energy levels from integer to half-odd-integer. Our model calculations fully reproduce the spectra of these two types of vortex bound states, suggesting the presence of topological and conventional superconducting regions that coexist within the same crystal. Our findings provide strong evidence for the topological nature of superconductivity in FeTe0.55Se0.45 and establish it as an excellent platform for further studies on MZMs., Comment: 22 pages, 12 figures

Topological insulators and semimetals as well as unconventional iron-based superconductors have attracted major recent attention in condensed matter physics. Previously, however, little overlap has been identified between these two vibrant fields, even though the principal combination of topological bands and superconductivity promises exotic unprecedented avenues of superconducting states and Majorana bound states (MBSs), the central building block for topological quantum computation. Along with progressing laser-based spin-resolved and angle-resolved photoemission spectroscopy (ARPES) towards high energy and momentum resolution, we have resolved topological insulator (TI) and topological Dirac semimetal (TDS) bands near the Fermi level ($E_{\text{F}}$) in the iron-based superconductors Li(Fe,Co)As and Fe(Te,Se), respectively. The TI and TDS bands can be individually tuned to locate close to $E_{\text{F}}$ by carrier doping, allowing to potentially access a plethora of different superconducting topological states in the same material. Our results reveal the generic coexistence of superconductivity and multiple topological states in iron-based superconductors, rendering these materials a promising platform for high-$T_{\text{c}}$ topological superconductivity., Comment: 9 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1803.00846, arXiv:1803.00845

Topological nodal-line semimetals are characterized by the line-contact bulk band crossings and the topological surface states. Breaking certain protecting symmetry turns this system into a Dirac semimetal or Weyl semimetal that hosts zero-dimensional isolated nodal points. Recent advances in band theory predicted a topological nodal-line semimetal state possessing a new type of nodal line in AlB$_2$-type diborides. Here, we report an experimental realization of nodal-line fermions and associated surface states near the Fermi energy in ZrB$_2$ by angle-resolved photoemission spectroscopy combined with first-principles calculations. The Dirac nodal lines in ZrB$_2$ wind into two groups of nodal rings, which are linked together along the $\Gamma$-$K$ direction. We further observe a distinct surface state connecting to each nodal line, indicative of the nontrivial topological nature of the bulk nodal lines. Therefore, our results provide convincing experimental evidence of the nodal-line semimetal states in ZrB$_2$ both in the bulk and on the surface, suggesting ZrB$_2$ as a remarkable platform for discovering unique phenomena induced by nodal-line fermions., Comment: 24 pages, 4 figures

Topological Dirac semimetals (TDSs) exhibit bulk Dirac cones protected by time reversal and crystal symmetry, as well as surface states originating from non-trivial topology. While there is a manifold possible onset of superconducting order in such systems, few observations of intrinsic superconductivity have so far been reported for TDSs. We observe evidence for a TDS phase in FeTe$_{1-x}$Se$_x$ ($x$ = 0.45), one of the high transition temperature ($T_c$) iron-based superconductors. In angle-resolved photoelectron spectroscopy (ARPES) and transport experiments, we find spin-polarized states overlapping with the bulk states on the (001) surface, and linear magnetoresistance (MR) starting from 6 T. Combined, this strongly suggests the existence of a TDS phase, which is confirmed by theoretical calculations. In total, the topological electronic states in Fe(Te,Se) provide a promising high $T_c$ platform to realize multiple topological superconducting phases., Comment: 6 pages, 4 figures

Superconducting and topological states are two distinct quantum states of matter. Superconductors with topologically nontrivial electronic states provide a platform to study the interplay between them. Recent study revealed that a bulk superconductor PdTe2 is a topological Dirac semimetal with type-II Dirac fermions. However, the Dirac fermions in PdTe2 have no contribution to the superconducting pair because the Dirac points reside far below the Fermi level (EF). Here, we show that in the isostructural compounds (Ir1-xPtx)Te2, the type-II Dirac points can be adjusted to EF by element substitution at x ~ 0.1, for which the bulk superconductivity appears near 2 K. The (Ir1-xPtx)Te2 superconductor with the Dirac points at EF paves the way for studying the relevant exotic physical phenomena such as topological superconductivity in Dirac semimetals., Comment: 12 pages, 4 figures

ZrSiS is the most intensively studied topological nodal-line semimetal candidate, which is proposed to host multiple nodal lines in its bulk electronic structure. However, previous angle-resolved photoemission spectroscopy (ARPES) experiments with vacuum ultraviolet lights mainly probed the surface states. Here using bulk-sensitive soft X-ray ARPES, we acquire the bulk electronic states of ZrSiS without any interference from surface states. Our results clearly show two groups of three-dimensional bulk nodal lines located on high-symmetry planes and along high-symmetry lines in the bulk Brillouin zone, respectively. The nodal lines on high-symmetry planes are enforced to pin at the Fermi level by carrier compensation and constitute the whole Fermi surfaces. This means that the carriers in ZrSiS are entirely contributed by nodal-line fermions, suggesting that ZrSiS is a remarkable platform for studying physical properties related to nodal lines., Comment: 16pages, 3figures