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Register a new userScalable Majorana vortex modes in iron-based superconductors
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A vortex in an s-wave superconductor with a surface Dirac cone can trap a Majorana bound state with zero energy leading to a zero-bias peak (ZBP) of tunneling conductance. The iron-based superconductor FeTe$_x$Se$_{1-x}$ is one of the material candidates hosting these Majorana vortex modes. It has been observed by recent scanning tunneling spectroscopy measurement that the fraction of vortex cores possessing ZBPs decreases with increasing magnetic field on the surface of this iron-based superconductor. We construct a three-dimensional tight-binding model simulating the physics of over a hundred Majorana vortex modes in FeTe$_x$Se$_{1-x}$ with realistic physical parameters. Our simulation shows that the Majorana hybridization and disordered vortex distribution can explain the decreasing fraction of the ZBPs observed in the experiment. Furthermore, we find the statistics of the energy peaks off zero energy in our simulation with the Majorana physics in agreement with the analyzed peak statistics in the vortex cores from the experiment. This agreement and the explanation of the decreasing ZBP fraction lead to an important indication of scalable Majorana vortex modes in the iron-based superconductor. Thus, FeTe$_x$Se$_{1-x}$ can be one promising platform possessing scalable Majorana qubits for quantum computing. In addition, we further show the interplay of the ZBP presence and the vortex locations qualitatively agrees with our additional experimental observation and predict the universal spin signature of the hybridized multiple Majorana vortex modes.
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Majorana zero mode is an exotic quasi-particle excitation with non-Abelian statistics in topological superconductor systems, and can serve as the cornerstone for topological quantum computation, a new type of fault-tolerant quantum computation architecture. This review paper highlights recent progress in realizing Majorana modes in iron-based high-temperature superconductors. We begin with the discussion on topological aspect of electronic band structures in iron-based superconductor compounds. Then we focus on several concrete proposals for Majorana modes, including the Majorana zero modes inside the vortex core on the surface of Fe(Te,Se), helical Majorana modes at the hinge of Fe(Te,Se), the Majorana zero modes at the corner of the Fe(Te,Se)/FeTe heterostructure or the monolayer Fe(Te,Se) under an in-plane magnetic field. We also review the current experimental stage and provide the perspective and outlook for this rapidly developing field.
The vortex of iron-based superconductors is emerging as a promising platform for Majorana zero mode, owing to a magic integration among intrinsic vortex winding, non-trivial band topology, strong electron-electron correlations, high-Tc superconductivity and the simplification of single material. It overcomes many difficulties suffered in heterostructure-based Majorana platforms, including small topological gap, interfacial contamination, lattice imperfections, and etc. Isolated zero-bias peaks have been found in vortex of several iron-based superconductors. So far, studies from both experimental and theoretical aspects strongly indicate the realization of vortex Majorana zero mode, with a potential to be applied to topological quantum computation. By taking Fe(Te,Se) superconductor as an example, here we review original idea and research progress of Majorana zero modes in this new platform. After introducing the identifications of topological band structure and real zero modes in vortex, we summarize the physics behaviors of vortex Majorana zero modes systematically. Firstly, relying on the behavior of the zero mode wave function and evidence of quasiparticle poisoning, we analyze the mechanism of emergence of vortex Majorana zero modes. Secondly, assisted with some well-established theories, we elaborate the measurements on Majorana symmetry and topological nature of vortex Majorana zero modes. After that, we switch from quantum physics to quantum engineering, and analyze the performance of vortex Majorana zero mode under real circumstances, which may potentially benefit the exploration of practical applications in the future. This review follows the physics properties of vortex Majorana zero modes, especially emphasizes the link between phenomena and mechanisms. It provides a chance to bridge the gap between the well-established theories and the newly discovered iron home of Majoranas.
In the superconducting regime of FeTe$_{(1-x)}$Se$_x$, there exist two types of vortices which are distinct by the presence or absence of zero energy states in their core. To understand their origin, we examine the interplay of Zeeman coupling and superconducting pairings in three-dimensional metals with band inversion. Weak Zeeman fields are found to suppress the intra-orbital spin-singlet pairing, known to localize the states at the ends of the vortices on the surface. On the other hand, an orbital-triplet pairing is shown to be stable against Zeeman interactions, but leads to delocalized zero-energy Majorana modes which extend through the vortex. In contrast, the finite-energy vortex modes remain localized at the vortex ends even when the pairing is of orbital-triplet form. Phenomenologically, this manifests as an observed disappearance of zero-bias peaks within the cores of topological vortices upon increase of the applied magnetic field. The presence of magnetic impurities in FeTe$_{(1-x)}$Se$_x$, which are attracted to the vortices, would lead to such Zeeman-induced delocalization of Majorana modes in a fraction of vortices that capture a large enough number of magnetic impurities. Our results provide an explanation to the dichotomy between topological and non-topological vortices recently observed in FeTe$_{(1-x)}$Se$_x$.
There has been experimental evidence for the Majorana zero modes (MZMs) in solid state systems, which are building blocks for potential topological quantum computing. It is important to design devices, in which MZMs are easy to manipulate and possess a broad topological non-trivial parameter space for fusion and braiding. Here, we propose that the Majorana vortex states in iron-based superconducting nanowires fulfill these desirable conditions. This system has a radius-induced topological phase transition, giving a lower limit to the radius of the nanowire. In the topological phase, there is only one pair of MZMs in the nanowire over a wide range of radius, chemical potential, and external magnetic field. The wavefunction of the MZM has a sizable distribution at the side edge of the nanowire. This property enables one to control the interaction of the MZMs in neighboring vortex nanowires, and paves the way for Majorana fusion and braiding.
Majorana quasi-particles may arise as zero-energy bound states in vortices on the surface of a topological insulator that is proximitized by a conventional superconductor. Such a system finds its natural realization in the iron-based superconductor FeTe$_{0.55}$Se$_{0.45}$ that combines bulk $s$-wave pairing with spin helical Dirac surface states, and which thus comprises the ingredients for Majorana modes in absence of an additional proximitizing superconductor. In this work, we investigate the emergence of Majorana vortex modes and lattices in such materials depending on parameters like the magnetic field strength and vortex lattice disorder. A simple 2D square lattice model here allows us to capture the basic physics of the underlying materials system. To address the problem of disordered vortex lattice, which occurs in real systems, we adopt the technique of the singular gauge transformation which we modify such that it can be used in a system with periodic boundary conditions. This approach allows us to go to larger vortex lattices than otherwise accessible, and is successful in replicating several experimental observations of Majorana vortex bound states in the FeTe$_{0.55}$Se$_{0.45}$ platform. Finally it can be related to a simple disordered Majorana lattice model that should be useful for further investigations on the role of interactions, and towards topological quantum computation.
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